A STUDY OF THE EWEGTS 0F BlOLOGlCALLY

RELEVANT PHYSJCS TBK'WM. MATER‘AL 0N STUDENT

ATTITUDES AND ACHIEVEMENT M PHYSiCS 231

AT WESTERN KENTUCKY UN!

Dissertation for the Degtee of Ph. D.
mum STATE UNNERSHY
SOHN MU? HOLDEN

1973

"Hist?

Date [€//ZAA§/

0-7 639

  
 
 

LIBRARY

R, 3.1:, .
xvqlc.t-;:’..!1 State

&

UHth .‘ I‘Sl L‘y

W

This is to certify that the

v

. a- i

thesis entitled!

 

A Study of the Effects of Biologically Relevant
Physics Textual Material on Student Attitudes
and Achievement in Physics 231 at Western
Kentucky university

presented by

John Philip Holden

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in fldmmfi Isral‘l can
A] lq)\3l'\L'Y‘ Ed.

 

 

4)

 

3 s

Major professor

 

 

ABSTRACT

A STUDY OF THE EFFECTS OF BIOLOGICALLY
RELEVANT PHYSICS TEXTUAL MATERIAL ON
STUDENT ATTITUDES AND ACHIEVEMENT IN

PHYSICS 231 AT WESTERN KENTUCKY
' UNIVERSITY

BY

John Philip Holden

PUI’EOSE

It is the purpose of this study to assess and
compare the effects of experimental textual material in
college physics, written within a biological framework,
on the attitudes and achievement of undergraduate life
science students. Of central concern is the increasing
need which students preparing for medicine and the life
sciences have for understanding the principles, laws, and

methods of physics.

Procedures

 

Forty-eight undergraduate students enrolled in the
course, Introduction to Physics and Biophysics 231, at
Western Kentucky University during the Fall semester of the
1972-1973 academic year were the subjects of a study com-
paring the attitudes and achievement in college physics in

terms of the textual material assigned to them.

John Philip Holden

Three groups of eight students each, one group from
each of three lecture sections of Physics 231, received
special textual material. These groups were designated the
treatment groups.

Three groups of eight students each, one group from
each of three lecture sections of Physics 231, received no
special textual materials. These groups were designated the
control groups.

Following a period of approximately three weeks the
treatment and control groups were tested for achievement
and attitude differences as determined from separate achieve-

ment and attitude tests.

Findings

Multivariate analysis of variance was used to
analyze the data obtained from the achievement and attitude
tests. Testing at the 0.05 level of significance greater
achievement was found to be associated with the special
textual material than with instructor designated (control)
textual material. No treatment by class interaction effects
on attitudes or achievement, and no achievement or attitude
differences between classes were found.

The findings of this study indicate that biologi—
cally oriented physics textual material can aidin improving

the achievement of life science students in college physics.

A STUDY OF THE EFFECTS OF BIOLOGICALLY
RELEVANT PHYSICS TEXTUAL MATERIAL ON
STUDENT ATTITUDES AND ACHIEVEMENT IN

PHYSICS 231 AT WESTERN KENTUCKY

UNIVERSITY

BY

John Philip Holden

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Administration and Higher Education

1973

x :2 ACKNOWLEDGMENTS
I; ‘ 23'

“”93

'0

many peOple who gave their time, talents and support.

The writer wishes to express his appreciation to the

To Dr. William Sweetland, Chairman of the Guidance
Committee, whose thoughtful and constructive assistance was
freely given during the entire doctoral program.

To Dr. John I. Johnson, Chairman, Department of Bio~
physics, for his interest and constructive suggestions.

To Dr. Martin Hetherington and Dr. T. wayne Taylor
for friendly advice and initial encouragement.

To Dr. Thomas Coohill and Dr. James Parks for the
opportunity afforded me at Western Kentucky University.

To Mr. Robert Karr for his assistance in the analysis
of the data.

To Professor F. Gaynor Evans for tabulated data used
in the special Physics Textual Material.

Finally, to my wife, Linda, and to my parents for

their confidence in me, their support and their empathy.

ii

LIST OF
LIST OF
Chapter

I.

II.

III.

TABLE OF CONTENTS

TABLES O O O O O O O

APPENDICES . . . . . .

THE PROBLEM . . . . . .

Need . . . . . . . .
Purpose . . . . . . .
Hypotheses . . . . . .
Theory . . . . . . .
Definitions of Terms . .
Limitations of the Study .
Overview . . . . . . .

REVIEW OF THE LITERATURE .

Literature Categories . .
Existing Textual Material .
Opinion Articles . . . .
Existing Courses . . . .
Summary . . . . . . .

DESIGN AND IMPLEMENTATION OF

Overview . . . . . . .
The Population . . . . .
1he Sample . .

Threats to Internal Validity

Threats to External Validity
Interaction of Selection and

Reactive Arrangements. . .

Instrumentation . . . .
Achievement Test '. . . .
Attitude Test . . .

Data Collection Procedure .
Hypotheses . . . . . .
Analysis of Data . . . .
Summary . . . . . . .

iii

Page

vi

3O

3O
3O
31
33
34
36
36
39
39
4O
42
42
45
46

Chapter Page

IV. ANALYSIS OF RESULTS . . . . . . . . . 48

Tests of the Achievement Hypotheses . . . . 51
Tests of the Attitude Hypotheses . . . . . 53
Summary of Results . . . . . . . . . 55

v. SUMMARY AND CONCLUSIONS . . . . . . . . 57
Summary of the Results of Hypotheses
Testing . . . . . . . . . .
Conclusions . . . . . 59

Implications from the Study. . . . 60

I 58
Recommendations for Future Investigators . . 51

APPENDIX . . . . . . . . . . . . . . . 53

BIBLIOGRAPHY . . . . . . . . . . . . . . 144

iv

Table

LIST OF TABLES

Controls on Threats to Internal Validity .
Achievement and Attitude Mean Scores . .
Correlation Coefficients Between Variables
ANOVA Table for Adjusted Achievement Scores

Multiple R Correlation Coefficients Between
Predicted and Measured Attitude Scores .

Page
35
49
50
53

54

Appendix

A.

LIST OF APPENDICES

Page

Explanatory Letter To The Students of

Physics 231 at Western Kentucky Uni—
versity . . . . . . . . . . . . 64
Physics Achievement Test . . . . . . . 67
Likert Type Attitude Scale . . . . . . 73
Experimental Textual Material . . . . . 81
Elastic Properties of Matter . . . . . 32
Fluid Mechanics I . . . . . . . . . 101

Fluid Mechanics II . . . . . . . . 112
Fluid Mechanics III . . . . . . . . 133

Vi

CHAPTER I

THE PROBLEM

Need

 

Education in basic physics is of increasing
importance to students of the life sciences. This
fact is the source of a particularly acute problem in
the undergraduate education of life science students.
Major requirements for life.science students in many
colleges include courses of study in College Physics,
in the belief that knowledge of basic laws and princi—
ples of physics is necessary to»‘understanding of
many biological phenomena. This need is apparent
both in an interpretation of specific structural and
functional aspects of living organisms and in under-
standing the physical mechanisms by which biological
structural and functional parameters are determined.
Writing on the future of physics, Freeman Dyson,

Professor of Physics at Princeton's Institute for Advanced
Study, clearly suggests that adequate education in physics
will require greater attention to modern biology.

I take it as self evident that physics will not

flourish in isolation from the rest of science.

In particular, physics should keep in close touch

with biology, as biology rather than physics is
likely to be the central ground of scientific

advance during the remainder of our century . . .

I think it is true now, just as it was in 1946, that
a tremendous opportunity exists for making major
advances in microbiology by means of physical
techniques . . . . The idea that physics has to be
pure in order to be good, that work on the border—
line between physics and biology is beneath the
dignity of a true physicist, was wrong in 1946

and is still wrong today.

The science of physics is deeply rooted in biology.
For the Greeks, the relevance of physics to biology
was such a paramount problem that it ultimately led
to the codification of the first main type of physics
in which organismic concepts became predominant . . .
Mechanism was a study to be governed by the concepts
of vitalism and not vice versa.
It was Robert Boyle, who in the 17th century in
commenting on Harvey‘s investigation of the movement of
the heart and blood in animals, said that it was the
presence of "valves in the veins of so many parts of the
body" that convinced him of the correctness of the mechanical
approach to the problem of the circulation of blood.3
And, in the 18th century, during which the methods of
classical physics became highly developed, the eXperi-
mental work on combustion and respiration of Laplace and

Lavoisier in studying metabolism clearly shows the appli-

cation of physics in interpreting biological processes.

 

lFreeman Dyson, "The Future of Physics," Physics
Today (September, 1970): P. 23.

2Stanley L. Jaki, The Relevance of Physics
(Chicago: The University of Chicago Press, 1966) p. 283.

3

 

Ibid., p. 287.

4Antoine Lavoiser and Pierre Laplace, Memoir on Heat
(Paris: The Academy of Science, 1780).

 

In 1865, Claude Bernard, in his Introduction to

 

the Study of Experimental Medicine, although recognizing
the limitations of physical methods in biological studies,
not only acknowledges the "powerful support of physico-
chemical sciences," but he also repeatedly urges the
exactness of physics as a goal to be emulated in physio—
logical research.5

In the mid 19th century the contributions to
physics by physicians and physiologists were remarkable.
Prominent among such contributors were Thomas Young, who
developed the basis for the modern wave theory of light;
Mayer, who first announced the principle of the mechanical
equivalence of heat; and Helmholtz, whose contributions
to acoustics, optics, and nerve transmission were out—
standing.6

Later in the 19th century the alliance between
physics and biology was to suffer a severe setback which
even today holds the sciences apart to some extent. The
disintegration of physics and biology came about largely
due to the publication of Darwin's theory of biological
evolution. The confrontation between the biologists and
the classical physicists grew from the lack of precision

in Darwin's evolutionary timetable and the physicists'

 

5Claude Bernard, Introduction to the Study of

Experimental Medicine, 1865.

 

 

6Jaki, op. cit., p. 296.

insistence on quantifiable precision in science. The
attack on Darwin was lead by Kelvin, who challenged
evolutionary biology on the basis of classical estimations
of the age of the Earth which were much shorter than the
‘time required for biological evolution according to
Darwin. At issue was the question as to whether science
can be good and yet not quantifiable in the sense of
precise physical terms. No doubt the controversy was
also nurtured by the Christian beliefs professed by many
of the outstanding physicists of that age.7
The discovery and investigation of radioactivity
in the early 1900's provided the key which was to open
the barriers which evolution had placed between physics
and biology. By means of radioactive dating, physics
almost overnight doubled the estimated age of the Earth
and allowed for the time.required for the evolution of
life proposed by Darwin.8 Recently radioactive tracer
methods have further advanced the credibility of
Darwinian evolution in revealing that the nearer two

species are on the evolutionary ladder the more readily

their DNA strands combine with one another.9

 

71bid., p. 299.

81bid., p. 314.

9B. H. Hoyer, B. J. McCarthy, and E. T. Bolton,
"A Molecular Approach in the Systematics of Higher

Organisms, " Science, CXLIV (1964), p. 959.

Currently the interface between biology and
physics evidences some very productive advancements
in both disciplines. Two examples which illustrate
activity at the interface of biology and physics are
the development of biobatteries, in which electrical
energy is generated through the catalytic action of
certain bacteria on otherwise unusable fuels, and
studies of photoreception, in the eyes of fish, frogs
and beetles, which is providing valuable information
in photoelectronics.lo

Thus, fortunately, the dividing lines between
physics and biology are giving way to a new science
in which knowledge derives from the active application
of physics to biological phenomena. Here, however, a
word of caution must be given. Although biological
knowledge has significantly expanded as a direct result
of the application of the quantifying methods of physics,
nonetheless, to plead for a complete reduction of biology
to physics would overlook the nonequantifiable aspects
of biological phenomena upon which the life sciences
have largely developed. The present spirit of mutual
cooperation between biology and physics must not fail

to maintain the recognition of the wholeness of science

 

10Ernest Gardner, Fundamentals of Neurology

(Philadelphia: W. B. Saunders Company, 1968), Ch. 13,
p. 190.

 

lest the 19th century fragmentation within science be
repeated.11 This realization is particularly important
as it pertains to physics curriculum development which
until recently has been narrow to the extent of almost
total ignorance of education and research in the life
sciences.

Until recently very little attention has been
given to designing the textual material used in general
physics courses so that the biological significance of
the topics treated is emphasized. College physics texts
in recent years have tended to present physics on a
highly technical level. One undesirable consequence has
been to give basic physics an appearance of irrelevance
to other sciences, in particular to the life sciences.
Thus at present there is a clear need to improve the
presentation of fundamental physics in textual form
so as to make its content meaningful to life science
students.

In order to determine just how this need is to
be met research is required to determine what means, if

any, can be established to accomplish the task.

 

llMedewar, "Zoology," Scientific Thought in
the Twentieth Century (London: Watts, 1951), p. 188.

 

 

PUEEOSG

This study, is based upon the assumption
that there is a need for improved textual material in
College Physics courses for life science students.
It is an inquiry into the effects of physics textual
material, written within a framework of biological
phenomena, on student attitudes and achievement in
one unit of the course, Introduction to Physics and
Biophysics 231, offered by the Department of Physics
and Astronomy of Western Kentucky University.

Three goals consistent with this purpose have

been established.

1. To determine what effect, if any, Physics
Textual Material written within a biological
framework has on student achievement in the
General Physics course.

2. To determine what effect, if any, physics
textual material written within a biological
framework, has on attitudes of life science
students toward physics itself.

3. To determine what effect, if any, physics
textual material written within a biological

framework has on attitudes of life science
students toward physics textual material.

Hypotheses

 

To investigate attitude and achievement changes
associated with experimental physics material written
within a biological framework the following hypotheses

will be tested:

l.- There will be no significant differences
in achievement in physics when the text
material is biologically relevant.
2. There will be no significant differences
in attitudes toward physics itself when
the textual material is biologically
relevant.
3. There will be no significant differences
in attitudes toward physics textual material
which is written to be biologically relevant.
The above hypotheses are stated in test form in

Chapter III.

Theory
The research to test the above stated hypotheses

has been motivated by years of experience on the part of
the investigator in teaching a spectrum of undergraduate
physics courses. In teaching courses in General Physics
largely populated by life science students the investi—
gator has noted difficulties which these students have
commonly shared.. These difficulties have seemed generally
to arise from two sources: the failure of the course to
relate its content to the special interests of the life
sciences, and the failure of life science students to
appreciate the significance of the course topics toward
increasing understanding of biological processes. Prompted
by observations which seemed to indicate an increase in
favorable attitudes toward the course and an increase in
cognitive learning when topics were presented in a biological

setting the decision to test the stated hypotheses was made.

Definition of the Terms

Attitudes - Attitudes as used in this study refer to

 

affective reactions toward the subject matter of physics

and the textual material used in teaching physics.

Achievement - Achievement as used in this study refers to

 

cognitive understanding of the content of the course unit,
Static and Dynamic Properties of Solids and Fluids,
presented.ianhysics 231 at Western Kentucky

University, as determined from responses to multiple
choice type problems written and administered by the

course instructors at the close of the unit.

Biologically Relevant Physics F Biologically relevant
physics as used in this study refers to the concepts,
principles, definitions and formulas of physics presented
within a framework of their significance to various

life processes.

Traditional Physics — Traditional physics as used in this

 

study refers to the concepts, principles, definitions,
and formulas of physics where they are treated in

isolation from other scientific disciplines.

College Physics — College Physics as used in this study

 

refers to those course offerings traditionally called

General Physics and/or Introductory Physics.

10

Limitations of the Study

 

ways:

This study will be limited in the following

1.

The study will be limited to investigation
of the achievement and attitudes of students
participating in Physics 231 at Western
Kentucky University during the Fall semester
of 1972.

The data for the study will be limited to
the responses to the attitude question-
naire written and administered by the
investigator and to the responses to the
achievement examination written and
administered by the course instructors.

The biologically relevant physics materials
used in this study will be written by

the investigator and will be limited

to the unit: Static and Dynamic Properties
of Solids and Fluids.

 

 

The topics covered in the unit: Static
and Dynamic Properties of Solids and
Fluids will be limiEéd to those estab-
lished by the instructors.

The topics covered in the unit: Static and
Dynamic Properties of Solids and Fluidsm
have been established by the course
instructors to be:

 

 

a. the basic definitions of stress and
strain

b. tensile stress, shearing stress, and
bulk stress

c. tensile strain, shearing strain and
bulk strain

d. Young's Modulus, the rigidity modulus
and bulk modulus

e. the definition of viscosity

f. the rate of flow of viscous liquids,
i.e., Poiseuille's Equation

g. Newtonian and non—Newtonian liquids

h. Stoke's Law and its relationship to
sedimentation rates

1. diffusion in liquids

11

j. osmosis and a simple model to explain
osmosis

k. surface tension and how it is measured

1. the equation of continuity for incom-
pressible fluids

m. Bernoulli's Equation for non—viscous
fluids

Overview

In this chapter, the circumstances suggesting
a need for studies pertaining to the effects of textual
materials in College Physics on the attitudes and achieve—
ment of the life science studentshave been presented.

The purpose of the study, as related to the stated needs,
followed by the research hypotheses, definitions of
terms and limitations of the study have been presented.

In Chapter II, the literature currently being
used in the teaching of College Physics to life science
students is reviewed, as are pertinent research studies
supporting the research of this dissertation.

The selection of design, a description of the
sample and population, instrumentation, and data analysis
procedures are presented in Chapter III.

The analysis of data and results of the analysis

are presented in Chapter IV. The final chapter contains

the conclusions and implications of this study.

CHAPTER II

REVIEW OF THE LITERATURE

I Literature which pertains to the teaching of
physics within a biological framework can be classified
within three categories. The literature in each of
these categories supports the premise of need for
general text material in which physics is presented
in a biologically relevant manner. The review of
literature on the following pages is intended to
demonstrate the urgent need for development of textual
material in which physics is presented in a biologically
relevant manner and for studies to determine the effect
of such material on the achievement and attitudes

acquired by life science students in physics.

Literature Categories

 

1. Existing textual material in which physics
is presented within a framework of bio-
logical relevance

2. Opinion articles which call for integration
of physics and the life sciences

3. Descriptions of existing courses in which

physics is presented in a biologically
relevant manner

12

13

Existing Textual Material

 

Contemporary textual materials used in teaching
fundamental physics commonly present physics as a dis-
cipline unto itself remote from biological phenomena.

A broad review of current introductory textbooks in
general physics reveals little, if any, content with
apparent biological relevance. Two general physics
texts published in the 19505, however, do use biological
phenomena in part to illustrate fundamental physics.

These texts are: Physics, Its Laws, Ideas and Methods,

 

by Alexander Kolin, and Essentials of Biological and

 

Medical Physics, by Stacy, Williams, WOrden and McMorris.

 

The text by Kolin, written as the text for the
college course in physics at the University of Chicago
in the early 19505, is designed to accomplish two purposes:
to satisfy the requirements of the Division of
Biological Sciences in regard to the training in
physics of students entering that division, and
to satisfy the general education objectives of
the college in regard to the training of students
in the methods of the physical sciences.
Although Kolin's text does contain frequent refer-
ences to biological phenomena, these references are largely

restricted to the sections on fluid mechanics and optics.

That the material in the text is not closely related to

 

12Alexander Kolin, Physics, Its Laws, Ideas and
Methods (New York: McGraw Hill Book Company, 1950),
p. vii.

 

l4

biology is clearly acknowledged by the author: "no
attempt has been made to present a complete survey of
applications of physics to biology."13
Essentials of Biological and Medical Physics,
by Stacy, Williams, WOrden and McMorris presents physics
entirely within the framework of biological phenomena.
This text, therefore, may be properly classified as a
text in biophysics. However, the level at which it is
written precludes its use as a basic text for introductory
physics; the text assumes an undergraduate background in
physics and mathematics. Each chapter closes with
references to a variety of undergraduate textbooks in
physics and mathematics to aid the student having insuf-
ficient preparation for the content of the chapter.
Although this text is written above the introductory
level, it could serve as a valuable reference for a course
in College Physics, especially for its chapters on
Elasticity and the Breaking Strength of Bones, Mechanical
Engineering of the Body, The Living Body of Sound,'
Geometrical Optics and Vision, and sections of the chapter

on fluid mechanics.14

 

l31pm.

14Ralph W. Stacy, David T. Williams, Ralph E.
Worden, and Rex O. McMorris, Essentials of Biological

and Medical Physics (New York: McGraw Hill Book Company,
1955).

 

 

15

Three currently available general physics texts
intended specifically for use by life science and pre-
medical students are: Physics for Biology and Pre-Medical
Students, by Desmond M. Burns and Simon G. MacDonald,
College Physics, A Text with Applications to the Life
Sciences, by Donald E. Tilley and Walter Thumm, and
Physics for Biology and Medicine, by I. W. Richardson
and Eiler B. Neergaard.

Although it is not a general physics text in the
usual sense, Physics - UnderstandingAOur Environment, by
Charles H. Bachman, might also be considered because of its
presentation of qualitative descriptions of certain bio-

related physical principles.

Burns and MacDonald.——Physics for Biology and

 

 

Pre-Medical Students, by Desmond M. Burns and Simon G.
MacDonald, (1970) is a text in general physics intended
for use by biology and pre—medical students. The text
covers topics ranging from kinematics and classical
mechanics through thermodynamics, classical Optics,
electricity, magnetism and modern physics. The text is
unusual in several respects, notably in that it includes

a chapter on probability and statistics and a large number
of chapter sections devoted to biological applications of
physics. Frequently, however, as in the case of the

sections on biological applications of alternating current,

16

the material appears to be thrown in as an after thought
following a nonebiological treatment of the chapter topic.
In summary, the Burns and MacDonald book adequately
presents the usual topics covered in a College Physics text.
The presentation is traditional, except for scattered bio—
logical illustrations of physics. Probably the mathe-
matical sophistication required of the reader exceeds

that of the usual undergraduate life science student.15

Tilley and Thumm.—-College Physics, A Text with

 

 

Applications to the Life Sciences, by Donald E. Tilley
and Walter Thumm, is one of a multitude of introductory
physics textbooks which attempt to introduce physics
within the framework of twentieth century advances in
physical knowledge. The text is permeated with atomic
and nuclear theory, and General and Special Relativity.
The chapters on classical physics give only brief
treatments of Newtonian mechanics, electromagnetic
theory and thermodynamics. Other than scant references
to medical applications, direct relevance of this text
to the life sciences is left to the imagination of the

reader. In terms of a meaningful portrayal of physics

 

15Desmond M. Burns and Simon G. MacDonald, Physics
for Biology and Pre—Medical Students (Reading, Massa—
chusetts: Addison Wesley Publishing Company, 1970).

 

17

in biological phenomena the text is a total failure.16

The text was apparently written as a general physics
text, with a few sectional topics of the medical appli-
cations of x—rays and radioactive tracers thrown in to

attract a wider adoption of the text.

Richardson and Neergaard.—~Physics for Biology

 

 

and Medicine, by I. W. Richardson and E. B. Neergaard

 

is a well organized text which directly pertains to
biological phenomena and medical topics. The text
contains only classical treatments of physical phenomena.
No modern physics is included. The presentation is rather
sophisticated, with the fundamentals of Newtonian
mechanics, fluid dynamics, thermodynamics, current
electricity, molecular transport theory, acoustics and
optics developed in using the calculus of single
variables. Absent is any discussion of rotational
mechanics, magnetism, static electricity and atomic
theory.

Although this text gives a thorough treatment of
the topics it presents, the mathematical abilities required

of the reader probably exceed those of most undergraduate

 

16Donald E. Tilley and Walter Thumm, Colle e

Physics, A Text with Applications to the Life SCIences
(Menlo Park, California: Cummings Publishing Company,
1971).

 

18

life science students. The physics is not presented

with a biological basis, although there are numerous
biological references. Probably the text is well suited to
a one semester course in physics for graduate students

in medicine and the life sciences, although it is not
suitable for use as the sole text in a one year under—
graduate general physics course taken by biology

students.17

Bachman.-—Physics - Understanding Our Physical

Environment, by Charles H. Bachman is uncommon among

 

introductory physics texts. The text is almost entirely
descriptive and as such it can not be considered as a
text in physics in the usual sense. In Part five of the
book, entitled, Physical Principles Applied to the Human
Body, the author treats optics and vision, sound and
hearing, body mechanics and electricity and radiation

in relation to the human body. The entire text is based
upon the premise that important concepts in physics can
be presented nonquantitatively without losing legitimacy.
Accordingly the text lacks the usual rigor required to
unify physics under the general notions of conservation

laws and physical principles. After reading Part Five of

 

171. W. Richardson and E. B. Neergaard, Physics
for Biology and Medicine (New York: John Wiley and Sons,
1970).

 

19

this text, one is left with only a vague understanding of
the unity of physics. The author is to be commended,
however, in that he clearly recognizes the stumbling
block which mathematical formalism presents to beginning
students and, especially,to life science students.
Unfortunately, Bachman's book is too qualitative to
adequately prepare students.for the formalism required in

more advanced study.18

Opinion Articles

 

The need for a general introductory text in which
the fundamentals of physics are presented from within the
setting of biological phenomena is clearly suggested by
Philip Handler:

Until the laws of physics and chemistry had been
elucidated it was not possible even to formulate
the important, penetrating questions concerning
the nature of life. For centuries students of
biology, in considering the diversity of life,
its seeming utter distinction from inanimate
phenomena, and its general unlikelihood, found
it necessary, in their imagination, to invest
living objects with a mysterious life force,
"vitalism," with which all living organisms

were endowed. But in the late eighteenth
century, Lavoiser and Laplace were able to

show that within the not inconsiderable limits
of error of the methods available to them,

the recently formulated laws of conservation

of energy and mass were valid also in a living

 

18Charles H. Bachman, Physics — Understanding Our
Physical Environment (Croton on Hudson, New York:
Bogden and Qngley, 1970).

 

 

20

guinea pig. The endeavors of thousands of life
scientists over the next two centuries have gone

far to document the thesis thus begun. Living
phenomena are indeed intelligible in physical

terms. And although much remains to be learned

and understood, and the details of many processes
remain elusive those engaged in such studies hold

no doubt that answers will be forthcoming in the
reasonably near future . . . . Biology has become

a mature science as it has become precise and
quantifiable. The biologist is no less dependent
upon his apparatus than the physicist. Yet the
biologist does not use distinctively biological

tools. He is an opportunist who employs a nuclear
magnetic resonance spectrometer, a telemetry assembly,
or an airplane equipped for infravred photography,
depending upon the biological problem he is attacking.
In any case, he is always grateful to the physicists,
chemists and engineers who have provided the tools

he has adapted to his trade.19

Addressing himself to current changes in physics
and education in physics, H. William Koch, Director of
the American Institute of Physics, emphasizes that the
trend is away from isolation of physics from the other
sciences. In particular Dr. Koch sees an amalgam of
physics with chemistry and biology insupport of research
and education in the future.20

If today physics is unpopular in the minds of a
large segment of the population of undergraduate students

then attention must be given to this attitude. Writing

on this subject, Dr. Adolph Baker maintains that the

 

19Philip Handler, Biology and the Future of Man
(New York: Oxford University Press, I970), p. 3

20H. William Koch, "An Age of Change," Physics
Today, (March, 1970), p. 35.

 

21

~golden age in which physics was held in high esteem in
the student mind is past, that in order to maintain a
dominant position in the undergraduate curriculum physics
must now compete for students.21

Although a working knowledge of fundamental physics
is necessary to an understanding of much of modern bio-
logical science this fact is not apparent to the casual
observer nor to the beginning undergraduate. In order
to attract students to physics Baker maintains that intro-
ductory physics can no longer be taught as a discipline
unto itself in a language which is foreign to the student.22

Baker's point must be considered in the development
of textual materials in general physics for life science
students.

An area of growing popular concern in which physics
and the life sciences will increasingly blend together is
environmental science. In an article pertaining to
contributions which physics can make toward solutions
of environmental problems, Marvin Goldberger, Chairman of

Princeton's Physics Department proposes that the present

undergraduate physics curriculum be modified to include an

 

, 21Adolph Baker, "Physics and Antiphysics," Physics
Today! (March, 1970), p. 35

ZZIbid.

22

emphasis on applications of physics to a wide range of

environmental problems.23

Although Goldberger would
leave the content of the introductory physics courses
essentially unchanged, he does advocate modifying third
and fourth year physics courses to include environmental
topics. Arguing for the introduction of environmentally
related material into the physics curriculum Goldberger
writes:
What is done at present, to a greater or lesser extent,
is to ignore essentially everything in the intro-
ductory course and to start over again giving finer
derivations and so on. My proposal for those two
years (the last two years in undergraduate physics)
is to teach applications of physical principles to
a wide range of (environmental) problems, developing
and deepening the theory, as one goes along and as
it is needed.

In 1969 the president of The National Academy of
Sciences appointed The Physics Survey Committee for the
purpose of evaluating the status, opportunities and problems
of physics in the United States. The report of the
committee's panel on Physics in Biology is presented in
Volume 1 of Physics in Perspective. Regarding the inter—

action between university physics departments, departments

of biophysics and the life sciences the panel reports:

 

3Marvin Goldberger, "How Physicists Can Contribute,‘
Physics Today, (December, 1970), p. 26

24Ibid.

 

23

In practice these departments (Biophysics and the

life sciences) do not interact to a large extent

with physics departments, although physics courses

are increasingly important to their students. In

this respect, it is generally felt that physics
department do less than chemistry departments to
accommodate such students among whom are an increasing
number of preemedical students who desire some physics
courses. Revision of the physics curricula to
accommodate the needs of these students would be

one way in which the interaction of physics and

the life sciences could be strengthened.

In an article pertaining to the teaching of
physics to nonscience students, John M. Fowler and
Richard West of the Commission on College Physics, have
written of teaching physics to captive students—-students
_required to take physics in fulfillment of curricular
requirements set by other departments within the university.

These are the preprofessional students in medicine,
architecture, dentistry and nursing, who are forced
into physics classes by curricular requirements.
Problems associated with teaching these captives
seemiin some ways less difficult than the problems

of teaching the broader group of nonscientists. The
students are, afterall, already in our classes. They
are motivated by other professional requirements, and
a good grade (at least in the case of premeds) is
desirable in itself. We have, however, largely avoided
the deeper problem of understanding why physics is
required of these students, and what it is that their
curriculum advisers expect in the way of skills,
knowledge and learned processes. With the changes
that have taken place in most introductory courses,
the time for investigation of these deeper problems
and clear statements of objectives is overdue.

 

25National Research Council, Physics in Perspective,
Vol. 1, (Washington, D.C.: National Academy ofISciences,
1972), p. 308.

26John M. Fowler and Richard West, "What our Left
Hand Has Been Doing," Physics Today, (March, 1970), p. 24.

 

 

24

The unmistakable message of this article, and those
others quoted above is that there is an urgent need for
curriculum revision in the general physics courses taken
by life science students. This need is further supported
by the survey of the historical interaction between physics
and the life sciences and by an examination of existing

physics courses populated by students from the life sciences.

Existing_Courses

 

The lack of available textual material in which
basic physics is presented within a biological framework
is paralleled by the absence of contemporary courses in
which physics is presented as it pertains to biology. There
is, however, a growing interest in developing college
physics courses in which biological topics play an important
role.

The School of Physics and Astronomy of the
University of Minnesota is presently actively engaged in
developing biologically based laboratory experiments for
use in the general physics sequence (Physics 1104, 1105
and 1106). Already in use in these courses are experiments

entitled: The Cow's Eye—-A Natural Optical System,

 

Construction of a Microscope and Telescope, and The

 

Electrocardiogram. In the hope of further developing

 

the lectures which accompany these laboratories and designing

other laboratory eXperiments members of the Minnesota

25

Physics Faculty are currently attending lectures in the
university‘s School of Medicine in order to appraise the
potential needs of presmedical students. At present the
text used to support the lectures in Physics 1104, 1105
and 1106 is,Physics,by Atkins. According to Dr. Bruce
Eaton, Professor of Physics, University of Minnesota, this
text is being used simply because of the lack of a good
text with a biological emphasis.2
The 1972-1973 catalog course description of

Physics 231 and Physics 232 at Western Kentucky University
reads:

. . . a basic course for students of the life sciences,

with emphasis on an understanding of the physical

principles operative in biological systems and on

the application of physical methods in biology and

medicine.
During 1972-1973 academic year Physics 231 and Physics 232
have been offered with no specified course textbook,
although, frequent references have been made to, Physics
for Biology and Pre—Medical Students, by Burns and MacDonald.
According to the course instructors this situation, again,
derives from the absence of an available general text
written with a biological emphasis at a level within the

grasp of beginning students.28

 

27Bruce Eaton, Physics Department, The University of

Minnesota, Private Correspondence.

28James Parks and Thomas Coohill, Department of
Physics and Astronomy, Western Kentucky University, Private
Correspondence.

26

At Michigan State University, the course sequence
in college physics is offered in two tracks, one intended
for life science students and one for general education.
At present the text used in both tracks is,Principles of
thsics,by F. Bueche. This text contains no direct
reference to biological phenomena. In order to overcome
this deficiency, Dr. Jerry Cowen, the lecturer, in the
bio-track sequence, supplements his presentations with
biological illustrations. However, course study guides
written by Dr. Cowen during the 1972—1973 academic year
contain no direct biological input.29

A novel approach in teaching physics to life
science students is offered at Gustavus Adolphus College
in St. Peter, Minnesota. There students take a 14—week
course in which they study the physics of instruments
commonly used in experimental psychology and biological
research. The course includes laboratory eXperiments in
living animals, and the physics of hearing.30

Until recently, the Santa Fe Preparatory School,
Santa Fe, New Mexico, offered a physics course in which

biological illustrations were frequently used. According

to the course instructor:

 

29Jerry Cowen, Department of Physics, Michigan
State University, Private Correspondence.

3°Ibid.

27

. . . Any phenomenon which may serve to elucidate

a fundamental physical principle is a most welcome
addition to the class discussion and it is my thesis
that, if this example can be drawn not from a purely
physical system but from a biologic one, the class
gains markedly thereby.3l

At Coe College, Cedar Rapids, Iowa, each summer
the Physics Department offers a general course largely
attended by life science and pre—medical students from
the University of Iowa. This course is unique in that it
compresses the usual one year college physics course into
the six—week summer term. This is accomplished by giving
a two—hour lecture followed by a one-hour recitation
session each morning and a 3 hour laboratory
period each afternoon. In recent years the text material
in this course has not been biologically related due to
the unavailability of a suitable textbook. However, when
the course was taught by this writer an attempt was made
to relate the class topics to biological phenomena whenever
possible.

Although no longer active, a two-year core course
for science majors has been offered by Portland State
University. The course attempted to integrate the material
normally covered in introductory physics, chemistry and

biology courses. Although the course was not specifically

designed to teach physics in a biological setting,

 

31Peter Thompson, "High School Biophysics," The
Physics Teacher (October, 1967), p. 322.

 

“T.

.-

““b-fl -

28

Dr. Arnold Pickar, Associate Professor of Physics at
Portland State University writes:

Concerning those students who are intimidated by
the physics we should offer this observation: We
suspect that a few students in the course owe their
progress through the physics material to the fact
that it came in sections of at most five weeks and
had a recognizable relationship to biology; we

are not certain they would have been as successful
in the conventional physics course.32

And, speaking of the textual material used in
the course, Dr. Pickar further comments, "No single

suitable textbook is available, hence conventional texts

have been used."33

Student appraisal of the course is reflected in

the statement:

A preliminary evaluation study in which attitudes

of students in the core course were compared with
those of matched groups of students in the con-
ventional introductory science courses has shown

a significantly higher level of overall satisfaction
with the core course.3

Summary

From the above literature review it is apparent

that textual material in which biological phenomena pro-

.v.....

 

32Richard Fuller, Physics Department, Gustavous
Aldolphus College, Private Correspondence.

33Arnold D. Pickar, Physics Department, Portland
State University, Private Correspondence, April, 1973.

34Arnold D. Pickar, "Core Course for Science Majors
Combining Material from Physics, Chemistry and Biology,"
American Journal of Physics (February, 1960), p. 260.

29

vide a basis for illustrating and applying the general
laws and principles of physics is not commonly available
today. The need for such material is reflected in current
attempts to incorporate biological phenomena into the
content of college physics courses. Chapter III of this
study describes the design of an eXperiment in which bio-
logically oriented textual material was evaluated for its
effects on student attitudes and achievement in college

physics.

CHAPTER III
DESIGN AND IMPLEMENTATION OF THE STUDY

Overview

This investigation originated with the development
of textual material for experimental use in the course
Introduction to Physics and Biophysics 231 at Western
Kentucky University during the Fall semester of the
1972—1973 academic year. Use of the eXperimental textual
material and collection of data occurred during November,
1972.

The purpose of the study was to determine the
relative effects of eXperimental textual material,
combining physics and biology on student attitudes and
achievement contrasted with attitudes and achievement
where conventional college physics textual material was
assigned reading.

The effects of the experimental materials were
measured in terms of attitudes towards physics, attitudes

towards physics textual material and achievement in physics.

The Population

 

The study was conducted with undergraduate students
at Western Kentucky University. The students were sopho-
mores, juniors, and seniors majoring in the health and life

sciences. These students were taking the course to fulfill

3O

31

curriculum requirements established by their major
departments, and in this sense they may be considered
as captives. Thus, the usual motivational problems
associated with non major required courses were
encountered.

Physics 231 is taught in three separate lecture
sections, two under one professor, and one under another.
Due to the fact that sectional enrollment was designated
by the individual students at the time of registration
sectional equality, as established under a random assign—

ment procedure, could not be established.

The Sample

 

For purposes of the experiment each of the three
lecture sections of Physics 231 were divided into two
randomly selected groups. In each section one group
received the experimental textual material and the other
received no special material.

From the total enrollment of 74 students in the
three lecture sections of Physics 231, 62 students co—
operated fully in the experiment by returning both achieve—
ment and attitude tests pertaining to the eXperiment.
From these students one treatment group of 8 randomly
selected subjects, and one control group of 8 randomly
selected subjects, were established in each of the three

lecture sections of Physics 231. Thus, the sample consisted

32

of three randomly selected treatment groups, and, three
randomly selected control groups corresponding to the

three lecture sections of Physics 231. Each student in
each treatment group had received a copy of the experi—
mental physics textual material whereas each student in
each control group had received no special textual material.

Early in the design of the study, the possibility
of exchange of trial materials between the treatment and
control groups was a matter of concern. Consideration
was given to limiting access to the experimental material
by placing it on reserve limited to the designated treatment
subjects. However, constraints of this nature were
rejected on the basis that they impose unusual and
artificial study conditions, which could confound the
effects of the treatment. Thus, the students participating
in this study experienced no unusual controls beyond random
assignment to reading materials.

Following the course unit in which the experimental
materials were used an achievement examination of the
multiple choice type, written by the course instructors,
was administered to all students in the experiment. The
achievement examination was administered by the regular
course instructors as a normal unit examination. Following
the achievement examination, the investigator administered
the attitude inventory, a Likert-type attitude inventory

written by the investigator.

33

The design of this experiment, The Post Test-Only

 

Control Grogp_Design, is described by Stanley and Campbell
as a True Experimental Design. The design may be rep—

resented symbolically as:

R X 0

R X 0

Here R represents random assignment of respondents to the
treatment and to the control groups, X represents the
treatment and 01 and 02 represent the achievement and
attitude tests administered to the treatment and control
groups respectively.

This design was selected for several reasons.
Primary among them are the controls which the design

offers in limiting the effects of the threats to internal

and external validity listed below.

Threats to Internal Validity

 

1. History, the specific events occuring between
the first and second measurement in addition
to the experimental variable.

2. Maturation, processes within the respondents
operating as a function of the passage of
time per se (not specific to the particular
events), including growing older, growing
hungrier, growing more tired and the like.

3 Testing, the effects of taking a test upon
the scores of a second testing.

34

4. Instrumentation, in which changes in the
calibration of a measuring instrument or
changes in the observers or scorers used
may produce changes in the obtained measure—
ments.

5. Statistical regression, operating where groups
have been selected on the basis of their
extreme scores.

6. Biases, resulting in differential selection
of respondents for the comparison groups.

7. Experimental Mortality, or differential loss
of respondents from comparison groups.

8. Selection-Maturation interaction, etc., which
in certain of the multiple—group quasi-
experimental designs, . . . is confounded
with, i.e., might be mistaken for, the
effect of the experimental variable.3S

Specifically, the controls on these factors under the Post
Test—Only Control Design are indicated by the following

table.

Threats to External Validity

 

Threats to external validity, threats which may
invalidate the findings of a study as they might apply to
the external population are difficult to delineate. The
primary source of this difficulty lies in the tentativeness

of inductive logic.

Interaction of Testing and Treatment

%
—

Under the assumption of limited generalization, the
Post Test-Only Control Group Desigp avoids the external

interaction effect of testing and treatment. This threat

 

35J. C. Stanley and D. T. Campbell, Experimental
and Quasi-Experimental Designs for Research (Chicago:
Rand McNally and Company, 1966), p. 5.

 

TABLE 3.1.--Controls on

35

Threats to Internal Validity.

 

 

Threat Control
History No Pretest
Maturation No Pretest
Testing No Pretest
Instrumentation No Pretest
Regression No Pretest

Selection Biases

Experimental Morality

Selection-Maturation
Interaction

Random Assignment of
Control and Treatment
Respondents

Random Selection of
Respondents from whom
data is considered in
Analysis

Short Experimental Period,
Randomization

 

to external validity is particularly troublesome in

attitudes where the attitude tests themselves may

introduce attitudes which heretofore are not present in

the sample.36

In that testing only followed treatment in this

study this threat of interaction of testing and treatment

was reduced by design.

 

36

Ibid., Stanley and Campbell, p. 18.

36

Interaction of Selection
andITreatment

 

 

The threat posed by the interaction of selection
and treatment is difficult, if not impossible, to control
in any experimental design. All that can be said with
regard to this threat as it may have affected this study
is that the course in which the experiment was conducted
is offered without unusual conditions by two professors
having distinctly different personal backgrounds. Although
the students who comprised the control and treatment groups
may reflect demographic characteristics peculiar to the
South Central United States, these characteristics would
seem difficult to differentiate from those of other general
physics students in small public universities elsewhere
in the Central United States. Whether the willingness of
the faculty of the Department of Physics and Astronomy of
Western Kentucky University to accommodate this study is
unusual and introduces selective biases can not be estab-

lished.

Reactive Arrangements

 

The threat to external validity posed by the so-
called reactive arrangements effect, that is, the effect
in which the simple awareness of participating in an experi-

ment may influence the outcome, is impossible to control or

37

evaluate in the Post TestvOnly Control Group Design.
However, certain precautions were taken to reduce this
threat. The trial fixeatment)material (physics textual
material) was carefully written to present only content
which was prescribed by the unit syllabus, written by the
course instructors far in advance and independent of the
eXperiment. This fact, along with a strongly worded
statement to all students in Physics 231, indicating that
the trial material did not differ in physics content from
the usual reading material, was intended to effectively
overcome reactive arrangement effects. Furthermore, the
students were pre-advised that the achievement examination
over the unit, would be written by the regular course
instructors without regard for any particular textual
material.

At the onset the investigator considered writing
placebo material for the control group. However, on the
advice of personnel within the Office of Research Consult—
ation of the Michigan State University College of Education
the use of placebo materials was abandoned. This action
was justified on two bases: (1) a placebo itself can not
actually replicate other textual material which the trial
material is intended to contrast, and (2) any placebo
written well enough to appear as an improvement over

standard contemporary textual material might produce

38

effects which would confound effects of the actual experi—
mental material.

Finally, the threat of confounding the effects of
multiple treatments and thereby jeopardizing the external
validity of the findings of this study was reduced by

design in the following manner.37

The possibility of
effects due to changes in the established classroom
procedures was avoided by allowing the instructors to
continue their presentations without experimental alter—
ation. Although,in writing the trial material it was
necessary for one of the two instructors to read the
trial material and to confer with the writer as to its
suitability to the course, the second instructor,
responsible for two of the three lecture sections, did
not read the trial material prior to or during the
experiment. This reduced the possibility of treatment
biases creeping into his class-lecture presentations.
Furthermore, as described in Chapter IV, the Finn Program
was set up to test for differences due to Teacher—Class
interactions in order to detect any treatment effects
which could be attributed to factors external to the

reading materials.

 

37Lee J. Cronbach, Essentials of Psychological
Testing, 2nd Edition (New York: Harper and Row, 1960)
p. 103.

 

39

Instrumentation

 

The instruments used in this study consisted of a
twenty—five item multiple choice type examination covering
the physics content of the course unit to which the experi-
ment was limited, and a Likert type attitude inventory
scale designed to measure student attitudes towards
physics itself and attitudes towards textual materials

covering the unit.

 

Achievement Test
The achievement test was written and administered

by the course instructors independent of contact with the
investigator in order to reduce possible reactive
effects. This procedure was instigated following the
advice given by Stanley and Campbell:

The present authors are gradually coming to the

View that eXperimentation within schools must be

conducted by regular staff of the schools concerned,

whenever possible, especially when findings are to

be generalized to other classroom situations.38
At the suggestion of the investigator, the instructors
included only multiple choice type questions on the
achievement test. This suggestion was made in order to

give each item equal weight in the final analysis. Due

to the test's construction by the course instructors, the

 

38Stanley and Campbell, op. cit., p. 21.

40

content validity, as well as the reliability of the
test depended entirely on the judgment of the instructors
alone.

At the outset it was recognized that achievement
tests based entirely on multiple choice type questions
suffer from at least two serious limitations, (1) the
fact that the students are confronted with a series of
choices knowing that at least one is correct ignores the
real possibility that without that knowledge a correct
response might not be given, and (2) the multiple choice
examination does not provide for means of testing the
student's ability to express himself clearly, to demonstrate
his ability to organize data, and to systematically arrive
at some desired conclusion. Nonetheless, in View of the
need for strict objectivity in scoring the examination
in order to compare performance between the treatment and
control groupslthe multiple choice test appeared to be

the most suitable choice among alternatives.39

Attitude Test

 

The attitude test administered to the treatment and
control groups was designed according to the Likert Scaling

Procedure. The test was written by the investigator and

 

39Frederick L. Ferris, "Testing for Physics
Achievement", Achievement Testing in Physics (New York:
American Institute of Physics, 1960Y} p. 22.

 

41

it incorporates 50 item statements each allowing a set

of 5 responses, (1) Strongly Agree, (2) Agree, (3) Un-
decided or Neutral, (4) Disagree, (5) Strongly Disagree.
Of the 50 item statements 28 were judged by independent
observers to pertain to attitudes directly related to
physics textual material, and 22 items were judged to
pertain to physics itself. Of the 28 items pertaining

to textual material, 10 item statements were judged to

be negative in viewpoint, whereas 18 were judged as
positive. And of statements pertaining to physics itself,
10 were judged as positive and 12 were judged negative

in point of view. Each of the attitude statements was
approved by personnel in the Office of Research Consult-
ation of the Michigan State University College of
Education on the basis of their individual apparent
validity and reliability as discriminating indicators

of attitudes towards physics and attitudes towards physics
textual material. The statements intended to determine
attitudes toward physics itself were, for the most part,
based on The Revised Mathematics Attitude Scale, by Aiken

and Dreger.40

 

 

40Aiken and Dreger, "The Revised Mathematics

Attitude Scale", ed. Marvin E. Shaw and Jack M. Wright
Scales for the Measurement of Attitudes, (New York:
McGraw Hill, 1967).

 

42

Data Collection Procedure

Due to the Post-Test Only Control Group Design
used in this study the only experimental data consist
of the achievement test and attitude test scores obtained
at the end of the experiment. After initially distributing
the trial textual materials and a cover letter addressed
to all students in Physics 231 in early November, 1972,
the investigator returned to Western Kentucky University
after a period of roughly three weeks at which time the
tests were administered. The achievement test was admins
istered by the regular course instructors in the absence
of the investigator during pre—established examination
periods. Following completion of the achievement test,
requiring roughly 40 minutes, the investigator was called
to the examination room where he distributed the attitude
test which was completed and returned by the students
within a period of 10 to 15 minutes. The achievement
tests were marked by the course instructors and the
results were then given to the investigator. The attitude
tests were marked by the investigator. The test results

are reported in Chapter IV.

Hypotheses

 

This study is concerned with testing three univariate
hypotheses concerning achievement and three multivariate

hypotheses concerning attitudes. Each of the multivariate

43

hypotheses involves two dependent variables which can
be individually tested under separate univariate hypo-
theses. The statistical test employed using multi-
variate analysis of variances is designed to test the
multivariate hypotheses. Only if significance is
demonstrated for the multivariate F—ratios in testing
the multivariate hypotheses is post hoc testing for the
univariate hypotheses conducted. The post hoc testing
makes use of step—down F-ratios applicable to each of
the two dependent variables included in the test of the
multivariate hypotheses. The hypotheses are stated

below in the null form.

Univariate Hypothesis 1

 

There will be no differences in achievement
between treatment and control groups as determined from

the unit physics examination.

Univariate Hypothesis 2

 

There will be no differences between teacher-class
combinations in achievement as determined from the unit

physics examination.

Univariate Hypotheses 3

 

There will be no treatment by class interaction
effects on achievement as determined from the unit physics

examination.

44

Multivariate Hypothesis 1
There will be no differences between treatment and
control groups in attitudes toward physics and/or physics

textual materials as determined from the Likert instrument.

Univariate Hypothesis 1.1
There will be no differences between treatment and
control groups in attitudes toward physics as determined

from the Likert Instrument.

Univariate Hypothesis 1.2
There will be no differences between treatment and
control groups in attitudes toward physics textual material

as determined from the Likert Instrument.

Multivariate Hypothesis 2
There will be no differences between classes in
attitudes toward physics and/or physics textual materials

as determined from the Likert Instrument.

Univariate Hypothesis 2.1

 

There will be no differences between classes in
attitudes toward physics as determined from the Likert

Instrument.

Univariate Hypothesis 2.2

 

There will be no differences between classes in
attitudes toward physics textual materials determined

from the Likert Instrument.

45

Multivariate Hypothesis 3
There will be no treatment by class interaction
effects on attitudes toward physics and/or physics

textual materials as determined from the Likert Instrument.

Univariate Hypothesis 3.1

 

There will be no treatment by class interaction
effects on attitudes toward physics as determined from the

Likert Instrument.

Univariate Hypothesis 3.2

 

There will be no treatment by class interaction
effects on attitudes toward physics textual materials

as determined from the Likert Instrument.

Analysis of Data-

 

Research specialists within the Office of Research
Consultation of the Michigan State University College of
Education assisted in determining appropriate statistical
procedures, computer program and data processing pertaining
to this study. Upon its recommendation, the Finn program,
A Generalized Univariate and Multivariate Analysis of

. . . 41
Var1ance, Covariance, and Regress1on Program was used.

 

 

41Jeremy D. Finn, A Generalized Univariate and

Multivariate Analysis of Variance, Covariance andIRegression
Program (Buffalo, New York: State University of New York
at Buffalo, 1966).

 

46

In the Finn Program univariate analysis of
covariance procedure an F ratio was computed for each
of the two main effects (materials and teacher class)
hypotheses adjusted on achievement and an additional
F ratio was computed to test for interaction of teacher-
class and materials.

In the multivariate analysis of variance procedure,
two types of F ratios are computed, the multivariate F
ratio to test for main effects on attitudes and univariate
F ratios to test for significance of the individual
dependent variables incorporated in the multivariate
hypotheses. In other words, here the multivariate F
ratio determines whether all dependent variables (two)
have combined significance at a specified alpha level,
and if significance is found, then univariate F ratios
for each dependent variable in the multivariate hypotheses
are computed to determine if that variable is significant

at a specified alpha level.

Summary

Forty—eight undergraduate students enrolled in
Introduction to Physics and Biophysics 231 during the
Fall semester of the 1972-1973 academic year at Western
Kentucky University and were the subjects in a study
comparing the attitudes and achievement in college physics

in terms of the textual material assigned to the students.

47

Three groups of eight students each, one group
from each of three lecture sections of Physics 231,
received no experimental textual material. These groups
were designated the treatment groups.

Three groups of eight students each, one group
from each of three lecture sections of Physics 231,
received experimental textual materials. These groups
were designated the control groups.

Following a period of approximately three weeks
the treatment and control groups were tested for achieve-
ment and attitude differences as determined from separate

achievement and attitude tests.

CHAPTER IV

ANALYSIS OF RESULTS

A description of the experiment upon which this
study is based is provided in Chapter III. In this
chapter we examine the eXperimental hypotheses stated in
Chapter III.

Table 4.1 below displays the mean achievement and
attitude scores of the 48 randomly selected treatment and
control students from which the data of this experiment
were obtained. The table lists achievement and pre achieve-
ment mean scores within the range of 0 to 100, and attitude
mean scores within the range of 2 to -2. The achievement
mean scores are based on the unit achievement examination
(see appendix), the pre achievement mean scores are based
on two previous hourly examinations, and the attitude mean
scores were determined from the Likert Attitude Scale
(see appendix).

The correlation coefficient relating attitudes
toward physics and attitudes toward physics textual
materials (0.51) is stronger and tends to support the
notion that favorable attitudes toward textual material

are associated with favorable attitudes toward the subject.

48

49

TABLE 4.1.--Achievement and Attitude Mean Scores.

 

 

Achievement Preachieve- Attitude Attitude
ment Materials Physics
T 89.5 72.8 -0.27 0.36
Class 1
C 79.1 66.4 -0.08 0.43
T 88.0 77.5 0.66 0.66
Class 2
C 82.5 82.8 0.34 0.39
T 84.8 88.7 0.39 0.74
Class 3
C 82.5 84.7 0.10 ,0.45

 

T denotes treatment group, C denotes control group.

Operating on the assumption that previously
demonstrated ability in the course would be predictive
of achievement in the experiment the two previous
achievement test scores were averaged and used as the
covariate designated preachievement.

Significance at the 0.05 level requires that the
sample correlation coefficient must be equal to, or
greater than, 0.288 for a sample size of 48.42 The

correlation coefficients between the four experimental

variables, Achievement (Ach), Attitudes Toward Physics

 

42A. L. Edwards, Statistical Methods for the

Behavioral Sciences (New York: RInehart and Winston,
1960), p. 502.

 

 

50

Textual Materials (ATPTM), Attitudes Toward Physics (ATP),

and Preachievement (Preach), are presented in Table 4.2.

TABLE 4.2.--Correlation Coefficients Between Variables.

 

 

Ach. ATPTM ATP Preach.
Ach. 1.000
ATPTM 0.189 1.000
ATP -0.036 0.51 1.00
Preach. 0.423 0.31 0.245 1.00

 

From Table 4.2 the only significant correlations
are between the attitudes toward physics and the attitudes
toward physics materials, and, between preachievement and
attitudes toward physics textual materia. The relation-
ship between preachievement and attitudes toward physics
textual material, although statistically significant
(Correlation Coefficient = 0.310) is not strong.

Within the Finn Program a measure of the effective—
ness of this covariate as a predictor of achievement on
the trial unit achievement test was calculated. The
measure involved calculation of a correlation coefficient
between the observed achievement score and a predicted
achievement score based on preachievement. This correla—
tion coefficient was tested for significance by means of
an F ratio. The calculated value of the correlation

coefficient between the actual achievement score of one

51

individual and the predicted achievement score for that
individual was based on a least squares regression line
for achievement using preachievement as a predictor. This
correlation coefficient (Multiple R correlation coeffi-
cient) calculated to be 0.423 indicated no significant
relationship between preachievement scores and scores on
the achievement examination. The F ratio, 0.0736, which
tested for the significance of this correlation coeffi-
cient had a significance level of 0.7875 indicating that
for any reasonable alpha level (i.e., 0.05) there is no
relationship between preachievement scores and achievement

on the trial achievement examination.

Tests of the Achievement Hypotheses

 

Although Univariate Hypothesis 1 is the hypothesis
of primary interest logic suggests that a test of Univariate
Hypothesis 3 should be performed first, for, if a
significant treatment by class interaction effect exists
a test of Univariate Hypothesis 1, pertaining to achievement
differences between treatment and control groups, may be
logically meaningless.

Univariate Hypothesis 3 was tested in the Finn
program by calculating the F ratio (MS for interaction/

MS error) and its associated P value. The P value is the
probability of finding a value of the F ratio equal to, or

greater than, the particular computed F ratio (0.68).

52

Comparison of the P value (0.51) with the designated alpha
level of 0.05 shows no basis for rejecting Univariate
Hypothesis 3. That is, due to the fact that P is greater
than 0.05, Univariate Hypothesis 3 was not rejected. If
the P value had been less than the chosen alpha level the
computed F value would have fallen in the region of rejec-
tion for Hypothesis 3. Fortunately for this study, based
on this evidence, there is no reason to believe that there
is a teacher-class interaction affecting achievement.

Having found no significant teacher-class inter-
action effect on achievement we now examine Univariate
Hypothesis 1 and Univariate Hypothesis 2.

From Table 4.3 the P value for Univariate Hypothesis
1 (0.04) is less than the designated alpha level (0.05).
Therefore, based on this fact, Univariate Hypothesis 1,
that there will be no differences in achievement between
treatment and control groups, is rejected. An estimate of
the differences between control and treatment materials
indicates that use of the treatment materials resulted in
higher adjusted achievement than did use of non treatment
materials. The computed estimate of difference between the
adjusted achievement scores is 5.99 favoring the experimental
physics textual materials.

Turning now to Univariate Hypothesis 2, and again
referring to Table 4.3, we find the P value for this

hypothesis, 0.88, is greater than 0.05 (the designated

53

TABLE 4.3.--ANOVA Table for Adjusted Achievement Scores.

 

 

Adj. MS Signifi-
Source df Between F P cant
H1 Treatment 1 429.24 4.49 0.04 yes
H2 Teacher-Class 2 12.73 0.13 0.88 no
H3 Interaction 2 65.13 0.68 0.51 no
Error 41

 

df denotes computed degrees of freedom; Adj. MS denotes

adjusted mean squares.

alpha level).

Based on this fact, Univariate Hypothesis 2,

that there will be no differences between teacher—class

combinations in achievement, is not rejected.

Tests of the Attitude Hypotheses

 

As in the above analyses, where preachievement is

used as a covariate with achievement as the dependent

variable, in the following analysis where the dependent

variables are attitude measures, again preachievement is

used as the covariate.

However, just as in the case of

achievement, little relationship was found between pre—

achievement scores and attitude scores.

This fact is

demonstrated in Table 4.4 by the low values of the Multiple

R correlation coefficients between attitude scores pre-

dicted on the basis of preachievement scores and the measured

attitude scores.

54

TABLE 4.4.--Multiple R Correlation Coefficients Between
Predicted and Measured Attitude Scores.

 

Multiple R Correlation

 

Variable Coefficient F P less than
ATPTM 0.307 4.27 0.045
ATP 0.245 2.62 0.114

 

The basic design for testing the hypotheses per—
taining to attitudes is identical to the design for testing
the hypotheses pertaining to achievement. Hence here we
repeat the logic of examining first the test for class by
materials interaction.

The results of this test indicate no evidence of
such interaction. The computed F ratio for Multivariate
Hypothesis 3, 0.8199 for 4 and 80 degrees of freedom yields
a P value of 0.5163. Since this test of Multivariate
Hypothesis 3 indicates no significant interaction, further
testing of Univariate Hypothesis 3.1 and Univariate
Hypothesis 3.2 would be pointless and, therefore, is omitted.

Turning to Multivariate Hypothesis 1, under which
differences in attitudes between treatment and control
groups are tested, we find no significant differences in
attitudes toward physics textual materials, nor toward
physics itself. The F ratio for testing Multivariate Hypo-
thesis 1 was calculated to be 0.957, which with 2 and 40

degrees of freedom yielded a P value of 0.393. Uni-

55

variate Hypotheses 1.1 and 1.2 were not examined
separately.

In examining Multivariate Hypothesis 2, under
which differences in attitudes between classes was tested
no significant differences were found. The F ratio for
testing Multivariate Hypothesis 2 was calculated to be
1.215, with 2 and 40 degrees of freedom yielding a P value
of 0.311. Again, because of multivariate non-significance
Univariate Hypotheses 2.1 and 2.2 were not examined

separately.

Summary of Results

 

1. Testing Univariate Hypothesis 1 indicated
directional differences in achievement between treatment
and control groups as determined from the unit physics
examination favored the experimental physics textual
material.

2. Testing Univariate Hypothesis 2 indicated no
differences between teacher-class combinations in achieve-
ment were determined from the unit physics examination.

3. Testing Univariate Hypothesis 3 indicated no
treatment by class interaction effects on achievement as
determined from the unit physics examination.

4. Testing Multivariate Hypothesis 1 indicated no
differences between treatment and control groups in attitude
toward physics and/or physics textual materials determined

from the Likert instrument.

56

5. Testing Multivariate Hypothesis 2 indicated
no differences between classes in attitudes toward physics
and/or physics textual materials as determined from the
Likert instrument.

6. Testing Multivariate Hypothesis 3 indicated no
treatment by class interaction effects on attitudes toward

physics as determined from the Likert instrument.

CHAPTER V

SUMMARY AND CONCLUSIONS

The purpose of this study was to compare and assess
the effects of contemporary and experimental college
physics textual materials on attitudes and achievement in
Physics 231 at Western Kentucky University during the fall
semester of the 1972-1973 academic year. The effects
examined fell into three categories: Content Achievement,
Attitudes Toward Physics Textual Materials, and Attitudes
Toward Physics.

A 25 item unit examination of the multiple choice
type, written by the course instructors, comprised the
instrument which measured achievement. A Likert type
attitude scale, written by the investigator, was used to
assess the attitudes. Both the achievement examination and
the attitude scale were administered as post tests only at
the close of the experimental course unit.

The hypotheses of the experiment were tested using
the multivariate analysis of variance procedure provided by
the Finn Program. The univariate hypotheses pertaining to
achievement, and the multivariate hypotheses pertaining to
attitudes, were tested at the 0.05 level of significance.
The summary below describes the pertinent results of this

study. , 57

58

Summary of the Results of
Hypothesis Testing

 

 

Univariate Hypothesis 1

 

Greater achievement was associated with the
treatment material than with instructor designated

(control) textual material.

Univariate Hypothesis 2

 

No differences were found between teacher~class
combinations in achievement as determined from the unit

physics examination.

Univariate Hypothesis 3

 

There were no treatment by class interaction
effects on achievement as determined from the unit physics

examination.

Multivariate Hypothesis 1

 

No differences were found between treatment and
control groups in attitudes toward physics and/or physics

textual materials as determined from the Likert instrument.

Multivariate Hypothesis 2

 

No differences were found between classes in
attitudes toward physics and/or physics textual materials

as determined from the Likert instrument.

59

Multivariate Hypothesis 3

 

No treatment by class interaction effects on
attitudes toward physics and/or physics textual materials
were determined by the Likert instrument.

Due to the failure to find significance in testing
Multivariate Hypotheses l, 2 and 3, Univariate Hypotheses

1.1 1.2, 2.1, 2.2, 3.1 and 3.2 were not tested.

Conclusions

 

Based on the findings of this study the following
conclusions seem justified.

l. Achievement in college physics on the part of
life science students can be improved by use of textual
material in which physics is presented within a framework
of direct biological relevance.

2. Achievement in college physics on the part of
life science students can be improved by use of textual
material in which physics is presented within a framework
of direct biological relevance without regard to particular
teacher-class combinations.

3. Achievement in college physics on the part of
life science students does not appear to be influenced by
unique interactions between the material, the instructor

and the class which it is used.

60

4. The attitudes of life science students toward
physics and/or physics textual material do not appear to
depend on the biological relevance of physics textual
material.

5. The attitudes of life science students toward
physics and/or physics textual materials do not appear to
differ between teacher—class combinations.

6. The attitudes of life science students toward
physics and/or physics textual materials do not appear to
indicate unique interaction effects between the textual
materials and teacher-class combinations. Experience of
this investigator, however, suggests that this conclusion

be regarded as tentative.

Implications from the Study

 

Based on the findings of this study the following
implications are presented for consideration.

1. Achievement in physics on the part of life
science students is in part related to the context in which
physics textual materials is presented. The content of
college physics textbooks should increasingly relate to
the major areas of interest of student readers. College
physics courses intended for life science students should
incorporate biologically relevant textual readings in order

to improve achievement in physics.

61

2. Although the differences in attitudes toward
physics and physics textual materials between treatment
and control groups in this study were not statistically
significant, it seems reasonable to speculate that attitude
differences may become significant over an extended
experimental period. This may be particularly true where
the biologically related textual material is introduced
early in the physics course, thus avoiding the establishment
of attitudes which may be difficult to change in a short
period toward the completion of the course, as was the case
in this study.

3. From the survey of currently available college
physics textbooks (Chapter II) and the findings regarding
achievement (Chapter IV) it is apparent that immediate
attention should be given to publication of textual
materials in which biological phenomena, requiring general
physical principles for understanding, provide the frame-
work in which physics is presented.

Recommendations for Future
Investigations

 

 

The following recommendations are made based on
the findings, conclusions, and implications of this study.
1. A basic assumption of this study is that
learning from textual materials is related to the expressed

major academic interests of students in general level

62

courses. Further studies are needed to determine the
validity of this assumption.

2. The attitude measures of this study were made
following a brief (3 week) experimental period. Studies
are needed to determine the validity and reliability of
measures pertaining to improving attitudes over brief
periods.

3. The increased achievement associated with the
trial reading material of this study is encouraging.
Comparative long term studies of achievement based on
extensive readings are needed to determine the strength
of the findings of this study.

4. Based on the assumption that historical factors
of widely different varieties influence the attitudes and
achievement of students investigations are needed to
delineate these factors as they pertain to the education
of life science students in basic physics.

5. Just as special textual materials may be
valuable in teaching physics to life science students so
may it be that other special physics textual material
written for students of psychology, the earth sciences,
etc., may be valuable. Such materials should be written

and evaluated.

APPENDICES

63

APPENDIX A

EXPLANATORY LETTER TO THE STUDENTS OF
PHYSICS 231 AT WESTERN KENTUCKY

UNIVERSITY

64

To The Students of Physics 231, Fall Semester, 1972—

Western Kentucky University

Your cooperation is requested in support of a
study of reading materials which have been written for
use in this course. The class is being divided into two
groups for the purpose of the study. You will be assigned
to one of these groups. One group will be requested to
read the normal reading materials selected by your
instructor. The other group will be assigned to read
some materials which have beenwritten to cover the same
topics, but in a somewhat different manner.. If you are
selected to read the normal course readings, please do not
read the materials which will be assigned to the other
group. In other words, we will appreciate your cooperation
in reading only the materials which are assigned to you.

This study is being made by personnel from The
Science and Mathematics Teaching Center of Michigan State
University. The results of the study may have significant
effect on the writing of other materials for use in courses
such as Physics 231.

Your grade in this course, Physics 231, will not
depend on which materials you are assigned to read since

each set contains the same physics. At the end of the unit

65

66

you will be examined in the normal way by your instructor.
His examination will not be geared to either group, but

rather to the material covered in the course.

APPENDIX B

PHYSICS ACHIEVEMENT TEST

67

Fall, 1972

Name

 

PHYSICS 231

PROPERTIES OF MATTER

A technical name given to force per unit area is

a.
b.
c.
d.
e.

The
the

a.
b.
c.
d.
e.

stress

strain

modules

tensile strength
shear

direction of motion of the diffusing particles in
process of diffusion is

same as the concentration gradient

opposite the concentration gradient
perpendicular to the concentration gradient
dependent on the type of particle
irrelevant

A shearing stress that acts on a body affect its

a.
b.
c.
d.

length
width
Volume
shape

Poiseuille, while studying the flow of water through
narrow tubes, found that

the rate of flow was directly proportional to the
pressure gradient

the rate of flow was independent of area

the rate of flow was independent of viscosity

the rate of flow was directly proportional to
viscosity

The retarding force on a small sphere moving with
velocity v in a viscous fluid may be calculated using

Newton's third law
Ficke's Law
Stoke's law
Pitot's law

Stefan's law
68

10.

Blood and synovial fluid are examples of liquids
which

a. are Newtonian

b. are non—Newtonian

c. flow as Poiseuille

d. have flow rates proportional to the pressure
gradient

e. are conservative

For equally applied pressures, the rate of flow of
water through a hypodermic needle twice the diameter
of another but equal in length is

a. 1/2 as great
b. 1/4 as great
c. 2 times as great
d. 4 times as great
e. 16 times as great

Bernoulli‘s equation is a consequence of the law of
conservation of

a. mass

b. energy
c. momentum
d. fluid

e. intensity

Ficke's law states that the rate of diffusion per
unit area

a. is inversely proportional to the concentration
gradient of the solute

b. is directly proportional to the viscosity of the
liquid

c. is directly proportional to the concentration
gradient of the solute

d. is independent of concentration

If fluid is flowing through the pipe and P and P2 and
P are the values of the pressure at the points
indicated, then

P1 P2 P3

. Pl > P2 P3
c. Pl < P2 < P3
d. Pl < P2 > P3

69

ll.

12.

13.

14.

15.

16.

Archimedes principle states that the bouyant force on
an object is equal to

a. the force of gravity

b. the weight of the displaced fluid
c. the viscosity gradient

d. the surface tension of the object

Hooke‘s Law states that

a. stress is equal to strain

b. strain is independent of stress

c. stress is directly proportional to strain

d. shear is directly proportional to the bulk modulus

Besides Hooke's Law - Robert Hooke is famous for

a. the discovery of cytoplasm
b. the discovery of bacteria

c. the discovery of the cell

d. the discovery of the nucleus

The diffusion coefficient of Urease in a water like
medium is 2.5 x 10 cm2 /sec and Urease has a
molecular weight of 5 x 105 daltons. The time it
takes a ureas molecule to traverse a cell of diameter
10-3 cm is

a. 1.4 sec
b. 1.0 sec
c. 0.05 sec
d. 0.50 sec

The terminal velocity of a sphere falling in a viscous
medium is

a. directly proportional to the viscosity
b. independent of gravity

c. independent of the density of the fluid
d. can be increased by centrifugation

According to Stoke's Law the retarding force = F is

4 3
b. j W a pg
A a2 V
C. 9 n
V
do (p-po) g E

70

17.

18.

19.

20.

21.

 

A.
"I: M B w
W VVWM" "

 

Fluid connects piston A to piston B. If B = 10A in
area, what is the upward force on B when there is a
downward force of 5 newtons on A

a. 2
b. 50
c. 25
d. 5

Active transport across cellular membranes can be
fully explained by

a. diffusion

b. osmosis

c. osmosis and diffusion

d. can‘t be fully eXplained

When a pearl is dropped in a bottle of Prell, it's
velocity quickly becomes const (acc=0) because

a. there are no net unbalanced forces on the pearl

b. the bouyant force is balanced by the viscous force

c. the viscous force is greater than the force of gravity
d. the weight of the pearl is negligible.

The osmotic pressure is found by experiment on weak
solution to be

a. directly proportional to the volume of the solution

b. inversely proportional to the temperature

c. directly prOportional to the concentration of solute

d. inversely proportional to the thickness of the
membrane ‘

e. directly proportional to the area of the membrane

Blood leaves the heart through the aorta with a velocity
of 40 cm/sec. If the cross sectional area of the aorta

is 2 cm2 and the density of blood is l gm/cm3, the mass

transport of blood will be

a. 80 gm/sec
b. .016 gm/sec
c. 251 gm/sec
d. 504 gm/sec

71

22.

23.

24.

25.

Whenever possible liquids tend to assume the shape with
the least surface area (usually a sphere). This is a
result of

a.
b.
c.
d.

their inherent viscosity
their molecular weight
cohesive forces in the liquid
laminar flow

The stress
passed its

a.
b.
c.
d.

return
remain
return

on a body is removed after the body has
elastic limit. The body will now

to its original shape
deformed
to a smaller size than it was originally

oscillate indefinitely

The critical vel at which 1amuar flow changes to
turbulent flow can be calculated from

d.

(pm);
10000n

pR

1/2hpgr

P + 99h

The pressure at any point in a liquid does not depend

on
a.
b.
c.
d.

the denisty of the liquid

the distance from the free surface (height)
the acceleration due to gravity

the shape of the vessel

72

APPENDIX C

LIKERT TYPE ATTITUDE SCALE

73

Attitudes Toward Physics
Your response to the following items will permit
us to determine what life science students think about
certain aspects of physics. There are no right or wrong
responses to the Items in this questionnaire and the
results will not be used in any way for grading purposes

in this course.

 

Please indicate the degree to which you agree or
disagree with each of the statements by responding once
to each Item on the separate answer sheet. Mark your
response to each Item by selecting one of the following
responses:

1. Strongly agree

2. Agree

3. Undecided or neutral

4. Disagree

5. Strongly disagree

PLEASE RESPOND TO ALL ITEMS

74

-8.
9.
10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

I plan to take more physics than is required for
my major.

I am always under a terrible strain in physics classes.

The theory of elastic materials has little relation to
biology.

When lihear the word physics I have a feeling of
dislike.

Physics makes me feel secure and at the same time it
is stimulating.

Understanding how solutes diffuse in solutions interests
me.

The reading material for this unit increased my interest
in the physics of living organisms.

I am interested in learning more about surface tension.
The feeling I have toward physics is a good feeling.

A knowledge of Poiseulli's Equation would be helpful
to a medical doctor.

It is my belief that physics is very important to
understanding anatomy.

Biological illustrations tend to make physics more
confusing.

I might like to be a biophysicist.

It is my belief that a course in physics should be
required for biology majors.

Physics makes me feel as though I am lost in a jungle
of formulas and I can't find my way out.

I might recommend the reading material for this unit
to a friend in biology.

Biology is more interesting if you know some physics.

Physics makes me feel uncomfortable, restless, irritable,
and impatient.

Physics is fascinating and fun.

75

20.
21.

22.
23.

24.
25.

26.

27.

28.

29.

30.

31.

32.

33.
34.

35.

36.

37.

38.

I do not like physics, it scares me to have to take it.

Stoke's Equation for bodies falling in viscous media
is very interesting.

Physics is a subject which I have always enjoyed.

Readings in physics reflect little concern for the
interests of biologists.

I really like physics.

Very little physics can be learned from studying living
organisms.

I feel at ease in physics, and I like it very much.

Physics is more relevant to biology than I thought it
was.

Bernoulli's Principle is difficult to understand.

Physics is not very important in understanding life
processes.

I feel a definite positive reaction to physics; it is
enjoyable.

I have never like physics, it is my most dreaded subject.

Knowing some physics tends to make biology appear more
difficult.

I am happier in physics classes than in other classes.

I wish that I could see more relevance of the material
in this unit to biology.

I approach physics with a feeling of hestiation result—
ing from a fear of not being able to do the problems.

I am more interested in physics than I was several months
ago.

Physics is very interesting and I enjoyed this unit more
than others.

A medical doctor should have a general competence in
physics

76

39.
40.

41.

42.

43.

44.

45.
46.

47.
48.

49.
50.

I felt less secure in this unit than in others.

This unit was more interesting than I though it would
be.

The reading material in this unit was a relief from
other reading material used before in the class.

It makes me nervous to think that physics may be
important in biology.

My mind goes blank, and I am unable to think clearly
when working a physics problem.

The difficulty of physics outweighs its value to
biology students.

I was happier in this unit than in others.

It is my belief that biologists should have a general
competency in physics.

I would be glad just to pass this course.

I might be inclined to put off taking this course until
I am a senior.

I would like more readings like the ones for this unit.

Knowing some biology tends to make physics seem less
relevant to biology.

77

Answer Sheet - Attitudes Toward Physics

Item Number Response
1 2 3 4
l. _____ _____ ______ ______
2. _____ ______ ______ ______
3. __ __ __ __
4. _____. ._____ ______ ______
5. ._____ ______ ______ ______
6. ______ _____ _____ ._____
7. _____ _____ _____ _____
8. ______ ______ ______ ______
9. ______ ._____ ______ l_____
10. _____ _____ _____ _____
ll. _____ ._____ ._____ ._____
12. ______ _____ ______ ._____
l3. ______ ______ ‘_____ _____
l4. ______ ______ ______ ______
15. _____ ______ _____ I_____
16. ______ ______ ._____ ______
l7. ______ ______ ______ _____
18. ______ ______ ______ ______
l9. _____ ._____ _____ ._____
20 ______ ______ ______ ______
21. ______ _____ ._____ ______
22. __ __ _________

 

78

23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.

79

48.
49.
50.

80

APPENDIX D

EXPERIMENTAL TEXTUAL MATERIAL

Elastic Properties of Matter
Fluid Mechanics I
Fluid Mechanics II
Fluid Mechanics III

81

ELASTIC PROPERTIES OF MATTER

This paper is intended to present some of the
basic notions involved in the study of elastic materials.
After you have read this paper you will be eXpected to be
able to write quantative descriptions of elastic materials
using the definitions of tensile stress, shearing stress,
bulk stress, tensile strain, shearing strain, and bulk
strain. In addition, you will be expected to be able to
write the equations representing Young's Modulus, the
modulus of rigidity, and bulk modulus, and to verbally
explain the meanings of each of these. Your instructor
may require you to use each of these definitions and

equations to solve basic physics problems.

 

In living animals certain motions arise from
elastic recoil which is the property of returning to an
initial form, or state, following deformation. Two
materials which are elastic and which partly account for
motion in animals are resilin, and abductin. These
materials compare in their elastic properties to soft
rubber. Resilin is found in the thoraxes and at the
wing bases of some insects and its elasticity contributes
to the flapping of the insects‘ wings. Abductin is an
elastic protein found in scallops, it composes the hinge
of the scallops' shell and by elastic recoil it acts to

spring open the shell. 82

83

For our purposes the actual physical forms of
resilin and abductin in insects and scallops is not import—
ant. The important thing is that both resilin and
abductin are elastic biological materials. The question
of physical interest to which we will direct ourselves
is, just how elastic are these springy biological sub—
stances? How is elasticity measured and how do resilin
and abductin compare to other elastic materials?

Actually the theory of elasticity is a detailed
and complicated part of physics which concerns the nature
of the atoms and molecules which make up the many elastic
materials. The elasticity of rubber, which is much like
that of resilin and abductin, is fundamentally different
from that of steel. The differences between these two
kinds of elasticity is account for by changes in the
entropy of the rubberlike molecules as they are stretched
and by changes in the internal energy of steel as its
atoms are displaced from their normal crystaline arrange—
ments. Rather than consider these microscopic character—
istics of elastic materials, we shall direct our attention
only to the macroscopic notions of elasticity.

Actually there are essentially three ways by which
elastic materials can be deformed. They can be pulled

gpart by tensile stresses, they can be sheared by shearing

 

 

stresses, and they can be compressed by bulk stresses.

 

84

As this suggests, the notion of stress is of
fundamental concern in the study of elasticity, and we
shall consider three types of stress, tensile stress,
shear stress, and bulk or compressional stress.

Tensile stress is defined as the ratio of the
distorting force to the cross sectional area of the
object in tension or linear compression. Consider the

sketches below:

 

 

 

 

 

 

 

 

 

In figure 1 the body experiences a tension force E
which is distributed over the perpendicular cross sectional
area A. Here the object experiences a tensile stress

defined as the ratio of the force F to the cross sectional

85

area A, i.e. tensile stress = F/A. In figure 11 we con—
sider a cross sectional area which is inclined at the angle

0 with respect to the perpendicular or normal cross sectional
area. We call this inclined cross sectional area A'. Now,
with respect to A' the force F has components Fn and Ft.
Fn is the component perpendicular to A' and it is called

the normal component of F. Ft lies along A‘ and it is
called the tangential component of F.

In the case of the hinge mechanism of the scallops,
the abductin material which composes the hinge experiences
both tangential and normal forces over any given cross
section when the scallops shells are closed. In all cases
where a given body experiences a normal force over a cross
section the ratio of the force Fn to the area of the cross
section to which it is perpendicular, is called the normal
or tensile stress. That is tensile stress = Fn/A'. Like-
wise the ratio of the tangential or shearing component
of force to the cross sectional area over which it is
distributed is called the tangential or shearing stress,
i.e. Shearing Stress = Ft/A‘

Associated with both normal and tangential stress
are physical deformations. For normal stress the associated
deformation is called normal, or tensile, strain. Normal,
or tensile, strain is defined as the ratio of the elongation

of the stressed body to its non-stressed length, that is,

tensile strain =Al/lo, where Al is the elongation and 10 is

86

the non—stressed length. And, in similar manner the

ratio of the tangential deformation, or bending of a body,
to the length of the body, is called shearing strain, i.e.
shearing strain = s/l, where s is the deflection of the
body from its‘ initial position and l is the length of

the body. The ratio, s/l is of course, the measure of

the deformation angle in radians provided that s is

small.

 

4— Q -—o-4-AR+ ‘I‘J-e As

 

 

 

 

 

Tensile Strain (

smauingshxein

There remains one other type of deformation to
which we must direct our attention. This type is known as
compression. Compression is associated with the change in
volume of a body experiencing applied pressure. A fish for
example eXperiences compression or bulk strain due to the
pressure of its surrounding water. Bulk stress is the
pressure associated with the change in volume of a body
corresponding to the applied pressure. Bulk stress is
therefore expressed by the ratio of applied force to the
area over which it is applied, F/A = compressional or

bulk stress . The corresponding strain is the measure of

87

the distortion of the body under the applied pressure.
It is the ratio of the change in the body's volume, AV

to the initial volume V0. Bulk or compressional strain =

AV/Vo.

The sketch below shows a transverse section of a
scallop. Note that the hinge is actually composed of an
outer and inner ligament, the inner ligament is compressed
and the outer is stretched while the shell is closed.

It is the combined action of the contraction of the outer
ligament and the expansion of the inner ligament which
"pops" open the shell upon release of the adductor muscle.

If removed from the shell the inner ligament bounces like.

rubber when dropped, thus demonstrating its elastic nature.

  

 

 

[7‘7
L-Inmm: - -
| Ouuflr}lhngelngamum

Now, an interesting prOperty of elastic materials
is that within certain limits, from a state of no stress
to a stress value at which permanent distortion occurs,
the stress is directly proportional to the corresponding

strain. For cases of tension and compression where strain

88

is measured as the ratio of the change in length A1, of
a body to its original length, l, the proportionality
constant, Y, is called Young's Modulus.

Stress = (Young's Modulus) (Strain)

or

F/A = Y (Al/lo)

Thus, by applying a certain stress to a body and
measuring the corresponding strain the value of Young's
Modulus for the material composing the body can be deter-
mined.

Y (Stress/Strain)

Y

(F/Ae(Al/lo)

For example, suppose that from the inner hinge
ligament of a scallop one cuts cylindrical segment, which
has a cross sectional area of 1/100 cm2 and a length of

1 cm. While under a tension of 500 dynes, it is observed

that the length of the segment increases by 1.25 x 10“3 cm.

Thus, for Young's Modulus we have:

500 dynes,/10'2 CM2

Y= _3
1.25 x 10

cm/ 1 cm
or
_ 7 2
Y — 4 x 10 dynes/cm
Actual measurements of the value of Young's Modulus
for the inner hinge ligament material of scallops yield

values ranging from 1.3 x 107 to 4 x 107 dynes/cm?

89

Here some attention should be given to the import—
ance of Young's Modulus. Young's Modulus is the pro—
portionality constant which indicates how elastic a
material is. From the first equation above, it is seen
that for any given stress applied to a body there is an
accompanying strain. For materials having large values
of Young's Modulus, the corresponding strain is less
than for materials having smaller moduli. Below is a
table which gives the values of Young's Modulus for
several biological and non—biological materials.

Notice the large range of values reported for
the various materials. Can you account for the tremendous
increase in the value of Young's Modulus in comparing
abductin, for example, with mild steel? See following
table.

Recalling that a body may be deformed under
shearing stress, Ft/A‘ and that the corresponding strain
is measured as the angular deformation of the body, 0=As/l,
we can write the eXpression for the shear modulus of a
substance as the ratio of the shearing stress to the shear
t is
the shearing component of the force which is distributed

strain. That is: Shear Modulus S=Ft/A' 0, where F

tangentially over the cross sectional area A'.
Shearing stresses and accompanying strain in bones
are reduced by muscular tension. For example, consider

the human forearm extended horizontally holding a heavy

MECHANICAL PROPERTIES OF VARIOUS MATERIALS

 

Metridium
mesogloea

Resilin

Abductin

Elastin

Collagen

Bone

Locust
cuticle

Lightly
vulcanized
rubber

Oak

Mild Steel

Young‘s
Modulus
(dyn/cmz)

c. 3 x 104
l 8 x 107

1—4 x 107

6 x 106
1010

1011

1011

l 4 x 10

1011

2 x 1012

Tensile
strength
Authority (dyn/cmz) Authority
Alexander,l962
1964a
Weis—Fogh,l961a 3 x 107 Weis—Fogh,
1961b

Kelly & Rice
1967

Bergel, 1961

Harkness, 1961 5-10 x 108 Elliott,

1965

Smith a 9 Evans,
Walmsley, 1959 10 1957
Jensen & Weis- 9 Jensen &
Fogh,l962 10 Weis—Fogh

1962
Ferry, 1961
Hodgman,l965 109 Hodgman,

1965
Hodgman,l965 5 x 109 Hodgman,

1965

90

91

object in the hand. The weight F of the object produces
a shearing stress at the wrist. This stress is reduced
by the tension force F' exerted by the brachioradialis,

biceps, and brachialis muscles.

 

Quantitative analysis of anatomical shearing stresses
and strains is difficult. However, shearing stresses and
strains have been measured in segments of biological materials
and shear moduli obtained. On the following pages are
tables listing elastic moduli of animal bones. These data
should be taken as only representative. Physical properties
of biological materials vary greatly depending on age, wet—
ness, etc. The tables following are from the text:

Mechanical Properties of Bone, 1973, Charles C. Thomas

 

Publisher.

The measurements reported in these tables are
useful in comparing the relative strength of bones and in
understanding the structural design of animal skeletons.
To illustrate this, let us determine the shear deformation
in a section of cattle femur measuring 40 cm. in length

2

and having an uniform cross sectional area of 50 cm . To

simplify let us assume the bone is homogeneous throughout

92

 

. mao.oama.o mmo.oams.o mmo.oamm.o moo.oams.o os.o sense
eao.oamm.o oao.oaea.o oHo.onmo.o aao.oaaa.o o~.oamm.o moo.oama.o Asses
ocom pox
coflummcoam ommucoouom mmeHuHD
u t sm.oao.ma mm.oam.ma oa.oae.aa . mseesm
. . H~.oaa.oa ma.oam.ma aa.oa~.ma I msumesm
. . mm.oaa.ma oa.ono.ma ma.oam.aa . sense
u I Ha.oam.oa ma.oam.aa ao.oam.ma ma.oaa.aa Haste
msom ceaseless
n em.oam.ma am.oao.oa Ha.oaa.ma ea.oam.ma o.ma weaves
. ~a.oam.oa ma.onw.m mm.oa~.oa so.ona.oa ma.oam.oa massage
. om.oao.aa am.oaa.oa mm.oam.ua m~.oam.ma m.aa sagas
m~.oaa.e om.oam.oa ma.oam.m a~.oao.oa a~.oam.aa ma.oaa.ma Hesse
mcom DOB
Amss\sxv eusemuem maamsme masseuse
mmsowuumo noon mmflm muoom OHHS oauuou momuom Doom

 

mcoo nommfioo OOHHUIHHD can uoz mo mowuuomonm OHHNGDBII.H manna

93

 

I coma came omma oama omma assume
I omma oeea came omma cake wettest
I some case case omam ommm sagas
came omen oaaH coma comm ommm Asses
ocom no:
lass\mxv seashemsam mo masses:
I I aao.oaem.o mmo.oaaa.o mao.oaaa.o I assess
I I omo.oaam.o amo.on~a.o aoo.oa~e.o I massage
I I amo.oaam.o ~ao.oaaa.o aoo.oaae.o I sense
I I oao.oaao.o emo.oama.o aao.oaaa.o Hao.onmm.o Haste
msom eoaupIuaa
I mao.oaflm.o mmo.oame.o mmo.oaam.o aoo.oaaa.o Ha.o assess
I mmo.oaoa.o mmo.oaoa.o amo.0Aaa.o moo.osea.o moo.OAme.o massage
muoom UHHE oauuou momuom Odom

MOEOAHHMO Home mmflm

 

emssaucooII.H passe

94

 

 

I I ovam ommm ovmm I msflcmm
I I omma coma ommm I mdumfidm
I I omom osma ommm I names
I I onwa omna ommm ommm HSEom
Dsom emeupIuee
monowuumo Homo mmflm mumom UHHZ mauumu momuom mcom

 

emssausOOII.H sense

4

kg/mmz) of wet

 

 

Table IIi.-—Modulus of rigidity (X10 long
bones, in anteroposterior bending

Source of Bone Femur Tibia Humerus Radius Ulna
Horses 28617 17835 11871 7317 —
Cattle 8445 5046 6230 2453 —
Wild Boars 671 228 363 87 86
Pigs 354 163 247 81 54
Dogs 42 35 5 10 8
Cats 37 46 5 7 l4
Rabbits 9 ll 5 l 0 0 9
Guinea Pigs 10 o. 0.7 o 2 o i
Domestic Fowls 13 23 8 0 9 6

 

 

 

 

 

 

 

 

96

 

 

 

 

 

 

 

 

 

 

 

 

 

mo.ona.~ mo.onm.a No.0nm.a mo.oam.a No.ouh.a v.m usEom

ocom umz

cofluomupcoo ommucooumm ouDEHuHD
I I h.vH m.ma I I mswomm
I I m.eH m.ma I I msumEdm
I I b.ea h.ma m.~m I Danae
I I ~.va o.mH m.mm ma.oum.ma HSEmm
Odom coaucIHflm

I -.oum.ma . oa.oah.oa ma.onm.ma ma.oum.ma w.ma msecmm
I ma.oam.ma ma.oam.oa ma.oao.aa ma.oue.va «.ma msHoEdm
I o~.oaa.va Ha.onm.oa -.onm.ma «H.o«m.ma m.ma mane?
mm.oao.ma ma.o«m.ma no.oao.oa Ha.oum.aa aa.o«h.va ma.onm.va peach

ocom #03

ANEE\mxv sumcouum D>HmmoudEoo DHDEHHHD
monownumo Homo mmwm muoom UHAS oauumu momuom ocom
econ uommfioo ODHMUIHHD cum um3 mo mmwuuomoum D>Hmmoudfioo II.HHH canoe

 

97

 

 

 

 

 

 

 

I owe omm. one I see assess
I oma oomw com I ooa massage
I com 3mH one I owe sagas

oemw can“ omen cos aka. be A ova Haste

ocom HOB
Amss\mxv suaoaummam no measeoz
I I mo.oeo.~w mo.oao.~ I I museum
I I mo.oao.mw ~o.oao.~ I I massage
I I ~o.oao.~_ uo.ouo.~ o.~ I sense
I I ~o.oao.~. mo.oao.~ o.~ mo.oaa.~ asses
Odom coaupIufim
I ~c.oas.a mo.oaa.a «o.oam.a No.oaa.a m.~ assume
I ~o.ops.a no.0Aa.H mo.oam.a mo.oaa.a mo.oao.~ maumssm
I mo.oae.a ~o.oaa.a mo.oaa.a mo.oam.a ~.~ sagas
mocowuuMo Home mmwm muoom UHH3 oauumu momnom mcom

 

 

 

 

 

emssausoOII.HHH Danae

 

98

 

 

 

I I omm . omw I I museum
I I owm . 0H5 I I msHmEdm
I I one omh omoa I Danes
I I o3 one omoa me a 83 Hosts
ocom cmfluquflm
moccauumo some wood mumom OHAS maupmu momuom mcom

 

 

 

 

 

 

omosflsool . HHH 63.3.

 

99

and that it is subjected to a normal shearing force of‘

6 x 103 newtons. From Table 11 the shear or rigidity

modulus of wet cattle femur bone is 8445 x 104 kg/mmz,

which equals 8.23 x lOlon/mz. Applying the defining
equation for shear modulus and solving for s we have:
s = 4 x Io’lm.(8 x 103n/5 x 10’3m?) 82.3 x 101°n/m2 l.
or

s = 7.7 x 10'5m = 0.08 mm

From this simplified calculation we see that indeed cattle

 

femur bone is quite rigid. This fact is quite important
to the non bow-legged cow!

Finally as an illustration, let us consider the
compressibility of solids. The bulk modulus of a solid
determines the extent to which a body of the material will
experience a volume change due to pressure applied
uniformly over its surface. Here the stress is the applied
pressure and the strain is the relative volume change.
Thus, we write the equation for bulk modulus as:

B = (F/A) e (AV/V0)

Suppose we use the bulk modulus of wet horse
humerus bone to determine the pressure required to crush
the bone to the extent that its volume decreases by 0.05%.
From table 111 we have: B=900 kg/mmz. Again, we may first

convert to proper mks units:

6 10

B= 900 kg/mm2 x 9.8 n/kg x 10 mmZ/m2= 8.82x10 n/m2

100

By direct substitution into the above equation we obtain:

10 4

8.882 x 10 n/m2 = (F/A+ 5 x 10—

or

 

F/A = 4.41 x 107 n/III2

7, n/m2 is roughly the

This pressure, 4.47 x 10
hydrostatic pressure of water at a depth of 4.4 km.
Unless our horse is a sea horse he need not worry about

the prospects of significant changes in his skeletal

volume due to compression!

 

FLUID‘MECHANICS‘I

 

Some knowledge of the mechanics of fluid motion is
necessary to understanding the means by which living
organisms maintain their vital functions. In this reading
we will consider only some of the fundamental concepts
of fluid mechanics. This subject is one of the most [-
difficult in physics. For this reason it is usually

treated rather lightly by life scientists. However, to

 

do so is to lose. an understanding of some of the most
fundamental aSpects of life supporting mechanisms.
After studying this paper the reader will be
eXpected to know the basic definition of viscosity and
to be able to express it in equation and verbal terms.
He should also expect to be called upon to solve ele-
mentary physics problem calculations by use of the
defining equation for viscosity. In addition the
reader will be held responsible for Poiseuille's
equation, he should be able to write the equation,
to use it in elementary calculations such as those
given in this paper, and he should be able to infer
certain real physical phenomena of fluid flow based
on an understanding of Poiseuille's equation. And,
finally the reader will be expected to be able to
distinguish between newtonian and non-newtonian fluids
and by so doing account for relevant characteristics

of fluids in motion.
101

102

The French physician, J.L.M. Poiseuille,
studying the flow of blood through capillary blood
vessels, observed the peculiar motion of red blood
corpuscles. As had been reported by others Poiseuille
noted that at times neighboring red corpuscles appeared
to move with equal speed, and then on occasions one
or more of them would change speed, rotate, and
continue to flow with the blood. This observation had
been previously used to support the idea that the
corpuscles possessed the ability to move by themselves.
However, as a consequence of his work, in 1843,
Poiseuille was able to account for this peculiar
red corpuscle motion on the basis of the dynamic
properties of fluids alone and thus to discredit the
notion of self moving red corpuscles. In order to
understand Poiseuille's eXplanation one must first
gain an understanding of some of the fundamental
properties of moving fluids. We shall thus begin our
study by considering the concept of viscosity, a
property of fluids which plays a very important role
in all fluid motion and in particular in Poiseuille's
explanation.

Perhaps viscosity may best first be understood
by thinking of a very wide and very long river having
a flat smooth bottom. Imagine the river to be flowing

such that its velocity at the lower surface increases

103

linearly from zero to a maximum value at the upper
surface. (The notion of zero velocity at the very
bottom should present no conceptual difficulty; after-
all fish resting in a stream use this fact in order

to remain in a stationary position . . . this is most
easily done near the bottom where the current decreases
to zero.) We will denote the height of the fluid above
the bottom as, y, and the current velocity at any
point in the river as v. From these terms we define
the velocity gradient of the river as the rate at
which the velocity increases with respect to height

above the river bottom. That is:

A V

Velocity Gradient =
Ay

The river bottom tends to drag the river in
the direction opposite to the flow. If we denote a
unit area (1 cm2) of the bottom water surface as A,
and the drag force of the bottom acting tangentially
over this area as F, we can define a shearing stress,
analogous to that which we studied for solids, applied

to the fluid composing the river as:

Shearing Stress = F/A

104

For many fluids the ratio of the shearing stress
to the velocity gradient is a constant which we shall

denote as n ; this constant is called the viscosipy of

 

the fluid.

Viscosity, n = (F/A)%-(Av/Ay)

Fluids for which this equation holds, that is fluids
for which the shearing stress is directly proportional

to the velocity gradient, are called newtonian fluids.

 

Fluids for which this relationship does not hold are

called non-newtonian fluids. Verbally we may define

 

viscosity as the drag force per unit area per unit
velocity gradient.
The common (C. G. S.) unit of viscosity is the

poise. The poise is defined from the above equation:

1 Poise (l dyne/ cmz) + (l cm/sec/cm)

1 dyne sec/cm2

The table below gives the viscosity of several newtonian

fluids at different temperatures.

Water at 0°C 0.0178

Water at 20°C 0.0100

Water at 100°C 0.0030
Mercury at 0°C 0.00125
Mercury at 100°C 0.00091
Glycerin at 20°C 6.8

Air at 0°, 760 mm of pressure 0.133 x 10'3

Air at 100°C, 760 mm of pressure 0.245 x 10"3

105

Consider now a tube in which a viscous fluid
is flowing. By comparison to the fluid motion in our
long and wide river we can see that the drag force of
the tube's wall acting on the fluid is greatest nearest
the wall and least in the center. It is from this basis
that Poiseuille determined the equation which expresses
the volume rate of discharge of a fluid flowing through
a pipe. This equation, Poiseuille‘s equation, may be

written as:

q = R4AP

8nL

Here q is the volume of fluid discharged through the
pipe per unit time (cm3/sec), R is the pipe's radius
(cm), P is the pressure difference (dynes/cmz) from
one end to the other over the length L (cm), and n
is the viscosity of the fluid (poise).

Although the theoretical development of this
equation lies outside of this presentation interested
students are referred to page 572 in the text: Physics

for Biology and Pre-Medical Students, by Burns and

 

MacDonald for an intuitively based development of
the equation.

From Poiseuille's equation we note some very
important aspects of fluid motion. As might be expected

the rate of discharge (q) is inversely proportional

106

to the length of the tube (L) and directly proportional
to the pressure difference along its length. More
surprisingly, however, is the fact that q is directly

proportional to the fourth power of the tube's radius;

 

thus for example, narrowing the radius of a tube to
one fourth of its initial size reduces the flow to
1/256 of its initial rate, or, tripling the radius
of a tube increases the rate of flow 81 times.

The circulation of flow through our tissues,
although not strictly described by Poiseuille's
equation, is controlled by the cross-sectional
changes of the blood vessels. In particular only
very small changes in the radii of capillary blood
vessels are required to produce tremendous effects
on blood flow. If the arteries had rigid walls the
blood would flow through them in spurts due only to
the pumping of the heart. This, however, is not the
case. The arteries swell slightly as the heart contracts,
storing blood and elastic energy. (The elastic energy
is stored largely in the elastin, an elastic protein,
which makes up a large portion of the arterial walls.)
Then by elastic recoil the stored blood is pumped on
through the capillaries with ease due to their slightly
expanded state as predicted by Poiseuille‘s equation.

Hence, due to this expansion, the flow rate is regulated

107

through the arterioles and capillaries, and less work
is required of the heart to pump the blood throughout
the body.

At this point it is perhaps worth mentioning the
long established medical practice of prescribing wine
in the treatment of "high blood pressure". Ethyl
alcohol, the alcohol in wine and other alcoholic
beverages, is readily absorbed into the bloodstream
whereupon there is a corresponding dilation of the
blood vessels. This eXpansion, by Poiseuille's equation,
is associated with a decrease in the pressure required
to maintain the bloodstream.

Although this phenomenum is suggested by
Poiseuille's equation,strictly speaking Poiseuille's
equation applies only to newtonian fluids, and, blood
is not a newtonian fluid. The reader will recall
that for newtonian fluids the velocity gradient is
directly prOportional to the shearing stress applied
to the fluid, F/A=nAv/Ay. This equation, which defines
n the viscosity of the fluid, does not hold for non-
newtonian fluids of which blood is one. Blood is made
up of component cells and molecules which, due to their
shapes and sizes become intertwined as the blood flows.
This intertwining disrupts laminar flow, the layered
flow exemplified by sheets of fluid slipping over

each other as in the case of our river imagined earlier.

108

In that example, and any other in which the flow is
laminar, fluid layers slip past each other without
exchanging material between adjacent layers. In fact
the term streamline comes from the notion of a line
lying along one of these layers which pass undisrupted
along in the direction of fluid motion. A streamline
is a line which indicates the direction of velocity
within a current in which there is no turbulence,Ior
exchange of matter across lamina.

We can now understand Poiseuille's explanation
regarding the peculiar motion of the red blood corpuscles.
The corpuscles, several microns across in size, occasionally
shift across streamlines. In crossing these streamlines
the corpuscles eXperience rotational forces which result
in applied torques which produce rotational acceleration
of the corpuscles and thus their peculiar observed motions.

The torques which long molecules eXperience in
crossing streamlines are due to the fact that the fluid
in the center of a tube flows more rapidly than the fluid
nearer the tube wall. This is consistent with the fact
that the viscous drag increases as the tube wall is
approached. Thus for fluid flowing in tubes of constant
radius we can visualize the flow as consisting of
concentric sleeves of fluid moving with increasing
velocity corresponding to decreasing radius. And by

use of some simple calculus and the assumption that the

109

fluid is flowing at a constant discharge rate;it can be
shown that the velocity of any particular sleeve of

fluid is given by the equation:

v = Pl-PZ (R2 _ r2)
4nL

Where Pl—P2

tube L, and n is the viscosity of the fluid. R is the

is the difference across the length of the

radius of the tube and r is the radius of the tube for
which v, the velocity, is being determined. It is
important to remember that this equation applies

ohly to newtonian fluids. The sketch below illustrates
the velocity distribution of streamlines for a newtonian
fluid flowing through a tube. Keep in mind that fluids
of homogeneous composition made up of spherically
symmetric molecules tend to be newtonian whereas

fluids composed of high polymers and solutions of high

polymers are non-newtonian.

viscous"drag" forces

ICZ/v/l I 3* \ fl 2
P1”2-<§>W1. “*F WOW__I)jf“ P2/:1r\‘ fluid
P

 

 

 

P I sleeve
1 5 _” ,"_”__”,, 2//
P P2 L >b ( tube
1) wall
\\J ' I
f
Pl ‘ I I
**,I"€-I
I l !
velocity vect s -—>' R ‘—

for individual
streamlines

_ Ave—M‘-

i9 .

AQ‘

 

110

For solutions of high.molecular weight polymers the
velocity gradient is not proportional to the shearing
stress; in fact, the viscosity generally decreases as
the stress and velocity gradient increase in these
solutions.

Perhaps here is a good point in which to give
a sample calculation based on the concepts we have been
discussing. Although blood, as indicated above, is
non-newtonian, we may, for slow discharge rates assume
that Poiseuille's equation applies to blood. This type
of assumption is common in physics where one wishes to
obtain an order of magnitude estimation under the
realization of the limitations underlying the assumptions
implicit in the estimation.

Let us calculate the pressure difference between
the ends of a capillary blood vessel which is 2 x lO-3cm
in diameter and has a length of 5 x lO—zcm/sec and that
the viscosity of blood is 7.2 x 10.2 Poise. First
off let us realize that the discharge rate of the blood
is given by the product of the cross-sectional area of
the capillary and the average velocity of the blood, i.e.,
q=(nR2) v. Then by rearranging Poiseuille's equation in
order to solve for P, the pressure difference, we obtain:

AP = —51——8 ”L
R

 

111

And, by substituting in the data given above we obtain

the desired pressure difference,

P = 9043 dynes/cm2

or

P = 9 x 103 dynes/cm2

The reader is strongly encouraged to perform

the above calculation in order to prove to himself the
validity of the result. His attention is called also
to the fact that this pressure difference corresponds
approximately to 1/100 atmospheres which is quite a

small pressure difference. (What is the driving force?)

FLUID MECHANICS II

This paper is intended to present a fundamental
description of the following topics: bodies falling in
viscous media, sedimentation rates, diffusion phenomena
in liquids, osmosis, and surface tension of liquids.
After reading the material below you will be expected
to be able to write Stoke‘s Equation and to use that
equation in explaining phenomena which are apprOpriately
described by it, e.g., preliminary diagnostic tests
for pregnancy, infection, and malignancy. Your instructor
may also ask you to use Stoke's Equation in solving
certain physics problems similar to the example given
in this writing. Concerning diffusion you will be
expected to know Fick‘s Equation, to be able to write
it and to know the meanings of the terms it includes,
i.e., the diffusion coefficient, the concentration
gradient, and the mass transfer rate. On osmosis you
will be held responsible for knowing the equation which
expresses the final osmotic pressure in a volume of
solution given its temperature, and concentration.
You should also be able to discuss the qualitative
aspects of osmosis at the level presented. And finally,
you will be eXpected to be able to write the definition
of surface tension, to write eXpressions for it in

terms of force and energy as given in the discussion.

112

113

The specific biological applications of each of the
above mentioned topics which are discussed in this
article should be also understood in order to exemplify

the physics inherent in them.

 

In 1938, E. Newton Harvey published an article

on properties of protOplasm in Volume 9 of The Journal

 

of Applied Physics (pp. 68-80). In his article

Dr. Harvey discusses the use of the centrifuge to

separate different materials contained in living

cells. This separation is in the form of layers
distinguished by the densities of the different materials.
Other scientists have used very high speed centrifuges

to separate biological materials, such as sugar molecules,
from their solutions, and to separate and thereby

identify different protein molecules from biological
fluids. Each of these procedures is an example of
sedimentation of objects within a viscous medium.

In each case individual particles are forced to settle
out of a fluid in which they are initially found.

Any object falling in a viscous fluid eventually
acquires a constant velocity called its terminal velocity.
Small objects, that is objects which have large cross-
sections compared to their volumes, have lower terminal
velocities than do large objects composed of the same

material. (Smoke particles fall slower than do lumps of

114

picnic charcoal!) A lump of charcoal 1 cm. in radius
has a maximum cross-sectional area to volume ratio of 3/4,
whereas, by comparison, a smoke particle having a

radius of 5 x 10_4cm. has a maximum cross-sectional

area to volume ratio of about 20 x 1048. The tremendous
difference in these ratios largely accounts for the
vastly different rates at which the bodies fall.

The parachute slows the rate of a body's fall
by increasing its cross-sectional area; the parachute
used artificially by man is naturally used by certain
animals and plant seeds to reduce the rates at which
they fall. Actually the sedimentation rates of small
objects falling in viscous media are determined not
only by their sizes but also by their densities. For
equal size the more dense the material the greater the
terminal velocity. The sedimentation rate of red blood
corpuscles in vitro is commonly used in medical diagnosis.
Sedimentation rates for red blood corpuscles may increase
from about 15 mm. per hour to 45 mm. per hour in cases
of pregnancy, infection, and malignancy.

A body of any shape will, of course, eXperience
Opposing drag as it falls in a viscous fluid. Due to
the mathematical complexities in calculating the drag
force which retards the motion of most bodies we will
consider only the case of a spherical body falling in

a viscous medium. Here the calculations are relatively

simple.

115

In 1845, George Stokes, an English physicist
and mathematician deduced an equation which expresses
the drag force acting on a spherical body moving with
velocity, VT, in a medium having viscosity, n; this
equation, Stokes' Equation may be expressed in the

following form:

Fd= 61rnrvT

Here Fd is the viscous drag force (dynes), n is the
viscosity of the medium in which a sphere of radius

r (cm) is falling at velocity v (cm/sec). Readers

T
interested in a dimensional analysis type develOpment
of this eXpression are referred to the text Physics
for Biology and Pre-Medical Students, by Burns and
MacDonald.

Now, from Newton's Law of Motion we know that
for a body moving at a fixed velocity the sum of the
external forces acting on the body is zero. The
gravitational force, Fg, which acts on a body, it's
weight, is simply the product of the body's volume,
density, and the gravitational field. For a Sphere
this product may be written as 4/3nr30g, where 4/31rr3
is the volume of a Sphere of radius r (cm), 0 is the
Sphere's density (gm/cm3), and g is the gravitational

field (cm/secz). Within a fluid this gravitational force

116

is always Opposed by the force of buoyancy (by
Archimede's Principle). The force of buoyancy is
simply the product of the volume of the fluid the
body displaces, the density of that fluid, and the
gravitational field. Thus, for a completely sub-

3D'g, where 4/3/nr3, the

merged sphere: Fb = 4/3nr
volume of the sphere is also the volume of fluid
displaced,p'is the density of that fluid, and 9, again,
is the local gravitational field. Pb is, of course,
the buoyancy force.

Having now established expressions for the
gravitational and buoyant forces which act on a
Spherical body we can add the viscous drag force

given by Stokes' Equation and equate the sum to zero

in accord with Newton's law.

b d
or

F+F +F =0
9

And, realizing that Fg acts downward in opposition to

Fb and Fd we may delete the negative Sign and write:

Now substituting in the eXpreSSionS for Fb' Fd’ and Fg'

from above we finally have:

3

4/3nr 0'g + 6IIr3 pg

 

117

Which may be solved for vt yielding:

2
_ 2/9 r g _ ,
vt — 0 (D D )

This expression, a very important one, gives us a
means of determining the terminal velocity (Vt) of
a Sphere falling in a viscous medium.

1 To illustrate let us use the above equation
to determine the rate at which some red blood corpuscle
of radius r = 4 microns (1 micron = 10-4cm) settles
out of blood plasma for which we will assume the density,
= 1.04. Here we are assuming that red blood corpuscles
are Spherical in shape where in fact they are more or
less saucer shaped. Let us further assume that the
density of the red corpuscle is 1.08, and that the
viscosity of blood plasma is 0.072 poise (remember
that l poise = l dyne sec/cmz). Making the appropriate

substitutions into the given expression we obtain:

vt = 2/9 (4 x 10"4czm)2 (9.8 x 102 cm/secz) (1.08 - 1.04) gm/Crn3

 

7.2 x 10.2 dyne sec/cm2

or

Vt = -.l96 cm/sec or 7051um0u:

This result is quite obviously at odds with the sedi-
mentation rates for red blood corpuscles reported earlier;

the difference in this result compared to the experimentally

118

reported values is_due to the assumption that the
corpuscle in our calculation is spherical--a very

bad assumption--saucers don't resemble Spheres very
well! Here, however, the reader is encouraged to
reflect on the importance of Shape in influencing the
rate at which bodies do fall in viscous media and

on the biological significance of altering shapes of
such important things as red blood corpuscles! One
can also speculate as to the shape of raindrops and
the possible effects of altering that Shape.

Here it should be emphasized that the dis-
crepancy in the experimentally reported sedimentation
rates and the result obtained in our example above
is intentional; the reader who may now have doubts
concerning the validity of Stoke's Equation for spherical
shaped objects falling in a viscous media is referred
to the classical Millikan Oil Drop Experiment from
which the fundamental unit of electrical charge was
determined thereby establishing the quantum nature
of electricity.

Life processes are abundant in phenomena in
which substances spontaneously diffuse from regions
of higher concentration into regions of lower con-
centration. The inky fluid secreted by squids and
octopi in time of danger quickly diffuses to form a

protective cloud about the animals, sugar molecules

119

diffuse from the chloroplasts in plant cells throughout
the cell protoplasm, and digestive enzymes diffuse within
the stomach fluid of animals. In all cases of spontaneous
diffusion the flow occurs across some physical gradient.
Electric charge diffuses across a gradient of electrical
potential, thermal energy diffuses across a temperature
gradient, and solutes diffuse across gradients of chemical
potential, or, as mentioned above, solutes diffuse from
regions of higher concentration into regions of lower
concentration. The rate of diffusion of a solute into

its solvent, across a concentration gradient, is described

by Fick's Equation which may be written as:

Am/At = - D A AC/AX

 

 

 

T’ "””
I
I
l
I

l
I
I
I
L >-.-(---—---—a»

 

 

 

 

 

Here Am is the mass of solute which diffuses Ax across
the area A during the time interval, At. AC is the

difference in concentration (Cl - C2) of the solute from

120

Side 1 to Side 2 of the partition shown in the sketch

above. D is the proportionality constant which determines

the rate of diffusion, and it is, therefore, called

the diffusion coefficient. Although, as in all equations

of physics, the units in Fick‘s Equation are arbitrary,

commonly m is in grams, t is in seconds, D is in meters2
per second, and C is in grams/meters3 and x is in

meters. In this unit system the diffusion coefficient

for biologically important molecules, according to

Burns and MacDonald, ranges from 1 x 10—11m2/Sec to

100 x lO—llmz/sec.

The diffusion coefficient in the above equation
actually depends on the temperature and viscosity of
the partition through which the solute passes as well
as on the size of the solute particles themselves.

The equation for the diffusion coefficient of solutes
in liquids was first obtained by Einstein; it is:

kT

D = 6nnr

23 joules/

Here k is Boltzmann's constant, 1.38 x 10—
deg Kelvin, T is the temperature in degrees Kelvin,

n is the viscosity in newton seconds per square meter,
and r is the radius in meters. (Note that in order to

determine the diffusion coefficient in m. k. 5. units

viscosity can not be given in poise units.) Readers

121

interested in the actual derivation of the expression
for the diffusion coefficient are referred to: Physical

Chemistry, by F. Daniels and R. A. Alberty.

 

One important consequence of the above equation
should be considered here; recalling that the mass
of a spherical particle is proportional to the cube of
its radius, or that the radius of a uniform Spherical
particle is inversely proportional to the cube root of
its mass we see that the diffusion coefficient for solutes
in liquids is inversely proportional to the cube root
of the solute particle mass. This, of course, assumes
that the particles are spherical, which in fact
is nearly so for many. The significance of this relation
of the diffusion coefficient to particle mass is demon—
strated by the fact that solute molecules of vastly
differing masses exhibit very nearly identical diffusion
coefficients. The table below by Dr. James Parks should

verify this fact.

Glycine 75 95 x 10’3 MZ/Sec.
Cytochrome C 1.3 x 104 10 x 10.3 "
Hemaglobin 6.8 x 104 6.2 x 10‘3 u
Urease 4.8 x 105 3.5 x 10’3 a
Southern Bean Mosaic Virus 6.0 x 106 1.34 x 10-3 "

8 4

Bacteriophage T 2.0 x 10 3 x 10- u

2

122

At this point the reader is cautioned that the
relationship, Dal/ml/Z, applies only to diffusion in
liquids. For gaseous diffusion the diffusion coefficient
is inversely proportional to the square root of the
mass of the diffusing particles, i.e., Dd 1/ml/2.

We now come to the topic of osmosis. Diffusion
and osmosis may well be the two most important life
supporting processes; it is by diffusion and osmosis
that food is ultimately absorbed by organisms. Osmotic
pressure (see below) plays a major role in the turgor of
plants. Plant root cells are separated from their
environment by a semi—permeable membrane and a rigid
cell wall. Exterior to the plant root the osmotic pressure
is lower than it is within the root. Hence, due to the
inelasticity of its epidermis, a given root maintains
its structural rigidity. Application of commercial
fertilizers in high concentration near the roots of
plants may reverse the osmotic pressure balance between
the root and the soil, and a corresponding limpness of
the plant may occur.

"Good Ole Kentucky Cured" hams also provide an
illustration of osmosis. The hams are actually preserved
due to difference in osmotic pressure across the cell
membranes of the ham. Corresponding to this pressure
difference is a decrease in the water content of the ham

and thus its preservation.

123

In order to understand osmosis consider the

figure below:

 

 

 

 

W
\

 

Here we have a cylinder C closed off by a membrane M
made perhaps of an animal bladder. The cylinder contains
a solution of salt, sugar, or some other easily soluble
substance, and the beaker into which the cylinder extends
is filled with pure water. At the outset the level of
the solution in the cylinder is adjusted to coincide

with the level of the surrounding water, but, in time

the solution in the cylinder rises to a definite height
above the water level as shown. This rise in the level
of the solution can be shown to be due to the water

passing from the beaker through the membrane into the

124

cylinder. That the solute in the cylinder barely passes
through the membrane into the beaker can be demonstrated
by chemically testing the contents of the beaker. The
membrane is thus said to be semipermeable. The pressure
required to lift the solution to the height h is called
the final osmotic pressure of the solution. This pressure
depends on the final concentration and temperature of

the solution, and in fact for dilute solutions it is equal
to the pressure which the dissolved substance would

exert if it were present as a gas in the volume occupied
by the solution. This fact is called Van't Hoff‘s rule.

It may be expressed as:
P V = n R T

Where in MKS units P is the osmotic pressure in newtons
per square meter, V is the volume in cubic meters, n
is the number of moles of the solute present, T is the
temperature in degrees Kelvin, and R is the universal
gas constant 8.31 Joules per mole-degree.

Actually, the final osmotic pressure of a solution
is the pressure at which there is no further increase
in the volume of a solution due to the influx of solvent
through the membrane. At this point an equilibrium is
set up where the amount of solvent entering the solution
exactly equals the amount of solvent leaving the solution;

prior to this point we may consider that there is only

125

solvent entering the solution, or, that the difference
between the influx of solvent and the efflux of solvent
is a positive value. At final osmotic pressure the
exchange of solvent across the membrane is zero. At
any time prior to reaching this final steady state the
osmotic pressure of the solution is less than the final
pressure and depends on the temperature and the con—
centration (higher) of the solute. For a detailed
discussion of this the reader is referred to the text:

Physical Chemistry, 2nd Edition, by Daniels and Alberty

 

(pp. 183 - 187).

By extending hair like appendages mosquito larvae
suspend themselves from the surfaces of water pools;
however, when the pools are sprayed with oil the mosquito
larvae sink and drown. Large water beetles are commonly
seen running over the surfaces of ponds, lakes, and
streams and yet these same beetles, when dead, tend to
sink when immersed in water. A significant number of
human babies (about 25,000) die in the United States
each year shortly after birth due to collapsed lungs,
and in recent years a number of patients, having under—
gone surgery with the aid of artificial heart and lung
machines, succumb to lung failure following the operation.
Each of these phenomena illustrate an important property

of liquid surfaces, surface tension.

126

Surface tension may be understood only by con-
sidering the composition of liquids. The freezing of
a liquid produces crystals which can be demonstrated
by x—ray techniques to consist of particles arranged in
orderly ways. It is reasonable to assume that these
particles are also the fundamental material of which
the unfrozen liquid is composed. Thus we may surmise
that the distinction between solid and liquid is that
while in the liquid state the particles (molecules
or atoms) are not held in rigid positions, but rather
that they are free to move amongst themselves whereas
in the solid crystal the particles.are each assigned
Specific sites.

Now, if one considers the liquid particles to
be exerting mutually attractive forces on each other
then it is easy to see that they would be pulled
together so as to occupy the least possible volume.
That this is in fact the case is demonstrated by liquid
drops which tend to be spherical. A sphere occupies the
least volume for a given surface area of all geometrical
forms.

Given that molecules of a liquid do exert
mutually attractive forces on each other, it is also
easy to see that the molecules lying at the surface

of a liquid are tightly bound to the liquid by these

127

cohesive attractive forces. This attraction compares
closely to that of objects lying on the Earth‘s surface
in which case they are held in position by the mutual
attraction of the Earth for them, or by their attraction
for the Earth. (The Earth weighs very little on the
surface of a pumpkin!) Thus_it is that the attraction
of liquid molecules one for another accounts for surface
tension. Molecules at the surface of a liquid resist
being separated and thus are able to support objects
more dense than the liquid itself. This phenomenon
may also be thought of in terms of potential energy;
the liquid molecules tend to arrange themselves such
as to reduce their potential energy to a minimum.
White blood corpuscles have as a primary function the
removal of dead particles and bacteria from the blood.
When a white corpuscle (lymphocyte) encounters a smaller
foreign particle the lymphocyte surrounds and ingests
the alien particle. This process can be shown to be
one of surface tension in which the lymphocyte material
actually ingests the foreign object by reducing their
mutual surface area and thereby their potential energy.
Another illustration of the biological importance
of surface tension is its contribution to the elasticity
of lungs. The lungs provide the largest surface of
the human body which comes into contact with the outside

environment. The total lung surface area of normal adults

128

is roughly equivalent to that of a tennis court.
This enormous surface area is due to the presence of
hundreds of millions of tiny air pockets called
alveoli. These alveoli expand and contract with
each breath and it is through them that oxygen is
absorbed into the blood. The surface tension of
the fluid which coats the individual alveolus has
been shown to account for most of the elasticity of
the lungs. By way of contrast to elasticity as pre—
viously discussed it must be mentioned here that
surface tension forces do not depend on the degree
to which a surface is deformed. It will be recalled
that materials which are truely elastic obey Hooke's
Law, which of course, expresses the restoring force
of an elastic material in terms of its deformation.
However the surface tension of a liquid can
be altered by changing the concentration of surface
active substances which may be added to it. Soaps
and synthetic detergents are common examples of sub—
stances which lower the surface tension of water. The
surface tension of the fluid which coats the alveoli
in mammalian lungs is altered by changing the con-
centration of a kind of detergent secreted by cells
proximal to the alveoli. This is done in a most

peculiar way which enables the lungs to perform their

129

vital functions. Inelasticity of infant lungs corres-
ponding to an invariant concentration of the lung fluid
detergent is associated with infant death due to respira-
tory failure. For detailed discussion of this phenomenon
readers are referred to studies by Charles Clifford Macklin
of the University of Western Ontario. We will return
to the topic only briefly at the close of this writing.

Up to this point our discussion has been
qualitatively descriptive; now we must quantitatively

define surface tension. Consider the figure sketched

W '
I/// 9F? 3.
K - "

/

below:

 

N
2°

 

 

 

 

/////////A

The figure portrays a U-shaped wire frame on which a
movable Slide wire is mounted. Within the region
bounded by the slide wire and the U is a liquid film,
perhaps a soap film. This film of course has two
surfaces, each of which joins the slide wire along
its length 1. Now, applyfixya static force F to the
slide wire is opposed by an equal force due to the

film. This opposing force is proportional to twice

130

the length of the slide since the slide is pulled upon
by both surfaces of the film along its length. Hence,

we may write the proportion:
Fa 2 '1

and by injecting the proportionality constant Y we have:
P = 2yl

y is the surface tension of the film. In words we may
thus define the surface tension as the ratio of the surface
force perpendicular to the length along which it acts.
Commonlyysurface tension is measured in units of dynes
per centimeter, dynes/cm. At body temperature the surface
tension of pure water is about 70 dynes/cm, that of blood
plasma is about 50 dynes/cm, and lung fluid varies from
a maximum of about 40 to a minimum of about 2 dynes/cm.

An alternate way of defining surface tension
is in terms of the work required to expand the surface.
Suppose that we move the slide wire in the figure above
a distance X perpendicular to its length 1. In so doing
we increase the total film surface by an amount given
by the product 2°l-X. The work done is simply
the product of the force F and the distance the slide
wire is moved X. Dividing this work by the increase in

area yields:

131

work = F°X
increase in area 2°l-X 2'1

 

This ratio, F/Z-l is our previous definition of surface
tension y. Thus, now we have a new way of defining
surface tension:
Surface tension is the work required per
unit area to increase the area of the
surface.
Here caution must be envoked not to equate the work
required to expand the surface with the increase in
surface energy. As the surface is expanded.energy is
lost corresponding to a decrease in the temperature
of the liquid. FOr a liquid in contact with its own
vapor the surface tension depends only on the composition
of the liquid and the temperature. To illustrate the

correspondence of surface tension and temperature

several data for water are listed here:

Surface Tension (dynes/cm) Temperature (°C)
75.6 0
72.8 20
66.2 60
58.9 100

One further point should be made concerning the new
definition of surface tension; from the cgs units of
work and area we see that the unit of surface tension
can also be given as ergs per cm2. Dimensionally, this

is equivalent to dynes per cm.

132

Now we can understand more about the role of
surface tension in mammalian lungs. In order for the
lungs to cyclicly expand and contract the surface tension
of the lung fluid must vary from a maximum of roughly
40 dynes/cm at full inflation to a minimum of only
several dynes/cm. This is necessary so that the lungs
may contract when filled with air and freely expand while
inhaling. The decrease in surface tension of the lung
fluid during contraction corresponds to an increase in
the concentration of the surface active detergent
secreted by the special cells mentioned earlier.

Likewise the necessary increase in surface tension of
the lung fluid on inhaling corresponds to a decrease
in the concentration of the lung detergent.

The decrease in temperature associated with
increasing surface tension is also important within
the lungs as they perform a major role in the regulation
of body temperature.

In the case of the infant respiratory distress
syndrome a deficiency of the lung detergent contributes

to the lack of elasticity necessary for breathing.

FLUID MECHANICS III

 

In this paper the reader will study two funda—
mentally important equations of fluid mechanics, the
equation of continuity and Bernoulli‘s Equation. These
equations are discussed in tenms of Specific biological
applications. After reading this paper the reader will
be expected to be able tOIvrite the equation of continuity
in the form it is given below, and, to be able to write
Bernoulli‘s Equation. He should also be able to discuss
each equation in terms of its physical significance, i.e.,
the reader Should be able to explain the limitations of
each equation as it applies to fluid motion and to account
physically for the terms in each equation. The instructor
may also assign calculations and inference deduction type
problems based on the equation of continuity and
Bernoulli's Equation; thus, special attention should be
given to the sample problems given in this writing. It is
recommended that the reader spend some time speculating
on applications of these equations outside of the specific
areas discussed here.

Rockets are prOpelled by the ejection of mass.

The propelling force, by Newton‘s Law, is the reaction
force to the exerted on the ejected mass by the rocket.
The velocity of a rocket can be determined by applying

the principle of conservation of momentum and derivations

133

134

of simplified equations of motion for rockets are commonly
given in textbooks and lectures on general physics. In
nature the squid is an organism which prOpelS itself by
ejecting mass (water), thus, in a way the squid itself may
be thought of as a living rocket. Deriving the equations
of motion for a squid would be a very difficult task if,

in fact, it could be done. However, we can study one

basic equation of fluid motion which is directly applicable
to the squid‘s motion. This equation is commonly known

as the equation of continuity.

 

Although the equation of continuity may be written
in several ways, each of which has vast applicability, we
will consider this important equation in only a limited and
Simplified form. For our purposes we will consider the
equation of continuity as simply a mathematical statement
of the fact that the rate at which mass flows into a
container must equal the rate at which mass flows from
the container if the net mass of the container remains
unchanged. Before actually writing the equation of
continuity, let us consider a part of the squid, the
funnel, as the container to which we will apply the
equation.

The funnel of the squid is shown in the diagram
on the next page. Immediately prior to executing escape

motion the squid fills its mantle cavity with water which

135

enters the cavity just inside the collar. When the mantle
contracts this water is tightly sealed inside and forced
into the funnel. The rapid escape motion of the squid

is attained by the ejection of this water through the
orifice of the funnel.

The motion of the squid attained by the discharge
of water through the funnel is like a torpedo, the head
of the squid and its enclosed funnel trails behind the
main body. It is important to notice that the funnel
itself varies in cross sectional area and is constricted
toward the opening. Water ejected by the squid, therefore,
passes through progressively smaller cross sectional areas
of the funnel as it is discharged. (See following diagram).

Now water is nearly incompressible. This suggests
that the rate of mass transfer of water (grams per second,
etc.) passing through a rigid closed tube must be the same
through all cross sections. In the squid the mass of
water per second flowing through the progressively
smaller cross sections of the funnel is identical for
each cross section.

This fact, that the rate of mass transfer of an
incompressible fluid through any cross-sectional area of
a closed rigid tube is expressed by the equation of
continuity. By letting p designate the mass density (mass

per unit volume, m/V) of an incompressible fluid, and v,

 

136

137

represent the fluid's average velocity (length travelled
per unit time, l/t), where A represents the crOSSesectional
area through which the fluid passes we note that the
product (pAav) is the rate at which the fluid mass passes
through any section of the tube of length l.

p°A°v = m/V ;A- l/t a m/V ~V/t =m/t
It should be noted that here the product of the cross
sectional area A, and its length l, is V the volume of
our chunk of fluid having mass m, And, because as we
have indicated, the rate at which fluid mass paSses through
any cross section (m/t) is the same for all cross sections,
we can write:

pAl-vl = pA2~v2
This expression is the more common form of the previous

equation. It is the equation of continuity, where Al is

 

the area of any cross section through which fluid flows
at velocity v1, and A2 is another cross section of the same

tube through which the fluid flows at velocity v The

2.

areas Al and A are represented in our figure of the squid.

2

For the squid the equation of continuity eXpresseS
the fact that the animal can eject water at a high velocity
v2 by slowly constricting its mantle cavity and inducing
water to flow through A1 at velocity v1.

In general in accord with the equation of continuity

the velocity of an incompressible fluid flowing in a rigid

138

tube increases at constrictions and decreases in expanded
regions of the tube. This fact is commonly observed when
fluid passes through any funnel. AS with all equations

of physics, the equation of continuity can provide meaning"
ful infbrmation only when a consistent set of units is
assigned to its terms. For example, if density is given

in grams per cm3 the velocity of the fluid Should be in

cm per second and the cross sections should be measured in
square centimeters.

Here an example calculation may illustrate the
usefulness of the equation of continuity. Suppose that
the diameter of the orifice of a certain squid's funnel
is 1 cm. and the diameter of the funnel internal to the
squid where water is flowing outward at 10 cm./sec. is
1.5 cm. what is the average velocity of the water as it
leaves the orifice? This problem may be solved by direct
substitution into the equation of continuity.

pAl vl = pA2 v2

2

l-(l.5/2)2cm.2 -(10 cm/sec) = l-(l/2)2cm -(v

2)
Thus, the velocity of efflux of the water is more than
doubled by reducing the diameter of this squid‘s funnel by
one-third.

At this point, before we consider the development

of Bernoulli's Equation, we must direct our attention to

considering a topic which is of crucial importance in the

139

approach we will take in understanding Bernoulli's Equation.
Let us consider a cylinder which is filled with a fluid
which is very slightly compressible. Imagine that this
cylinder contains a piston which has a cross sectional

area A which seals off the cylinder.
b

I " 11F
\6%a%;~76Zé?§/ v-' A8
Jun.“ /// “..,r"' _—

 

“ll||||l|‘

FLUID

 

 

 

Applying external force to the piston is evidenced
by a corresponding decrease in the volume of the fluid.
Under the influence of additional externally applied force
the piston moves to compress the fluid until the reaction
force of the compressed fluid just equals compressing
force. If we assume that the compression is only Slight
and can be measured by the small displacement Al the piston
moves then we can equate the work done on the fluid by the
piston with the product of the applied force F and the
distance moved Al. Now pressure is force per unit area.

Hence we can write:

140

P = F/A
and multiplying both the numerator and denominator of this
fraction by l we obtain:

P = F A l/AAl
This, by the equivalence of work and energy can simply be
rewritten as:

P = E/V
where E is the energy which the fluid obtains due to the
work done on it by the piston, and V is the volume equal
to the product of the crOSSesectional area A of the cylinder
through which the piston has moved the distance Al. From
this we see that pressure may be thought of as pressure
energy, i.e. pressure energy per unit volume. For detailed
presentations of this concept the reader may wish to refer
to any standard text on thermodynamics.

Now let us consider a horizontal tube in which a

unit volume (1 cm3) of liquid at position a has pressure
energy P. If the liquid is flowing in the direction shown

in the figure below and has velocity v at position 1, then

1
by the equation of continuity a unit volume will have
greater velocity v2 at position 11 where the tube is
constricted. Recalling that the kinetic energy of a body
of mass m (in this case the unit volume of liquid) is given

by the expression K.E = 1/2 m v2, where v is the velocity,

we see that the unit volume at 11 has greater kinetic energy

141

than the unit volume at 1. This increase in kinetic
energy is obtained at the eXpense of pressure energy.
That is as the unit volume of liquid increases it velocity
it pressure decreases. For the case where the flow is
horizontal we thus may write:

E = p + 1/2 (vaI
where E is the total mechanical energy of the unit volume
of liquid, is the density (mass per unit volume) of the
liquid, and v is its velocity.

This eXpression for total mechanical energy is not
complete, however; it does not include the gravitational
potential energy of the unit volume of liquid. This omission
is, of course, alright if in fact there is no change in
gravitational potential energy of the fluid as it flows
through the tube; this is the case for a horizontal tube.
However, we may assign a height hl to the segment of the
tube at position 1, in the second figure below, and a
height h2 to the segment at position 11. With these heights
in mind we can now write the gravitation potential energies

at the two positions as pgh and pgh2. Thus, by including

1
the gravitational potential energy of the unit volume of
fluid we can write:

_ 2 _ 2
E — Pl + 1/2 (pvl) + pghl - P2 + 1/q (pvz) + pgh2

This is Bernoulli's Equation. It is a statement of the

 

principle of conservation of energy.

142

 

 

 

 

 

 

 

Bernoulli‘s Equation provides the basis for understanding
the so called Bernoulli Effect. This effect is simply that
an in crease in the velocity of a fluid is accompanied by

a decrease in pressure. In order to understand this effect
let us consider a horizontal tube such as in the first
figure on the preceding page. Since the tube is horizontal,
and thus the gravitational terms on both side of the

equation are equal, we can write:

2 _ 2
Pl + 1/2 pvl - P2 + l/q pv2

or

2

— 2—
P — P + 1/2 p(vl v2)

2 l
where the subscripts l and 2 correspond to the regions 1
and 11 in the figure. From the equation of continuity we
know that V2>Vl’ thus, (vi — v3) is a negative number.
This implies that P2 is less than P1' or that for increased

velocity there is an accompanying decrease in pressure.

143

This fact has many important consequences. The
common eXperience of difficulty in breathing in a strong
wind is due to the fact that the flow of air beneath the
nostrils is accompanied by a decrease in pressure which
makes breathing difficult. The gliding flight of birds
and the lift of airplane wings is also largely due to the
Bernoulli Effect. In both cases air flows more rapidly
relative to the wing surface on the upper Side. The
corresponding pressure difference at the wing surfaces
accounts for the upward lift force. The curved flight of
a Spinning baseball is also due to the same principle.

As the ball spins the velocity of the air relative to the
ball is increased on one side and decreased on the other.
The force due to the pressure difference across the ball
accounts for the ball‘s curved flight. In order to make
this clear perhaps the reader should sketch a spinning

ball in flight and analyze the air velocity to the right

and left of the spinning ball.

BIBLIOGRAPHY

144

BIBLIOGRAPHY

Alexander, R. McNeill. Animal Mechanics. Seattle, Wash.:
University of Washington Press, 1968.

 

Bachman, Charles H. Physics-Understanding Our Physical
Environment. Croton on Hudson, New York.: Bogden
and Quigley, 1970.

 

Baker, Adolph. "Physics and Antiphysics", Physics Today
(March, 1970), p.35.

 

Bergel, D.H. "The Static Elastic Properties of the Arterial
Wall", Journal of Physiology. Vol. 156, 1961.

 

Bernard, Claude. Introduction to the Study of Experimental
Medicine. 1865.

 

Bluh, Otto. "Physics in Premedical Education", American
Journal of Physics. Vol. 17, 1949. p. 156.

 

Burns, Desmond M. and MacDonald, Simon G. Physics for
Biology and Pre-Medical Students. Reading, Mass.:
Addison Wesley Publishing Company, 1970.

 

 

Campbell, Donald T. and Stanley, Julian C. Experimental
and Quasi-Experimental Designs for Research.
Chicago, Illinois: Rand McNally & Company, 1966.

 

 

Cronbach, Lee J. Essentials of Psychological Testing,
2nd Edition, New York: Harper and Row, 1960.

 

Daniels, Farrington and Alberty, Robert A. Physical Chemistry

 

2nd Edition, New York: John Wiley & Sons, 1961.

Dyson, Freeman. "The Future of Physics", Physics Today,
(September, 1970): P. 23.

 

Edgington, J.A. and Sherman, H.J. Physical Science for
Biologists. London, England: Hutchinson University
Library, 1971.

 

Edwards, A.L. Statistical Methods for the Behavioral
Sciences. New York: Rinehart and Winston, 1960.

145

Elliott, D.H. "Structure and Function of Mammalism Tendon",
Biological Review. Vol. 40, 1965.

 

Evans, F. Gaynor. Mechanical Properties of Bone. Spring—
field, Illinois: C.C. Thomas, 1973.

 

Ferris, Frederick L. "Testing for Physics Achievement",
Achievement Testing in Physics. New York: American
Institute of Physics, 1960. p. 22.

 

Ferry, J.D. Viscoelastic Properties of Polymers. New York:
John Wiley and Sons, 1961.

 

Feynman, Richard P.; Leighton, Robert B.; and Sands,Mathew.
The Feynman Lectures on Physics. Vol. I, Reading,
Mass.: Addison Wesley Publishing Company, 1963.

 

Finn, Jeremy D. A Generalized Univariate and Multivariate
Analysis of Variance, Covariance and Regression
Program. New York: State University of New York at
Buffalo, 1966.

 

 

Fowler, John M. and West, Richard. "What Our Left Hand Has
Been Doing", Physics Today. (March, 1970), p. 24.

 

Gardner, Ernest. Fundamentals of Neurology. Philadelphia,
Pennsylvania: W.B. Saunders Company, 1968.

 

Giancoli, Douglas C. "A Course in Biophysics: An Inte-
gration of Physics, Chemistry and Biology", American
Journal of Physics. (July, 1971), p. 739.

 

Goldberger, Marvin. "How Physicists Can Contribute",
Physics Today. (December, 1970), p. 26.

 

Handler, Philip. Biology and The Future of Man., New York:
Oxford University Press, 1970.

 

Harkness, R.D. "Biological Functions of Collagen",
Biological Review. Vol. 36, 1961.

 

Harvey, E. Newton. "Properties of Protoplasm", The Journal
of Applied Physics. Vol. 9, p. 68.

 

Hodgman, C.D., ed. Handbook of Chemistry and Physics.
Cleveland, Ohio: Chemical Rubber Company, 1965.

Hoyer, B.H.; McCarthy, B.J.; and Bolton, E.T. "A Molecular
Approach in the Systematics of Higher Organisms",
Science. Vol. 144 (1964), p. 959.

146

Jaki, Stanley L. The Relevance of Physics. Chicago, Ill.:
The University of Chicago Press, 1966.

Jensen, M. and Weis—Fogh, T. "Biology and Physics of Locust
Flight V. Strength and Elasticity of Locust Cuticle"
Philosophical Transactions. 1962.

 

Kelly, R.E. and Rice, R.V. "Abductin: A Rubber—like Protein
from the Internal Triangular Hinge Ligament of Pecten"
Science. Vol. 155, 1967.

Koch, H. William. "An Age of Change", Physics Today.
(January, 1970).

 

Kolin, Alexander. Physics, Its Laws, Ideas and Methods.
New York: McGraw Hill Book Company, 1955.

 

Lagemann, Robert. "Physics and the Premedical Student",
American Journal of Physics. Vol. 26, 1958, p.301.

 

Lavoiser, Antoine and Laplace, Pierre. Memoir on Heat.
Paris: The Academy of Science, 1780.

 

Loofbourow, John R. "Biophysics", American Journal of
Physics. Vol. 15, 1947. p. 21.

 

Medewar. "Zoology", Scientific Thought in the Twentieth
Century. London: Watts, 1951, p. 188.

National Research Council. Physics in Perspective. Vol. 1

 

Washington, D.C.: National Academy of Sciences,
1972.
Pickar, Arnold D. "Core Course for Science Majors Combining

Material from Physics, Chemistry and Biology",
American Journal of Physics. (February, 1960),
p. 260.

 

Richardson, I.W. and Neergaard, E.B. Physics for Biology
and Medicine. New York: John Wiley and Sons, 1970.

 

Shaw, Marvin E. and Wright, Jack M. "The Revised Mathe-
matics Attitude Scale." Scales for the Measurement
of Attitudes. Ed. Aiken and Dreger. New York:
McGraw Hill Book Company, 1967.

 

 

Smith, J.W. and Walmsley, R. "Factors Affecting The
Elasticity of Bone," Journal of Anatomy. Vol. 93,
1959.

147

Stacy, Ralph W.; Williams, David T.; Worden, Ralph B.;

and McMorris, Rex 0. ‘Essentials of Biological
and Medical Physics. New York: McGraw Hill
Book Company, 1955.

 

Stewart, Peter A. "Physics and the Medical Student,"

Tilley,

Weis-Fogh, T.

American Journal of Physics. Vol. 26, 1958.
p. 304.

Donald E. and Thumm, Walter. College Physics,
A Text with Applications to the Life Sciences.
Menlo Park, California: Cummings Publishing
Company, 1971.

of Resilin, A rubber-like Protein" Journal of
Molecular Biology. Vol. I, 1961.

148

"Molecular Interpretation of the Elasticity

ER

”1111111111111!WI
3 1293 030

I "111111
15

LIBR

IIHI

4271

ARIES