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Section 17.6

<html><body>Section 17.6 Laws of Physics and Life

is one of the atoms in the amino acids that compose the protein molecules. In nature, nitrogen is composed primarily of the isotope 14N. Only 0.36% of natural nitrogen is in the form of the nonradioactive isotope 15N. Ordinarily the amino acids reﬂect the natural composition of nitrogen.

It is possible to synthesize amino acids in a laboratory. If the synthesis is

done with pure 15N, the amino acids are distinctly marked. The amino acid glycine produced in this way is introduced into the body of a subject where it is incorporated into the hemoglobin of the blood. Periodic sampling of the blood measures the number of blood cells containing the originally introduced glycine. Such experiments have shown that the average lifetime of a red blood cell is about four months.

Radioactive isotopes can be traced more easily and in smaller quanti

ties than the isotopes that are not radioactive. Therefore, in reactions with elements that have radioactive isotopes, radioactive tracer techniques are preferred. Since the 1950s, when radioactive isotopes ﬁrst became widely available, hundreds of important experiments have been conducted in this ﬁeld.

An example of this technique is the use of radioactive phosphorus in the

study of nucleic acids. The element phosphorus is an important component of the nucleic acids DNA and RNA. Naturally occurring phosphorus is all in the form 31P, and, of course, this is the isotope normally found in the nucleic acids. However, as discussed earlier, by bombarding sulphur 32 with neutrons, it is possible to produce the radioactive phosphorus 32P which has a half-life of 14.3 days. If the 32P isotope is introduced into the cell, the nucleic acids synthesized in the cell incorporate this isotope into their structure. The nucleic acids are then removed from the cell and their radioactivity is measured. From these measurements it is possible to calculate the rate at which nucleic acids are manufactured by the cell. These measurements, among others, provided evidence for the roles of DNA and RNA in cell functions.

Radioactive tracers have been useful also in clinical measurements. In

one technique, the radioactive isotope of chromium is used to detect internal hemorrhage. This isotope is taken up by the blood cells, which then become radioactive. The radioactivity is, of course, kept well below the danger level. If the circulation is normal, the radioactivity is distributed uniformly throughout the body. A pronounced increase in radioactivity in some region indicates a hemorrhage at that point. 17.6 Laws of Physics and Life

We have discussed in this book many phenomena in the life sciences that are clearly explained by the theories of physics. Now we come to the most fundamental question: Can physics explain life itself? In other words, if we

Chapter 17 Nuclear Physics

put together the necessary combination of atoms, at each step following the known laws of physics, do we inevitably end up with a living organism, or must we invoke some new principles outside the realm of current physics in order to explain the occurrence of life? This is a very old question which still cannot be answered with certainty. But it can be clariﬁed.

Quantum mechanics, which is the fundamental theory of modern atomic

physics, has been very successful in describing the properties of atoms and the interaction of atoms with each other. Starting with a single proton and one electron, the theory shows that their interaction leads to the hydrogen atom with its unique conﬁguration and properties. The quantum mechanical calculations for larger atoms are more complicated. In fact, so far a complete calculation has been performed only for the hydrogen atom. The properties of heavier atoms must be computed using various approximation techniques. Yet there is little doubt that quantum mechanics describes all the properties of atoms from the lightest to the heaviest. The experimental evidence gathered over the past 100 years fully conﬁrms this view.

The interactions between atoms, which result in the formation of molecules,

are likewise in the domain of quantum mechanics. Here again exact solutions of the quantum mechanical equations have been obtained only for the simplest molecule, H2. Still it is evident that all the rules for both organic and inorganic chemistry follow from the principles of quantum mechanics. Even though our present numerical techniques cannot cope with the enormous calculations required to predict the exact conﬁguration of a complex molecule, the concepts developed in physics and chemistry are applicable. The strengths of the interatomic bonds and the orientations of the atoms within the molecules are all in accord with the theory. This is true even for the largest organic molecules such as the proteins and DNA.

Past this point, however, we encounter a new level of organization: the cell.

The organic molecules, which are in themselves highly complex, combine to form cells, which in turn are combined to form larger living organisms, which possess all the amazing properties of life. These organisms take nourishment from the environment, grow, reproduce, and at some level begin to govern their own actions. Here it is no longer obvious that the theories governing the interaction of atoms lead directly to these functions that characterize life. We are now in the realm of speculations.

The phenomena associated with life show such remarkable organization

and planning that we may be tempted to suggest that perhaps some new undiscovered law governs the behavior of organic molecules that come together to form life. Yet there is no evidence for any special laws operating within living systems. So far, on all levels of examination, the observed phenomena associated with life obey the well-known laws of physics. This does not mean that the existence of life follows from the basic principles of physics, but it may. In fact the large organic molecules inside cells are suﬃciently complex to contain

within their structures the information necessary to guide in a predetermined way the activities associated with life. Some of these codes contained in the speciﬁc groupings of atoms within the molecules have now been unraveled. Because of these speciﬁc structures, a given molecule always participates in a well-deﬁned activity within the cell. It is very likely that all the complex functions of cells and of cell aggregates are simply the collective result of the enormously large number of predetermined but basically well-understood chemical reactions.

This still leaves the most important question unanswered: What are the

forces and the principles that initially cause the atoms to assemble into coded molecules which then ultimately lead to life. The answer here is probably again within the scope of our existing theories of matter.

In 1951, S. L. Miller simulated in his laboratory the type of conditions that

may have existed perhaps 3.5 billion years ago in the atmosphere of the primordial Earth. He circulated a mixture of water, methane, ammonia, and hydrogen through an electric discharge. The discharge simulated the energy sources that were then available from the sun, lightning, and radioactivity. After about one week Miller found that the chemical activities in the mixture produced organic molecules including some of the simple amino acids, which are the building blocks of proteins. Since then, hundreds of other organic molecules have been synthesized under similar conditions. Many of them resemble the components of the important large molecules found in cells. It is thus plausible that in the primordial oceans, rich in organic molecules produced by the prevailing chemical reactions, life began. A number of smaller organic molecules combined accidentally to form a large self-replicating molecule such as DNA. These, in turn, combined into organized aggregates and ﬁnally into living cells.

Although the probability for the spontaneous occurrence of such events is

small, the time span of evolution is probably long enough to make this scenario plausible. If that is indeed the case, the current laws of physics can explain all of life. At the present state of knowledge about life processes, the completeness of the descriptions provided by physics cannot be proved. The principles of physics have certainly explained many phenomena, but mysteries remain. At present, however, there seems to be no need to invoke any new laws.

EXERCISES 17-1. Describe the basic principles of magnetic resonance imaging. 17-2. What is your (considered) opinion of food preservation by radiation? 17-3. Through a literature search describe the most recent use of fMRI. 17-4. Discuss some of the most notable attributes of living systems that dis

tinguish them from inanimate ones.

Appendix A

Basic Concepts in Mechanics

In this section, we will deﬁne some of the fundamental concepts in mechanics. We assume that the reader is familiar with these concepts and that here a simple summary will be suﬃcient. A detailed discussion can be found in basic physics texts, some of which are listed in the Bibliography. A.1 Speed and Velocity

Velocity is deﬁned as the rate of change of position with respect to time. Both magnitude and direction are necessary to specify velocity. Velocity is, therefore, a vector quantity. The magnitude of the velocity is called speed. In the special case when the velocity of an object is constant, the distance s traversed in time t is given by s vt

(A.1)

In this case, velocity can be expressed as v s

(A.2) t

If the velocity changes along the path, the expression s/t yields the average velocity. 272

Section A.2 Acceleration A.2 Acceleration

If the velocity of an object along its path changes from point to point, its motion is said to be accelerated (or decelerated). Acceleration is deﬁned as the rate of change in velocity with respect to time. In the special case of uniform acceleration, the ﬁnal velocity v of an object that has been accelerated for a time t is v v0 + at

(A.3)

Here v0 is the initial velocity of the object, and a is the acceleration.1 Acceleration can, therefore, be expressed as a v − v0

(A.4) t

In the case of uniform acceleration, a number of useful relations can be

simply derived. The average velocity during the interval t is vav v + v0

(A.5)

2

The distance traversed during this time is s vavt

(A.6)

Using Eqs. A.4 and A.5, we obtain s v0t + at 2

(A.7)

2

By substituting t (v − v0)/a (from Eq. A.4) into Eq. A.7, we obtain v2 v2 + 2as

(A.8)

0

1Both velocity and acceleration may vary along the path. In general, velocity is deﬁned as the

time derivative of the distance along the path of the object; that is, s v lim

ds dt t → 0 t

Acceleration is deﬁned as the time derivative of the velocity along the path; that is,

ds a dv d

d2s dt dt dt dt 2

Appendix A Basic Concepts in Mechanics A.3 Force

Force is a push or a pull exerted on a body which tends to change the state of motion of the body. A.4 Pressure

Pressure is the force applied to a unit area. A.5 Mass

We have stated that a force applied to a body tends to change its state of motion. All bodies have the property of resisting change in their motion. Mass is a quantitative measure of inertia or the resistance to a change in motion. A.6 Weight

Every mass exerts an attractive force on every other mass; this attraction is called the gravitational force. The weight of a body is the force exerted on the body by the mass of the Earth. The weight of a body is directly proportional to its mass. Weight being a force is a vector, and it points vertically down in the direction of a suspended plumb line.

Mass and weight are related but distinct properties of an object. If a body

were isolated from all other bodies, it would have no weight, but it would still have mass. A.7 Linear Momentum

Linear momentum of a body is the product of its mass and velocity; that is,

Linear momentum mv

(A.9) A.8 Newton’s Laws of Motion

The foundations of mechanics are Newton’s three laws of motion. The laws are based on observation, and they cannot be derived from more basic principles. These laws can be stated as follows: First Law: A body remains at rest or in a state of uniform motion in a straight line unless it is acted on by an applied force.

Section A.9 Conservation of Linear Momentum Second Law: The time rate of change of the linear momentum of a body is equal to the force F applied to it.

Except at very high velocities, where relativistic eﬀects must be considered, the second law can be expressed mathematically in terms of the mass m and acceleration a of the object as2 F ma

(A.10)

This is one of the most commonly used equations in mechanics. It shows that if the applied force and the mass of the object are known, the acceleration can be calculated. When the acceleration is known, the velocity of the object and the distance traveled can be computed from the previously given equations.

The Earth’s gravitational force, like all other forces, causes an acceleration. By observing the motion of freely falling bodies, this acceleration has been measured. Near the surface of the Earth, it is approximately 9.8 m/sec2. Because gravitational acceleration is frequently used in computations, it has been given a special symbol g. Therefore, the gravitational force on an object with mass m is Fgravity mg

(A.11)

This is, of course, also the weight of the object. Third Law: For every action, there is an equal and opposite reaction. This

law implies that when two bodies A and B interact so that A exerts a force on B, a force of the same magnitude but opposite in direction is exerted by B on A. A number of illustrations of the third law are given in the text. A.9 Conservation of Linear Momentum

It follows from Newton’s laws that the total linear momentum of a system of objects remains unchanged unless acted on by an outside force.

2The second law can be expressed mathematically in terms of the time derivative of

momentum: that is,

mv(t + t) − mv(t) dv

Force

d (mv) m ma t → 0 t dt dt <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-295_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-295_2.png"/>

Appendix A Basic Concepts in Mechanics FIGURE A.1 The radian. A.10 Radian

In the analysis of rotational motion, it is convenient to measure angles in a unit called a radian. With reference to Fig. A.1, the angle in radian units is deﬁned as θ s

(A.12) r

where s is the length of the circular arc and r is the radius of rotation. In a full circle, the arc length is the circumference 2πr. Therefore in radian units the angle in a full circle is θ 2πr 2π rad r

Hence,

1 rad 360◦ 57.3◦

2π A.11 Angular Velocity

The angular velocity ω is the angular displacement per unit time; that is, if a body rotates through an angle θ (in radians) in a time t, the angular velocity is ω θ (rad/sec)

(A.13) t

Section A.14 Equations for Angular Momentum A.12 Angular Acceleration

Angular acceleration α is the time rate of change of angular velocity. If the initial angular velocity is ω0 and the ﬁnal angular velocity after a time t is ωf, the angular acceleration is3 ωf − ω0 α

(A.14) t A.13 Relations between Angular and Linear Motion

As an object rotates about an axis, each point in the object travels along the circumference of a circle; therefore, each point is also in linear motion. The linear distance s traversed in angular motion is s rθ

The linear velocity v of a point that is rotating at an angular velocity ω a distance r from the center of rotation is v rω

(A.15)

The direction of the vector v is at all points tangential to the path s. The linear acceleration along the path s is a rα

(A.16) A.14 Equations for Angular Momentum

The equations for angular motion are analogous to the equations for translational motion. For a body moving with a constant angular acceleration α and initial angular velocity ω0, the relationships are shown in Table A.1.

3Both angular velocity and angular acceleration may vary along the path. In general, the

instantaneous angular velocity and acceleration are deﬁned as ω dθ ; α dω d 2θ dt dt dt 2

Appendix A Basic Concepts in Mechanics TABLE A.1 Equations for Rotational Motion (angular acceleration, α constant) ω

ω +

0 αt θ

ω0t + 1αt2

2 ω2 ω2 + 2αθ

0

+ ω) ω

(ω0

av

2 A.15 Centripetal Acceleration

As an object rotates uniformly around an axis, the magnitude of the linear velocity remains constant, but the direction of the linear velocity is continuously changing. The change in velocity always points toward the center of rotation. Therefore, a rotating body is accelerated toward the center of rotation. This acceleration is called centripetal (center-seeking) acceleration. The magnitude of the centripetal acceleration is given by ac v2 ω2r

(A.17) r

where r is the radius of rotation and v is the speed tangential to the path of rotation. Because the body is accelerated toward its center of rotation, we conclude from Newton’s second law that a force pointing toward the center of rotation must act on the body. This force, called the centripetal force Fc, is given by Fc mac mv2 mω2r

(A.18) r

where m is the mass of the rotating body.

For a body to move along a curved path, a centripetal force must be applied

to it. In the absence of such a force, the body moves in a straight line, as required by Newton’s ﬁrst law. Consider, for example, an object twirled at the end of a rope. The centripetal force is applied by the rope on the object. From Newton’s third law, an equal but opposite reaction force is applied on the rope by the object. The reaction to the centripetal force is called the centrifugal force. This force is in the direction away from the center of rotation. The centripetal force, which is required to keep the body in rotation, always acts perpendicular to the direction of motion and, therefore, does no work

Section A.17 Torque TABLE A.2 Moments of Inertia of Some Simple Bodies Body Location of axis Moment of inertia

A thin rod of length l Through the center ml2/12

A thin rod of length l Through one end ml2/3

Sphere of radius r

Along a diameter

2mr2/5

Cylinder of radius r

Along axis of symmetry mr2/2

(see Eq. A.28). In the absence of friction, energy is not required to keep a body rotating at a constant angular velocity. A.16 Moment of Inertia

The moment of inertia in angular motion is analogous to mass in translational motion. The moment of inertia I of an element of mass m located a distance r from the center of rotation is I mr 2

(A.19)

In general, when an object is in angular motion, the mass elements in the

body are located at diﬀerent distances from the center of rotation. The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.

Unlike mass, which is a constant for a given body, the moment of inertia

depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus. The moments of inertia for a few objects useful for our calculations are shown in Table A.2. A.17 Torque

Torque is deﬁned as the tendency of a force to produce rotation about an axis. Torque, which is usually designated by the letter L, is given by the product of the perpendicular force and the distance d from the point of application to the axis of rotation; that is (see Fig. A.2), L F cos θ × d

(A.20)

The distance d is called the lever arm or moment arm. <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-299_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-299_2.png"/>

Appendix A Basic Concepts in Mechanics FIGURE A.2 Torque produced by a force. A.18 Newton’s Laws of Angular Motion

The laws governing angular motion are analogous to the laws of translational motion. Torque is analogous to force, and the moment of inertia is analogous to mass. First Law: A body in rotation will continue its rotation with a constant angu

lar velocity unless acted upon by an external torque. Second Law: The mathematical expression of the second law in angular

motion is analogous to Eq. A.10. It states that the torque is equal to the product of the moment of inertia and the angular acceleration; that is, L Iα

(A.21) Third Law: For every torque, there is an equal and opposite reaction torque. A.19 Angular Momentum

Angular momentum is deﬁned as

Angular momentum Iω

(A.22)

From Newton’s laws, it can be shown that angular momentum of a body is conserved if there is no unbalanced external torque acting on the body. <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-300_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-300_2.png"/>

Section A.20 Addition of Forces and Torques FIGURE A.3 The resolution of a force into its vertical and horizontal components. A.20 Addition of Forces and Torques

Any number of forces and torques can be applied simultaneously to a given object. Because forces and torques are vectors, characterized by both a magnitude and a direction, their net eﬀect on a body is obtained by vectorial addition. When it is required to obtain the total force acting on a body, it is often convenient to break up each force into mutually perpendicular components. This is illustrated for the two-dimensional case in Fig. A.3. Here we have chosen the horizontal x- and the vertical y-directions as the mutually perpendicular axes. In a more general three-dimensional case, a third axis is required for the analysis.

The two perpendicular components of the force F are Fx F cos θ

(A.23) Fy F sin θ

The magnitude of the force F is given by F F 2 x + F 2 y

(A.24)

When adding a number of forces (F1, F2, F3, . . .) the mutually perpendic

ular components of the total force FT are obtained by adding the corresponding

Appendix A Basic Concepts in Mechanics

components of each force; that is,

(FT)x (F1)x + (F2)x + (F3)x + · · ·

(A.25)

(FT)y (F1)y + (F2)y + (F3)y + · · ·

The magnitude of the total force is FT

(FT)2x + (FT)2y

(A.26)

The torque produced by a force acts to produce a rotation in either a clockwise

or a counterclockwise direction. If we designate one direction of rotation as positive and the other as negative, the total torque acting on a body is obtained by the addition of the individual torques each with the appropriate sign. A.21 Static Equilibrium

A body is in static equilibrium if both its linear and angular acceleration are zero. To satisfy this condition, the sum of the forces F acting on the body, as well as the sum of the torques L produced by these forces must be zero; that is, P P F 0 and L 0

(A.27) A.22 Work

In our everyday language, the word work denotes any types of eﬀort whether physical or mental. In physics, a more rigorous deﬁnition is required. Here work is deﬁned as the product of force and the distance through which the force acts. Only the force parallel to the direction of motion does work on the object. This is illustrated in Fig. A.4. A force F applied at an angle θ pulls the object along the surface through a distance D. The work done by the force is

Work F cos θ × D

(A.28) A.23 Energy

Energy is an important concept. We ﬁnd reference to energy in connection with widely diﬀerent phenomena. We speak of atomic energy, heat energy, potential energy, solar energy, chemical energy, kinetic energy; we even speak

Section A.24 Forms of Energy FIGURE A.4 Work done by a force.

of people as being full of energy. The common factor that ties together these manifestations is the possibility of obtaining work from these sources. The connection between energy and work is simple: Energy is required to do work. Energy is measured in the same units as work; in fact, there is a oneto-one correspondence between them. It takes 2 J of energy to do 2 J of work. In all physical processes, energy is conserved. Through work, one form of energy can be converted into another, but the total amount of energy remains unchanged. A.24 Forms of Energy A.24.1 Kinetic Energy

Objects in motion can do work by virtue of their motion. For example, when a moving object hits a stationary object, the stationary object is accelerated. This implies that the moving object applied a force on the stationary object and performed work on it. The kinetic energy (KE) of a body with mass m moving with a velocity v is KE 1 mv2

(A.29)

2

In rotational motion, the kinetic energy is KE 1 Iω2

(A.30)

2 A.24.2 Potential Energy

Potential energy of a body is the ability of the body to do work because of its position or conﬁguration. A body of weight W raised to a height H with respect

Appendix A Basic Concepts in Mechanics

to a surface has a potential energy (PE) PE WH

(A.31)

This is the amount of work that had to be performed to raise the body to height H. The same amount of energy can be retrieved by lowering the body back to the surface.

A stretched or compressed spring possesses potential energy. The force

required to stretch or compress a spring is directly proportional to the length of the stretch or compression (s); that is, F ks

(A.32)

Here k is the spring constant. The potential energy stored in the stretched or compressed spring is PE 1 ks2

(A.33)

2 A.24.3 Heat

Heat is a form of energy, and as such it can be converted to work and other forms of energy. Heat, however, is not equal in rank with other forms of energy. While work and other forms of energy can be completely converted to heat, heat energy can only be converted partially to other forms of energy. This property of heat has far-reaching consequences which are discussed in Chapter 10.

Heat is measured in calorie units. One calorie (cal) is the amount of heat

required to raise the temperature of 1 g of water by 1 C◦. The heat energy required to raise the temperature of a unit mass of a substance by 1 degree is called the speciﬁc heat. One calorie is equal to 4.184 J.

A heat unit frequently used in chemistry and in food technology is the kilocalorie or Cal which is equal to 1000 cal. A.25 Power

The amount of work done—or energy expended—per unit time is called power. The algebraic expression for power is P E

(A.34) t

where E is the energy expended in a time interval t.

Section A.26 Units and Conversions A.26 Units and Conversions

In our calculations we will mostly use SI units in which the basic units for length, mass, and time are meter, kilogram, and second. However, other units are also encountered in the text. Units and conversion factors for the most commonly encountered quantities are listed here with their abbreviations. A.26.1 Length SI unit:

meter (m) Conversions: 1 m 100 cm (centimeter) 1000 mm (millimeter)

1000 m 1 km 1 m 3.28 feet 39.37 in 1 km 0.621 mile 1 in 2.54 cm

In addition, the micron and the angstrom are used frequently in physics and

biology.

1 micron (μm) 10−6 m 10−4 cm 1 angstrom ( ˚

A)∗ 10−8 cm A.26.2 Mass SI unit:

kilogram (kg) Conversions: 1 kg 1000 g

The weight of a 1-kg mass is 9.8 newton (N). A.26.3 Force SI Unit:

kg m s−2, name of unit: newton (N) Conversions: 1 N 105 dynes (dyn) 0.225 lbs A.26.4 Pressure SI unit:

kg m−1 s−2, name of unit: pascal (Pa) Conversions: 1 Pa 10−1 dynes/cm2 9.87 × 10−6 atmosphere (atm)

1.45 × 10−4 lb/in2

1 atm 1.01 × 105 Pa 760 mmHg (torr)

Appendix A Basic Concepts in Mechanics A.26.5 Energy SI unit:

kg m−2 s−2, name of unit: joule (J) Conversion: 1 J 1 N-m 107 ergs 0.239 cal 0.738 ft-lb A.26.6 Power SI unit:

J s−1, name of unit: watt (W) Conversion: 1 W 107 ergs/sec 1.34 × 10−3 horsepower (hp)

Appendix B

Review of Electricity B.1 Electric Charge

Matter is composed of atoms. An atom consists of a nucleus surrounded by electrons. The nucleus itself is composed of protons and neutrons. Electric charge is a property of protons and electrons. There are two types of electric charge: positive and negative. The proton is positively charged, and the electron is negatively charged. All electrical phenomena are due to these electric charges.

Charges exert forces on each other. Unlike charges attract and like charges

repel each other. The electrons are held around the nucleus by the electrical attraction of the protons. Although the proton is about 2000 times heavier than the electron, the magnitude of the charge on the two is the same. There are as many positively charged protons in an atom as negatively charged electrons. The atom as a whole is, therefore, electrically neutral. The identity of an atom is determined by the number of protons in the nucleus. Thus, for example, hydrogen has 1 proton; nitrogen has 7 protons; and gold has 79 protons.

It is possible to remove electrons from an atom, making it positively charged.

Such an atom with missing electrons is called a positive ion. It is also possible to add an electron to an atom which makes it a negative ion.

Electric charge is measured in coulombs (C). The magnitude of the charge

on the proton and the electron is 1.60 × 10−19 C. The force F between two charged bodies is proportional to the product of their charges Q1 and Q2 and is inversely proportional to the square of the distance R between them; that is, F KQ1Q2

(B.1) R2 287 <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-307_1.jpg"/>

Appendix B Review of Electricity

This equation is known as Coulomb’s law. If R is measured in meters, the

constant K is 9 × 109, and F is obtained in newtons. B.2 Electric Field

An electric charge exerts a force on another electric charge; a mass exerts a force on another mass; and a magnet exerts a force on another magnet. All these forces have an important common characteristic: Exertion of the force does not require physical contact between the interacting bodies. The forces act at a distance. The concept of lines of force or ﬁeld lines is useful in visualizing these forces which act at a distance.

Any object that exerts a force on another object without contact can be

thought of as having lines of force emanating from it. The complete line conﬁguration is called a force ﬁeld. The lines point in the direction of the force, and their density at any point in space is proportional to the magnitude of the force at that point.

The lines of force emanate from an electric charge uniformly in all direc

tions. By convention, the lines point in the direction of the force that the source charge exerts on a positive charge. Thus, the lines of force point away from a positive source charge and into a negative source charge (see Fig. B.1). The number of lines emanating from the charge is proportional to the magnitude of the electric charge. If the size of the source charge is doubled, the number of force lines is also doubled.

Lines of force need not be straight lines; as we mentioned, they point in

the direction in which the force is exerted. As an example, we can consider the FIGURE B.1 Two-dimensional representation of the electric ﬁeld produced by a

positive point charge (a) and a negative point charge (b). <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-308_1.jpg"/>

Section B.4 Electric Current FIGURE B.2 Lines of force produced by a positive and a negative charge separated

by a distance d.

net ﬁeld due to two charges separated by a distance d. To determine this ﬁeld we must compute the direction and size of the net force on a positive charge at all points in space. This is done by adding vectorially the force lines due to each charge. The force ﬁeld due to a positive and negative charge of equal magnitude separated by a distance d from each other is shown in Fig. B.2. Here the lines of force are curved. This is, of course, the direction of the net force on a positive charge in the region surrounding the two ﬁxed charges. The ﬁeld shown in Fig. B.2 is called a dipole ﬁeld, and it is similar to the ﬁeld produced by a bar magnet. B.3 Potential Diﬀerence or Voltage

The electric ﬁeld is measured in units of volt per meter (or volt per centimeter). The product of the electric ﬁeld and the distance over which the ﬁeld extends is an important parameter which is called potential diﬀerence or voltage. The voltage (V ) between two points is a measure of energy transfer as the charge moves between the two points. Potential diﬀerence is measured in volts. If there is a potential diﬀerence between two points, a force is exerted on a charge placed in the region between these points. If the charge is positive, the force tends to move it away from the positive point and toward the negative point. B.4 Electric Current

An electric current is produced by a motion of charges. The magnitude of the current depends on the amount of charge ﬂowing past a given point in a given period of time. Current is measured in amperes (A). One ampere is 1 coulomb (C) of charge ﬂowing past a point in 1 second (sec). <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-309_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-309_2.png"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-309_3.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-309_4.jpg"/>

Appendix B Review of Electricity B.5 Electric Circuits

The amount of current ﬂowing between two points in a material is proportional to the potential diﬀerence between the two points and to the electrical properties of the material. The electrical properties are usually represented by three parameters: resistance, capacitance, and inductance. Resistance measures the opposition to current ﬂow. This parameter depends on the property of the material called resistivity, and it is analogous to friction in mechanical motion. Capacitance measures the ability of the material to store electric charges. Inductance measures the opposition in the material to changes in current ﬂow. All materials exhibit to some extent all three of these properties; often, however, one of these properties is predominant. It is possible to manufacture components with speciﬁc values of resistance, capacitance, or inductance. These are called, respectively, resistors, capacitors, and inductors.

The schematic symbols for these three electrical components are shown in

Fig. B.3. Electrical components can be connected together to form an electric circuit. Currents can be controlled by the appropriate choice of components and interconnections in the circuit. An example of an electric circuit is shown in Fig. B.4. Various techniques have been developed to analyze such circuits and to calculate voltages and currents at all the points in the circuit. B.5.1 Resistor

The resistor is a circuit component that opposes current ﬂow. Resistance (R) is measured in units of ohm (). The relation between current (I ) and FIGURE B.3 Circuit components. FIGURE B.4 Example of an electric circuit. <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-310_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-310_2.png"/>

Section B.5 Electric Circuits

voltage (V ) is given by Ohm’s law, which is V IR

(B.2)

Materials that present a very small resistance to current ﬂow are called conductors. Materials with a very large resistance are called insulators. A ﬂow of current through a resistor is always accompanied by power dissipation as electrical energy is converted to heat. The power (P) dissipated in a resistor is given by P I2R

(B.3)

The inverse of resistance is called conductance, which is usually designated by the symbol G. Conductance is measured in units of mho, also called Siemens. The relationship between conductance and resistance is G 1

(B.4) R B.5.2 Capacitor

The capacitor is a circuit element that stores electric charges. In its simplest form it consists of two conducting plates separated by an insulator (see Fig. B.5). Capacitance (C) is measured in farads. The relation between the stored charge (Q), and the voltage across the capacitor is given by Q CV

(B.5)

In a charged capacitor, positive charges are on one side of the plate, and

negative charges are on the other. The amount of energy (E) stored in such a conﬁguration is given by E 1 CV 2

(B.6)

2 FIGURE B.5 A simple capacitor. <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-311_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-311_2.png"/>

Appendix B Review of Electricity B.5.3 Inductor

The inductor is a device that opposes a change in the current ﬂowing through it. Inductance is measured in units called henry. B.6 Voltage and Current Sources

Voltages and currents can be produced by various batteries and generators. Batteries are based on chemical reactions that result in a separation of positive and negative charges within a material. Generators produce a voltage by the motion of conductors in magnetic ﬁelds. The circuit symbols for these sources are shown in Fig. B.6. B.7 Electricity and Magnetism

Electricity and magnetism are related phenomena. A changing electric ﬁeld always produces a magnetic ﬁeld, and a changing magnetic ﬁeld always produces an electric ﬁeld. All electromagnetic phenomena can be traced to this basic interrelationship. A few of the consequences of this interaction follow: 1. An electric current always produces a magnetic ﬁeld at a direction

perpendicular to the current ﬂow. 2. A current is induced in a conductor that moves perpendicular to a

magnetic ﬁeld. 3. An oscillating electric charge emits electromagnetic waves at the

frequency of oscillation. This radiation propagates away from the source at the speed of light. Radio waves, light, and X-rays are examples of electromagnetic radiation. FIGURE B.6 Circuit symbols for a battery and a generator.

Appendix C

Review of Optics C.1 Geometric Optics

The characteristics of optical components, such as mirrors and lenses, can be completely derived from the wave properties of light. Such detailed calculations, however, are usually rather complex because one has to keep track of the wave front along every point on the optical component. It is possible to simplify the problem if the optical components are much larger than the wavelength of light. The simpliﬁcation entails neglecting some of the wave properties of light and considering light as a ray traveling perpendicular to the wave front (Fig. C.1). In a homogeneous medium, the ray of light travels in a straight line; it alters direction only at the interface between two media. This simpliﬁed approach is called geometric optics.

The speed of light depends on the medium in which it propagates. In

vacuum, light travels at a speed of 3 × 108 m/sec. In a material medium, the speed of light is always less. The speed of light in a material is characterized by the index of refraction (n) deﬁned as n c

(C.1) v

where c is the speed of light in vacuum and v is the speed in the material. When light enters from one medium into another, its direction of propagation is changed (see Fig. C.2). This phenomenon is called refraction. The relationship between the angle of incidence (θ1) and the angle of refraction (θ2) 293 <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-313_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-313_2.png"/>

Appendix C Review of Optics FIGURE C.1 Light rays perpendicular to the wave front.

is given by

sin θ1 n2

(C.2)

sin θ2 n1

The relationship in Eq. C.2 is called Snell’s law. As shown in Fig. C.2, some of the light is also reﬂected. The angle of reﬂection is always equal to the angle of incidence.

In Fig. C.2a, the angle of incidence θ1 for the entering light is shown to

be greater than the angle of refraction θ2. This implies that n2 is greater than n1 as would be the case for light entering from air into glass, for example (see Eq. C.2). If, on the other hand, the light originates in the medium of higher refractive index, as shown in Fig. C.2b, then the angle of incidence θ1 is smaller than the angle of refraction θ2. At a speciﬁc value of angle θ1 called the critical angle (designated by the symbol θc), the light emerges tangent to the surface, that is, θ2 90◦. At this point, sin θ2 1 and, therefore, sin θ1 sin θc n2/n1. Beyond this angle, that is for θ1 > θc, light originating in the medium of higher refractive index does not emerge from the medium. At the interface, all the light is reﬂected back into the medium. This phenomenon is called total internal reﬂection. For glass, n2 is typically 1.5, and the critical angle at the glass-air interface is sin θc 1/1.5 or θc 42◦.

Transparent materials such as glass can be shaped into lenses to alter the

direction of light in a speciﬁc way. Lenses fall into two general categories: converging lenses and diverging lenses. A converging lens alters the direction of light so that the rays are brought together. A diverging lens has the opposite eﬀect; it spreads the light rays apart.

Using geometric optics, we can calculate the size and shape of images

formed by optical components, but we cannot predict the inevitable blurring of images which occurs as a result of the wave nature of light. <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-314_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-314_2.png"/>

Section C.2 Converging Lenses FIGURE C.2 (Top) Reﬂection and refraction of light. (Bottom) Total internal

reﬂection. C.2 Converging Lenses

A simple converging lens is shown in Fig. C.3. This type of a lens is called a convex lens.

Parallel rays of light passing through a convex lens converge at a point

called the principal focus of the lens. The distance of this point from the lens is called the focal length f. Conversely, light from a point source at the focal point emerges from the lens as a parallel beam. The focal length of the lens is

Appendix C Review of Optics FIGURE C.3 The convex lens illuminated (a) by parallel light, (b) by point source at

the focus.

determined by the index of refraction of the lens material and the curvature of the lens surfaces. We adopt the following convention in discussing lenses. 1. Light travels from left to right. 2. The radius of curvature is positive if the curved surface encountered by

the light ray is convex; it is negative if the surface is concave.

It can be shown that for a thin lens the focal length is given by

1

1

(n − 1)

− 1

(C.3) f R1 R2

where R1 and R2 are the curvatures of the ﬁrst and second surfaces, respectively (Fig. C.4). In Fig. C.4, R2 is a negative number.

Focal length is a measure of the converging power of the lens. The shorter

the focal length, the more powerful the lens. The focusing power of a lens is

Section C.2 Converging Lenses FIGURE C.4 Radius of curvature deﬁned for a lens.

often expressed in diopters deﬁned as

Focusing power

1

(diopters)

(C.4) f (meters)

If two thin lenses with focal lengths f1 and f2, respectively, are placed close together, the focal length fT of the combination is

1 1 + 1

(C.5) fT f1 f2

Light from a point source located beyond the focal length of the lens is

converged to a point image on the other side of the lens (Fig. C.5a). This type of an image is called a real image because it can be seen on a screen placed at the point of convergence.

If the distance between the source of light and the lens is less than the focal

length, the rays do not converge. They appear to emanate from a point on the source side of the lens. This apparent point of convergence is called a virtual image (Fig. C.5b).

For a thin lens, the relationship between the source and the image distances

from the lens is given by

1 + 1 1

(C.6) p q f

Here p and q, respectively, are the source and the image distances from the lens. By convention, q in this equation is taken as positive if the image is formed on the side of the lens opposite to the source and negative if the image is formed on the source side.

Light rays from a source very far from the lens are nearly parallel; there

fore, by deﬁnition we would expect them to be focused at the principal focal point of the lens. This is conﬁrmed by Eq. C.6, which shows that as p becomes very large (approaches inﬁnity), q is equal to f. <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-317_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-317_2.png"/>

Appendix C Review of Optics FIGURE C.5 Image formation by a convex lens: (a) real image, (b) virtual image.

If the source is displaced a distance x from the axis, the image is formed

at a distance y from the axis such that y q

(C.7) x p

This is illustrated for a real image in Fig. C.6. The relationship between p and q is still given by Eq. C.6. C.3 Images of Extended Objects

So far we have discussed only the formation of images from point sources. The treatment, however, is easily applied to objects of ﬁnite size.

When an object is illuminated, light rays emanate from every point on the

object (Fig. C.7a). Each point on the object plane a distance p from the lens

Section C.3 Images of Extended Objects FIGURE C.6 Image formation oﬀ axis. FIGURE C.7 Image of an object: (a) real, (b) virtual.

is imaged at the corresponding point on the image plane a distance q from the lens. The relationship between the object and the image distances is given by Eq. C.6. As shown in Fig. C.7, real images are inverted and virtual images are upright. The ratio of image to object height is given by

Image height −q

(C.8)

Object height p <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-319_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-319_2.png"/>

Appendix C Review of Optics FIGURE C.8 A diverging lens. C.4 Diverging Lenses

An example of a diverging lens is the concave lens shown in Fig. C.8. Parallel light diverges after passing through a concave lens. The apparent source of origin for the diverging rays is the focal point of the concave lens. All the equations we have presented for the converging lens apply in this case also, provided the sign conventions are obeyed. From Eq. C.3, it follows that the focal length for a diverging lens is always negative and the lens produces only virtual images (Fig. C.8). C.5 Lens Immersed in a Material Medium

The lens equations that we have presented so far apply in the case when the lens is surrounded by air that has a refraction index of approximately 1. Let us now consider the more general situation shown in Fig. C.9, which we will need in our discussion of the eye. The lens here is embedded in a medium that has a diﬀerent index of refraction (n1 and n2) on each side of the lens. It can be shown (see [15-3]) that under these conditions the relationship between the object and the image distances is n1 + n2 nL −n1 − nL − n2

(C.9) p q R1 R2 <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-320_1.jpg"/> <img src="./tmp/raw_656f49f53d8d3c5343596b2cc8b234fc-320_2.png"/>

Section C.5 Lens Immersed in a Material Medium FIGURE C.9 Lens immersed in a material medium.

Here nL is the refraction index of the lens material. The eﬀective focal

length in this case is

1 n2 −n1 − nL −n2

(C.10) f R1 R2

Note that in air n1 n2 1 and Eq. C.10 reduces to Eq. C.3.

The lens equations we have presented in this appendix assume that the

lenses are thin. This is not a fully valid assumption for the lenses in the eye. Nevertheless these equations are adequate for our purposes.

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15-5 Muntz, W. R. A. “Vision in Frogs,” Scientiﬁc American (March 1964),

110.

15-6 Ruch, T. C., and Patton, H. D. Physiology and Biophysics. Philadelphia,

PA: W. B. Saunders and Co., 1965.

15-7 Wald, George. “Eye and the Camera,” Scientiﬁc American (August

1950), 32. Chapters 16 and 17

16-1 Ackerman, E. Biophysical Sciences. Englewood Cliﬀs, NJ: Prentice

Hall, Inc., 1962.

16-2 Burns, D. M., and MacDonald, S. G. G. Physics for Biology and Pre- Medical Students. Reading, MA: Addison-Wesley Publishing Co., 1970.

16-3 Delchar, T. A. Physics in Medical Diagnosis. New York, NY: Chapman

and Hall, 1997.

16-4 Dowsett, D. J., Kenny, P. A., and Johnston, R. E. The Physics of Diagnostic Imaging. New York, NY: Chapman and Hall Medical, 1998.

16-5 Hobbie, R. K. Intermediate Physics for Medicine and Biology. New

York, NY: Springer, 1997.

16-6 Pizer, V. “Preserving Food with Atomic Energy,” United States Atomic

Energy Commission Division of Technical Information, 1970.

16-7 Pykett, I. L. “NMR Imaging in Medicine,” Scientiﬁc American (May

1982), 78.

16-8 Schr¨odinger, E. “What Is Life?” and Other Scientiﬁc Essays. Garden

City, NY: Anchor Books, Doubleday and Co., 1956.

Answers to Numerical

Exercises Chapter 1

1-1(b). F 254 N (57.8 lb) 1-3. θ 72.6◦ 1-4. Maximum weight 335 N (75 lb) 1-5(a). Fm 2253 N (508 lb), Fr 2386 N (536 lb) 1-6. Fm 720 N, Fr 590 N 1-7(a). Fm 2160 N, Fr 1900 N 1-8. Fm 103 N, Fr 84 N

1-10. x 19.6 cm, v of tendon 4 cm/sec, v of weight 38 cm/sec 1-11. Fm 0.47 W, Fr 1.28 W 1-12(a). Fm 2000 N, Fr 2200 N; (b). Fm 3220 N, Fr 3490 N 1-13. FA 2.5 W, FT 3.5 W Chapter 2

2-1(a). Distance 354 m; (b). Independ of mass 2-2(a). μ 0.067 2-3(a). μ 1.95; (b). with μ 1.0, θ 39.4◦, with μ 0.01, θ 0.6◦ Chapter 3

3-1. P 4120 watt 3-2. H 126 cm 310

3-3. Fr 1.16 W, θ 65.8◦ 3-4. T 0.534 sec 3-5(a). R 13.5 m; (b). H 3.39 m; (c). 4.08 sec 3-6. v 8.6 m/sec 3-7. r 1.13 m 3-8(a). v 8.3 m/sec; (b) 16.6 cm/sec 3-9. Energy expended/sec 1350 J/sec

3-10. P 371 watt Chapter 4

4-2. F 10.1 N 4-3. ω 1.25 rad/sec; linear velocity 6.25 m/sec 4-4. ω 1.25 rad/sec 33.9 rpm 4-5. v 62.8 m/sec 4-6. Speed 1.13 m/sec 4.07 km/h 2.53 mph 4-7. T 1.6 sec 4-8. E 1.64 mv2 4-9. Fall time 1 sec Chapter 5

5-1. v 2.39 m/sec (5.3 mph) 5-2. v 8 m/sec; with 1 cm2area v 2 m/sec 5-3. h 5.1 m 5-4. t 3 × 10−2 sec 5-5. v 17 m/sec (37 mph) 5-6. Force/cm2 4.6 × 106 dyn/cm2, yes 5-7. v 0.7 m/sec, no Chapter 6

6-1. F 2 W 6-2. 0.052 mm 6-3. h 18.4 cm 6-4. 10.3 cm Answers to Numerical Exercises Chapter 7

7-2. P 7.8 W 7-3. v [gV(ρw − ρ)/Aρw]1/2; P 1/2[W{(ρw/ρ) −1}3/2]/(Aρw)1/2 7-5. P 1.51 × 107dyn/cm2 15 atm 7-6. Volume of swim bladder 3.8% 7-7. ρ2 ρ1(W1/W1 − W2) 7-8. p 1.46 × 105 dyn/cm2

7-11. Perimeter 9.42 km 7-12. Speed 29 cm/sec Chapter 8

8-1. P 3.19 × 10−2 torr 8-2. P 4.8 torr 8-3. h 129 cm 8-4(a). p 61 torr; (b). p 200 torr 8-5(b). R1/R2 0.56 8-6. v 26.5 cm/sec 8-7. N 7.5 × 104 8-8. p 79 torr 8-9. P 10.1 W

8-10(a). P 0.25 W; (b). P 4.5 W Chapter 9

9-2. V 29.3 9-3(a). t 10−2 sec; (b). t 10−5 sec 9-5. N 1.08 × 1020 molecules/sec 9-6. No. breaths/min . 10.4 9-7(a). Rate 1.71 liter/hr-cm2; (b). diameter 0.5 cm 9-8. P 2.87 atm Chapter 11

11-2. t 373 hours 11-3. v 4.05 m3 11-4. t 105 days 11-5. Weight loss 0.892 kg 11-6. H 18.7 Cal/h

11-8(b). Change 22%; (c). Kr 6.0 Cal/m2-h-C◦ 11-9. Heat removed 8.07 Cal/h

11-10. Heat loss 660 Cal/m2-h 11-11. H 14.4 Cal/h Chapter 12

12-1. R 31.6 km 12-2. 1.75 times 12-3. p 2.9 × 10−4 dyn/cm2 12-6. D 11.5 m 12-8. Min. size 1.7 × 10−2 cm Chapter 13

13-1(a). No. of ions 1.88 × 1011; (b). no. of Na+ ions 7.09 × 1014/m;

No. of K+ ions 7.09 × 1015/m

13-8(a). no of cells in series 5000; (b). no of cells in parallel 2.7 × 109 Chapter 14

14-1. i 13.3 amp Chapter 15

15-1. Change in position 0.004 cm 15-3. For cornea 41.9 diopters; for lens, min power 18.7 diopters, max

power 24.4 diopters

15-4. 1/f −0.39 diopters 15-5. Focusing power ±70 diopters 15-6. p 1.5 cm 15-7(a). Resolution 2.67 × 10−4 rad; (b). Resolution 6.67 × 10−4 rad 15-8. D 20 m 15-9. H 3 × 10−4 cm

Index

Absorption

velocity and K c, 151–152

electromagnetic radiation, 123, 242

viscosity, 104

spectroscopy, 245

Airbag, 68–69

spectrum, 243

Alcohol, caloric value, 147

Acceleration

Aluminum

angular, 277

speciﬁc heat, 119

centripetal, 278–279

thermal conductivity, 122

deﬁned, 273

Alveoli, 129

equations of translational motion for,

size, 132 30–32

Amino acid, 271

gravitational, 5, 33

Ampliﬁcation, in human ear, 175

of jumper, 31–34

Ampliﬁer, 201

Accommodation of eye, 216–217, 230

transistor, 211

Angstrom, 285

Achilles tendon, 19

Angular acceleration, 277

Actin, 95, 96

Angular momentum

Action potential, 184–186

deﬁned, 280

in muscles, 194

equations of, 277–278

in plants, 196

Angular motion

measurement, 195

forces on a curved path, 45–48

propagation, 188–190

Newton’s laws, 280

Adhesion, 90–91

pendulum

strength of, 93

physical, 51–52

Adrenaline, 155

simple, 48–50

Aging, and vision, 216–217

running, 53–56

Air

vs. linear motion, 277

inspired vs. expired, 130–131

walking, 50–53

motion through, 40–42

Angular velocity, 276

pressure in ear, 170

maximum, 54, 78–79 314 Index

Animal

propagation vs. speed of light, 186

energetics, 136

resistance of, 186

motion, 1

sodium pump, 184

sounds produced by, 176

voltage, 184

Anvil (middle ear), 169

vs. electric cable, 186–188

Aorta, 106

blood pressure drop, 107–108

Back

turbulent ﬂow, 110–111

backaches, 18

Aperture of eye, 218–219

lever representation, 17–19

Apocrine sweat gland, 155

Bacteria, thermophilic, 145

Aqueous humor, 215–216

Ballistocardiograph, 115

Archimedes’ principle

Barth´elemy, Toussaint, 249

deﬁned, 87

Basal metabolic rate, 147

ﬁsh buoyancy and, power required to stay aﬂoat and,

Basilar membrane, 170 87–88

Bats

Arteriole, 106–107, 109

chirping, 175–176

Arterisclerosis, and blood ﬂow, 111–112

echo location, 175

Artery, 105

Battery, 292

elasticity, 112

Bernoulli’s equation, 101–102, 103

narrowing, 111, 112

stenosis and, 111

natural frequency, 112

Biceps, 7

plaque deposit, 111–112

movement of, 11–15

pressure drop, 107–108

Biological control system, 208

pulmonary, 105

features, 206–207

Astigmatism, 227

feedback, 208–210

lens for, 228, 229

in iris, 210

Atom

Biomechanics, 2

absorption spectrum, 243

Blood

energy state, 241–242

adrenaline in, 155

excitation of, 242–243

cells, radioactive, 269

interactions between, 270

circulation, 105–107

nucleus, 240, 256–257

ﬂow

structure, 239–240

arterisclerosis, 111–112

Atomic physics, 239

control, 109

Axon, 181

energetics, 110

action potential, 184–186

laminar, 103, 104, 110, 111

action potential propagation,

rate, 112–113 188–190

to brain, 109

capacitance and resistance of, 186

turbulence, 110–111

circuit, analysis of, diameter of, 183

velocity, 110, 178

electrical potentials, 183–184, 185

kinetic energy, 110

electrical properties, 186–187

pressure

length of, 181

arterial, 107–109

membrane

at capillaries, 107

as leaky insulator, 186

measurement, 113–114

permeability, 184

systolic and diastolic, 107

myelin, 181

venal, 109

myelinated, 192–193

sugar level, 245

myelinated vs. nonmyelinated, 187

venal, 136

nodes of Ranvier, 181

viscosity, 104 Index

Bohr model of atom, 240–241, 247

Center of mass motion

formation of chemical bonds,

in running, 57–58 243–244

in walking, 56–57

hydrogen, 241

Centrifugal force, 45–46, 47

Bohr, Niels, 240

deﬁned, 278

Boltzmann constant, 117–118

Centripetal acceleration, 277–278

Bone

Centripetal force, 46, 47, 277–278

density

deﬁned, 277

cuttleﬁsh, 88–89 137Cesium, 268

electricity and, 196–197

Chatecholamine, 109

fracture

Chemical bond, formation of, 243–244

energy involved, 64–66

Chemical energy, 139

force needed to cause, 67–68

Chemical fumigation, 267

neck, 69–70

Chlorine ion, and membrane potential, 184

NMR signal, 261

Chromium isotope, in medicine, 269

osteoblasts and osteoclasts, 197

Circulatory system, 105–107

Boyle’s law, 119

body heat transfer and, 151

Brain

mechanism of energy losses, 107

activity identiﬁcation, 265–266

turbulent ﬂow, 111–112 60

arteries, 109

Cobalt, 268

blood ﬂow to, 109

Cochlea, 170–171

diagnosing disorders, 204

implants, 211–213

ischemic stroke, 112

Coeﬃcient

nerve centers in, 150

convection, 122, 152

nerve impulses, 162

diﬀusion, friction, 24, 25, 46, 71

role in hearing, 175

kinetic, 25, 71

signal processing, 226

static, 25

Breathing

thermal conductivity, 121

cold-blooded animals, 132

Collision

heat loss by, 155–156, 157

automobile, 69–70

surfactants and, 132

duration of, 66–67

Broad jump

force of, 67–68

running position, 39–40

protective device, 68–69

standing position, 37–39

Compression, 61–62

Broca, Paul Pierre, 265

Computerized tomography, 250–251, 257

Broken heart syndrome, 109

Conductance (G), 291

Bruit, 111

Conduction, thermal, 120–121

Buoyancy, of ﬁsh, 88–89

in human body, 150, 151

Conductor, 291

Calorie, 119

Cones and rods, 222, 223, 224, 225–226

intake, 148

Confocal microscopy, 232–235

Capacitor, 291

Conservation

Capillary action, 91, 92, 93

energy, 135–136

Cardiomyopathy, stress, 109

Bernoulli’s equation and, 101–102

Cardiovascular disease

human physiology and, 136

arterisclerosis, 111–112

linear momentum, 275

stress cardiomyopathy, 109

Constructive interference, 166

Catﬁsh spine ﬁn, 27–29

Control system, 206–208

Cell, 270–271

feedback, 208–210

Center of gravity, 2

Convection, 121–122

human body, 3–4

in human body, 151–153 Index

Converging lens, 294, 295–298

molecular transport through,

Cooling mechanism, 136, 141, 150, 126–127 155–156, 158

random walk, 124–125

Cork, thermal conductivity of, 122

through biological membrane,

Cornea, 215 128–129

receive oxygen by diﬀusion, 133

Diopter, 219

refractive power, 220

Dipole ﬁeld, 289

Coulomb, 287

Diverging lens, 294, 300

Coulomb’s law, 287–288

DNA, 143–144, 248, 250, 269, 270, 271

Critical angle, 294

Doppler eﬀect, 178

Critical ﬂow velocity, 104

Doughnut, energy content, 43

Cromer, A. H., 43

Dyne, 285

Crystallography, CT scan, 250–251, Cut-oﬀ blood pressure measurement,

Ear, 168 113–114

ampliﬁcation in, 175

Cuttleﬁsh, bone density, 88–89

canal, horns, 211

Davidovits, Paul, 232, 233

inner, 170–171

da Vinci, Leonardo, 1, 7–8

balance maintenance, 21

De Broglie, Louis, 246, 247

middle, 169–170

Deﬁbrillator, 206

outer, 168–169

Dehydration, 155

performance, 171–172

Density

sound detection capability, 172–173

constant, 83

sound intensity, 173–175

of water, and ﬂoating, 87–88

threshold of hearing and pain, 173, 174

porous bones and swim bladders,

Eardrum, 162, 168, 169–170, 175 88–89

Earth, forces on, 33

Depth of ﬁeld, 219

Eccrine sweat gland, 155

Destructive interference, 166

ECG, See Electrocardiography

Diabetic retinopathy, laser treatment, 254

Echoes, bats and, 175

Diagnostic equipment

EEG, See Electroencephalography

computerized tomography, 250–251,

Eel, electric, 198 257

Egger, M. David, 232, 233

electrocardiograph, 195, 202–203

Einstein, Albert, 252

electroencephalograph, 195,

Elasticity, 61 203–204

artery, 112

electromyograph (EMG), 195

insect wings, 79–80

magnetic resonance imaging,

spring, 62–64 257–258

Elbow, movement of, 11–15

stethoscope, 111, 113, 177, X-rays, 249–250

Electrical technology, in biological

research, 200–202

Diastolic pressure, Diathermy, 178

Electric charge, 287–288

Diﬀraction, 168

Electric circuit, 290–292

in eye, 224

Electric current, 289

studies with molecules, 250

eﬀect on brain, 205

Diﬀusion, 123–125

sources, 292

coeﬃcient, 127

Electric eel, 198

contact lens and, 133

Electric ﬁeld, 288–289, 292

in respiratory system, 129–132

in water, 198

mean free path, 124

Electric ﬁsh, 197–198 Index

Electricity

consumption in physical activity,

as a natural phenomena, 180 42–43

in bone, 196–197

load carrying, 58–59

ﬁsh and, 197–198

running, 54–56

in plants, 196

electromagnetic, 122–123

magnetism and, 292

forms, 283

nervous system and, 180–196

from food, 147–149

physiological eﬀects, 204–206

internal, 117, 139

piezoelectricity, 196–197

involved in bone fracture, 64–66

Electric shock, 204–205

kinetic, 283

Electrocardiography (ECG), 195, 202–203

insect wing in ﬂight, 78–79

Electrode, 202

of particles in gas, 117

Electroencephalography (EEG), 195,

level, 241–242 203–204

mechanical, in ultrasonic wave, 178

Electromagnetic radiation, 214

requirements, 146–149

energy and, 122–123

during pregnancy, 149

excitation of atom and, 242–243

unit and conversion, 286

Electromyography (EMG), 195

Entropy, 142

Electron, 239, 240–241

Epilepsy, 205

binding energy, 243

Equilibrium

diﬀraction patterns, 247

human body considerations, 3–4

electric charge of, 287

stability and, 2–3

energy level, 241–242

static, 2–3, 282

excitation, methods of, 242

Eustachian tube, 170

excited state, 242

Evaporation, skin temperature control by,

ground state, 241–242 155–156

high-speed (Beta particles), 256

Excited state, 242

and food preservation, 268

Exercise, osteoarthritis and, 71

impact, 242

Eye

inner, 243

aging and, 216–217

in oscilloscope, 201

aperture and depth of ﬁeld, 218–219

orbital restrictions, 240–241

eyeglasses, 211

orbit around nucleus, 240

focusing, 216–217, 230

outer, 243

laser treatment, 253–255

radiation and, 122–123

lens system, 219–220

shared, 244

light intensity reaching retina,

wavelength, 247 207–208, 209

wavelike properties, 246

near point, 216–217

Electron microscope, 247–248

parameters, 220

EMG, See Electromyography

reduced, 220–222

Emission

resolution of, 223–225

spectroscopy, 245

structure, 215–216

spontaneous, 252

vs. camera, 217–218

stimulated, 252

Eyepiece, 230, 231

Emissivity, 123

of skin, 153

Falling

Endoscope, 236–237

fracture due to, 67–68

Energy, 282–283

from great height, 70

chemical, 139

on snow, 70

in food, 141

Farads, 291

conservation, 135–136

Fasting, world record, 149

Index

Feedback system, 208–209

ﬂuid, 82–86

negative feedback, 209

impulsive, 66–67

positive feedback, 209

bone fracture and, 67–68

Fetus

lines of, 288–289

energy required, 149

on a curved path, 45–48

heart, examination, 178

on the foot, 47

Fiber optics, 235

pressure in a ﬂuid and, 82–83

ﬁberscopes, 236–237

static, 1–2

Fibrillation, 205–206

stopping, 69

Field line, 288

unit and conversion, 285

Fish

Fourier, J. B. J., 171

buoyancy, 88–89

Fovea, 222

catﬁsh spine ﬁn, 27–29

Fracture

electric, 197–198

due to a fall, 67–68

electronic lures, 176

energy involved, 64–66

eye, lens focusing power, 219–220

neck bone, 69–70

Flight

Frequency

insect, 73–80

larmor, 259–261

hovering, 73–75

natural, of healthy artery, 112

Fluid

pendulum swings, 48–49

Archimedes’ principle, 87–89

resonant, 167

blood, See Blood

sound, 163, 164

body, 183

Friction, 23–24

deﬁned, 82

at hip joint, 26–27

force and pressure, 82–86

catﬁsh spine ﬁn and, 27–29

friction and, 103–104

coeﬃcient, 24, 25, 46, 71

motion of, 101

ﬂuid, in air, 40

Bernoulli’s equation, 101–102

standing at an incline, 25–26

laminar, 103, 104

viscous, 24, 103, 107

Poiseuille’s law, 103–104, 107–108

Frog

turbulent ﬂow, 104–105

alveolal radii, 132

viscous friction, 24, 103, 107

diﬀusion transfer of oxygen,

surface tension, 89–96 131–132

Flux, 126–127, 128

neurons in retina, 226–227

solar, 154

Fulcrum, 9–10

Focal length of lens, 295–297

Fumigation, chemical, 267

Focus, principal, of the lens, 295

Functional magnetic resonance imaging

Food

(fMRI), 265–266

composition and energy content, 148

Fur, 157

energy from, 141, oxidation, 147

Galvani, Luigi, 194

preservation by fumigation, 267

Gamma ray, use in food preservation,

preservation by radiation, 267–268 267–268

requirements for humans, 147–148

Gas

Force

behavior, 139

addition of torques and, 281–282

behavior of matter as a function of

adhesive vs. cohesive, 90

temperature in, 117–119

centrifugal, 45–46, 47, 278

diﬀusion, 125

centripetal, 46, 47, 277–278

greenhouse, 159

contraction of muscle, 96

noble, 244

deﬁned, 274

pressure, 118

ﬁeld, 288

Generator, 292 Index

Geometric optics, 293–295

unit of, 119, 284

Gland

vs. other energy forms, 138–140

apocrine, 155

Helicotrema, 170

eccrine, 155

Henry, 292

Glass

Hertz, 163

lens, 294

Hertz, Heinrich, 163

radiation and, 123, 249

High jump, 36–37

silica, 235

Hip joint

Glycerine, viscosity of, 104

friction at, 26–27

Gravitational force, 274

movement of, walking on injured, 17

Greenhouse eﬀect, 159

Hooke, Robert, 62, 63

Greenhouse gas, 159

Hooke’s law, 62, 79

Ground state, 241–242

Hormone, 109, 207

Gyromagnetic ratio, 258, 259

Hovering ﬂight, 73–75

power required, 76–79

Hales, Stephen, 113

Human body, See also Speciﬁc parts,

Hammer (middle ear), 169 organs and systems

Hearing, 168

adaptation for heat vs. cold, 156

aids, 211

critical temperature, 156

ear horns, 211

energy requirements, 146–148

brain’s role in, 175

food requirements, 147–148

cochlear implants, 211–213

metabolic rate, 146

in bats, 175–176

motion, 1–2

sound frequency and pitch, 172–173

oxygen requirements, 130–131

threshold of, 173, 174

posture, 19–21

transistorized aids for, 211

radiative heating, 154

Heart

resistance to cold, 156–157

aorta, 106

senses, limitations of, 200

atrium and ventricle, 105–106

sound production, 176

capillaries, 107

speciﬁc heat, stability of, 3–4

desynchronization of heart action,

under action of external force, 4–7 205–206

sweat production, 155–156, 209

fetus, examination, 178

temperature

power produced by, 112–113

regulation, 149–151

stress, 109

regulation by convection, 151–153

Heat, 284, See also Thermodynamics

regulation by evaporation, 155–156

cold and, 156–157

regulation by radiation, 153

deﬁned, 116

Hydrogen

latent, 120

Bohr model for atom of, 241

life and, 145–146

formation of molecule of, 244

loss by breathing, 155–156, 157

nuclear magnetic properties of, 258

radiative by sun, 153–154

Hydrostatic skeleton, 84–86

speciﬁc, 119, 284

Hyperopia, 227

therapeutic eﬀects, 161

lens for, 228, 229

transfer of

conduction, 120–121, 150, 151

Ice, speciﬁc heat of, 119

convection, 121–122, 151–153

Image

diﬀusion, 123–133

of extended objects, 298–300

in human body, 149–157

on retina, 217–218

radiation, 122–123, 139, 153–154

size, 221–222, 223, 229–230 Index

real, 297

Irradiation, food, 267–268

size of aperture and, 218–219

Ischemic stroke, 112

virtual, 297

Isotope, 256

Imaging

oxygen, 256

computerized tomography, 250–251, 257

radioactive, 257

magnetic resonance imaging (MRI),

tracers, 268–269 257–258

ultrasound, 177–178

Joint

with NMR, 262–265

hip

X-ray, 243, 249–250

friction at, 26–27

Impulsive force, 66–67

movement, 15–17

fracture and, 67–68

walking on injured, 17

Inductor, 292

knee problems, 71

Inertia, moment of, 279

osteoarthritis, 70–71

Infant respiratory distress syndrome, 132

Jump

Inner ear, 170–171

broad

balance maintenance, 21

from running position, 39–40

basilar membrane, 170

from standing position, 37–39

cochlea, 170–171

high, 36–37

implants, 211–213

vertical

helicotrema, 170

eﬀect of gravity on, 35

Insect

height of, 32–35

ﬂight, 73

hovering, 73–75, 76–79

Kilocalorie, 284

locomotion on water, 93–95, 99

Kinesiology, 2 Microvelia, 99

Kinetic energy

wing

deﬁned, 283

elasticity, 79–80

insect wing in ﬂight, 78–79

kinetic energy when in ﬂight,

of particles in gas, 117 78–79

Kinetic friction, 23–24

muscles, 75–76

coeﬃcient, 25, 71

Insulation, fur and feather, 122, 157

Kinetic theory of matter, 116–119

Insulator, 291

Knee joint, problems, 71

Intensity

Kuhne, W., 217, 218

of light

control, in reaching retina,

Laminar ﬂow, 103, 104, 110, 111 207–208, 209

Larmor frequency, 259–261

of sound, 163

Laser, 252–253

and loudness, 173–175

surgery, 253

Interference, 166–167

ophthalmological applications,

Internal energy, 117, 139 253–255

Internal reﬂection, total, 294, 295

LASIK (Laser-assisted in Situ Ker

Interneuron, 181

atomileusis), 254–255 131Iodine, 267

Latent heat, 120

Ion

Lauterbur, P. C., 263

membrane potential and, 183–184

Lavoisier, Laurent, 135, 136

negative, 287

Lens, 215

positive, 287

astigmatism, 228, 229

Iris, 215

contact lens and diﬀusion, 133

control system, 210

converging, 294, 295–298

deﬁned, 207

diverging, 294, 300

optical aperture, 218–219

eyepiece, 230, 231 Index

Lens (cont.)

Mayer, Robert, 135–136

immersed in a material medium,

Mean free path, 124 300–301

Medﬂy (Mediterranean ﬂy), control of,

myopia, 228, 229 177

objective, 230, 231

Membrane

of eye, 219–220

axon

focusing power, 216–217

as leaky insulator, 186

presbyopia and hyperopia, 228, 229

capacitance and resistance, 186

Lever, 9–11

permeability, 184

arm, 279

basilar, 170

elbow movement, 11–15

biological, diﬀusion through,

hip movement, 15–17 128–129

spine movement, 17–19

oval window in ear, 169

standing on tip-toe on one foot,

tympanic, 162, 168, 169–170, 175 19, 20

Membrane protein, solubility, 98

Light, 162, 214

Mercury, viscosity of, 104

emitted by laser, 252

Metabolic rate, 145–146

ﬁber-optic devices and, 237

deﬁned, 146

intensity at retina, 207–208, 209

for selected activities, 146

penetration through tissue, 232

Metabolism, 157

properties, 215

Mho, 291

speed, 293

Micron, 285

vision and, 214–215

Microscope, 231

Limping, 17, 18

compound, 231

Linear momentum, 274

confocal, 232–235

conservation, 275

electron, 247–248

Linear motion, 277

resolution, 231–232

Lines of force, 288 Microvelia, 99

Lipoprotein, solubility, 98

Middle ear, 169–170

Lithium, 241

Eustachian tube, 170

Load carrying, energy consumption, 58–59

hammer, anvil, stirrup, 169

Logarithmic sound intensity, 174

ossicles, 169, 170, 175

Long jump, See Broad jump

Miller, S. L., 271

Loudness, 173–175

Minsky, Marvin, 233

Lubrication, 25

Moisture tension in soil, 92–93

eﬀect on human hip joint, 27

Molecule

Lumbar vertebra, ﬁfth, 17–19

characteristic spectra, 244

Lung

diﬀraction studies with, 250

gas exchange in, 129–130

formation of hydrogen, 244

water vapor and, 155

organic, 270–271

X-ray, 250

transport through diﬀusion, 126–127

Moment arm, 279

Magnetic moment, 258, 259

Moment of inertia, 279

Magnetic resonance imaging (MRI), 257–

Momentum 258, 262–265

angular, 280

functional, 265–266

equations of, 277–278

Magnetism, electricity and, 292

linear, 274

Marangoni propulsion, 99

conservation, 275

Mass, 274

Motion, 1–2

unit and conversion, 285

angular

Matter, kinetic theory of, 116–119

Newton’s laws, 280

Maximum angular velocity, 54, 78–79

vs. linear, 277 Index

Newton’s laws, 274–275

Newton’s

rotational, 30, 31

laws of angular motion, 280

equations for, 278

laws of motion

thermal, 117, 124, 140

ﬁrst, 274

through air, 40–42

second, 275

translational, 30–32

third, 275

Motor neuron, 181 14Nitrogen, 269

MRI, See Magnetic resonance imaging

NMR, See Nuclear magnetic resonance

Muscle

Noble gas, 244

action potentials in, 194

Nodes of Ranvier, 181

biceps, 7, 11–15

Noise

contraction, 8, 95–96

bruit, 111

eﬃciency, 42–43

laminar ﬂow, 113

ﬁbers, 194

Nuclear magnetic resonance (NMR), 257–

insect wings, 75–76 262

myoﬁbrils, 95

imaging with, 262–265

skeletal, 7–9, 95–96

Nuclear spin, Nucleus, 240, 256–257

spindle, 194

transmutation, 257

stimulation by electric current, triceps, 7, 11, 12

Musculoskeletal system,

Objective lens, 230, 231

interconnectedness, 21

Ohm, 290

Myelin, 181

Ohm’s law, 205, 291

Myelinated axon, 192–193

Optical spectra, 243

vs. nonmyelinated, 187

Optics, 214

ﬁber, 235–237

Myoﬁbrils, 95

geometric, 293–295

Myopia, 227

vision and, 214–215

lens for, 228, 229

Oscilloscope, 201–202

Myosin, 95, 96

Osmosis, Ossicles, 169, 170, 175

Near point of the eye, 216–217

Osteoarthritis, 70–71

Neck bone, fracture, 69–70

exercise and, 71

Negative feedback, 209–210

Osteoblast, 197

Negative ion, 287

Osteoclast, 197

Nervous system

Oudin, Paul, 249

action potential, 184–186

Outer ear, 168–169

action potential, propagation, 188–190

ear canal, 169

electrical phenomena and, 180–181

pinna, 168

electrical potentials in axon, 183–184,

tympanic membrane, 162, 168, 169– 185 170, 175

signal propagation, 181

Oxidation of food, 147

surface potentials, 194–196

Oxygen

synaptic transmission, 193–194

consumption, calories produced by, 147

vision and, 226–227

diﬀusion through skin, 129

Neuron, 180, 181–183

small animals, 131–132

axons and dendrites, 181, 183, See also

isotopes of, 256

Axon

oxidation of food, 147

classes, 181

requirement for humans, 130–131

Neutron, Newton, 5

Pacemaker, 202

Newton, Isaac, 1

electronic, 206 Index

Particle, wavelike properties, 246–247

measurement, 113–114

Pascal (Pa), 83

systolic and diastolic, 107

Pascal’s principle, 83–84

venal, 109

Pastuerization, 267

deﬁned, 274

Pendulum

ﬂuid, 82–84

physical, 51–52, 54–56

gas, 118

simple, 48–50

in porous bones, 89

Period, of pendulum motion, 48–49

inside worm, 85

Phosphorus, radioactive, 257, 267, 269

on eardrum, 170

Photodetector, 245

Poiseuille’s equation and, 103–104

Photon, 215

sound, 164–165, 175

Photoreceptor, 222, 225–226

unit and conversion, 285

Photosynthesis, 214 Principia Mathematica, 1

Physics and life, 269–271

Projectile, range of, 37

Piezoelectric eﬀect, 196–197

Protein

Pinna, 168

caloric value, 147

Pitch of sound, 172–173

consumption during fasting, 149

Planck’s constant, 215, 246–247, 258

resilin, 79–80

Plant

solubility of membrane protein and

action potential in, 196

lipoprotein, 98

electricity in, 196

speciﬁc heat, 119

soil water and, 92–93

Proton, 239–240, 287

Plaque, arterial, 111–112

Pulmonary artery, 105

Poise, 103, 104

Pupil, 215

Poiseuille, L. M., 101

deﬁned, 207

Poiseuille’s law, 103–104

Pure tone, 163–164

estimation of blood pressure drop and, P wave, 203 107–108

Positive feedback, 209–210

Quality

Positive ion, 287

image, 218

Posture, 19–21

sound, 171

Potassium ion, axon potential and, 184

Quantum mechanics, 246–247, 270

Potential

axon, 184

Radian, 276

diﬀerence, 289

Radiation, 139

energy, 283–284

electromagnetic, 122–123, 214

Power, 284

food preservation by, 267–268

deﬁned, 78

human body, 153

generated by limbs, 88

solar, 153–154

produced by, 112–113

and soil, 159

required to hover, 76–79

therapy, 266–267

required to stay aﬂoat, 87–88

thermal, 122

unit and conversion, 286

Radioactive

Precession, 260

isotopes, 257

Pregnancy, energy requirements, 149

tracers, 269

Presbyopia, 217

Radioactivity, 256–257

lens for, 229

Random thermal motion, 124, 140

Pressure

Random walk, 124–125

Bernoulli’s equation and, 101

Real image, 297

blood

Reduced eye, 220–222

arterial, 107–109

Reﬂection, 165–166

at capillaries, 107

total internal, 294, 295 Index

Refraction, 165–166

Siemen, 291

deﬁned, 293

Silver, thermal conductivity of, 122

index of, 220

Simple harmonic motion, 48

refractive power of cornea, 219–220

walking in terms of, 50–51

Resilin, 79–80

Sinusoidal sound wave, 163–164, 171, 172

Resistance of air, 40–42

Skeletal muscle, 7–9

Resistivity, 290

contraction, 95–96

Resistor, 290–291

Skin

Resolution

convection and, 151–153

eye, 223–225

emissivity of, 153

microscope, 231–232

evaporative cooling, 156–157

Resonant frequency, 167

frostbite, 157

Respiratory system

oxygen diﬀusion through, 129

diﬀusion process, 129–132

radiative heating of, 153–154

surfactants and breathing, 132

temperature, 150–151

Retina, 215, 222–223

control, 151

cones and rods, 222, 223, 224,

Snell’s law, 235 225–226

deﬁned, 293–294

degeneration arrest, 253–254

Sodium

image size on, 221–222, 223,

ions, 184, 189 229–230

pump, 184

light intensity, control of, 207–208, 209

Soil

photographic ﬁlm and, 217–218

loam vs. clay, 93

Reynold’s number, 104

moisture tension, 92–93

Righting reﬂex, 21

speciﬁc heat, 119

Rods and cones, 222, 223, 224, 225–226

temperature, 158–159

Roentgen, Wilhelm Conrad, 249

water, 92–93

Rolling friction, 24

Solar radiation, 153–154

Root (plant), and pressure, 92

soil and, 159

Rotational motion, 30, 31

Somatosensory system, balance

equations for, 278

maintenance, 21

Running

Sound, 162

broad jump, 39–40

acoustic traps, 176–177

center of mass motion in, 57–58

bell in a jar, 163

energy expended in, 54–56

clinical uses, 177

metabolic rate, 43

frequency, 163, 164, 172–173

on a curved track, 47–48

intensity, 163

speed, 53–54

and loudness, 173–175

Rupture strength, 63

logarithmic, 174

Rutherford, E., 239, 240

perception of, pitch, 172–173

Sensitivity

produced by animals, 176

of ear, 169, 172, 174–175

properties, 162–165

logarithmic, 174

pure tone, 163–164

mechanical reasons for, 175

speed, 164

of eye, 226

wave, 162

Sensory aid, 211

wavelength (λ), 164

Sensory neuron, 181

Speciﬁc heat, 119, 284

Shannon, Claude, 143

Spectral line, 240

Shark, and electric ﬁeld, 198

Spectrometer, 245

Shock, electric, 204–205

Spectroscopy, 244–245

stimulation of muscle with, 206

absorption, 245 Index

Spectroscopy (cont.)

Sweating

emission, 245

as negative feedback, 209

Spectrum, absorption, 243

cooling mechanisms, 155–156

Speed

dehydration, 155

deﬁned, 272

rate, 155

light, 293

Synapse, 193

running, 53–54

synaptic transmission, 193–194

sound, 164

Synovial ﬂuid, 25, 27

walking, 52–53

Systems approach, 209–210

Spindle, 194

Systolic pressure, 107

Spontaneous emission, Spring, Squid, axon of, 183

Telescope, 230–231

Stability

Temperature, 117–118

equilibrium and, 2–3

body, regulation of, 149–151

human body, 4–7

critical, 156

Standing

deﬁned, 117

at an incline, 25–26

skin, 150–151

broad jump, 37–39

Terminal velocity, 41–42

tip-toe on one foot, 19, 20

Thermal conductivity, 120–121

Standing wave, 166–167

in human body, 150, 151

Static equilibrium, 2–3

Thermal motion, 117

deﬁned, 282

random, 124, 140

Static force, 1–2

Thermal radiation, 122

Static friction, 23–24

emitted by soil, 158–159

coeﬃcient, 25

Thermal velocity, 118

Stefan-Boltzmann constant, 123

Thermodynamics, See also Heat

Stenosis, 111, 112

deﬁned, 135

Stethoscope, 111, 113, 177

ﬁrst law, 135–136

electronic, 202

of living systems, 140–142

Stimulated emission, 252

second law, 137–138

Stirrup (middle ear), 169

information and, 143–144

Strength of material, 61

Thermophilic bacteria, 145

bone, 64–68

Thompson, J. J., 239

Stress

Threshold

deﬁned, 62

of hearing, 173, 174

stress cardiomyopathy, 109

of pain, 173, 174

Stretching

of vision, 225–226

longitudinal, 61–62

Tissue

spring, 62–64

light penetration, 232

Stroke, ischemic, 112

thermal conductivity, 122, 150 32Sulphur, 269

Tomography, computerized, 250–251, 257

Surface potential, 194–196

Torque, 279–280

recording of, 202–203

addition of force and, 281–282

Surface tension, 89–91

Torr, 83

insect locomotion on water and,

Torricelli, Evangelista, 83 93–95, 99

Total internal reﬂection, 294, 295

muscle contraction and, 95–96

Tracer, isotopic, 268–269

soil water, 92–93

Transistor ampliﬁer, 211

spherical liquid drops, 91–92

Translational motion, 30

Surfactants, 97–98

energy consumption, 42–43

breathing and, 132

for constant acceleration, 30–32

secreted by insects, 99

high jump, 36–37 Index

long jump

critical ﬂow, 104

standing, 37–39

deﬁned, 272

running, 39–40

terminal, 41–42

projectile range, 37

thermal, 118

through air, 40–42

Venule, 107

vertical jump, 32–35

Vertical jump

Transmutation of nucleus, 257

eﬀect of gravity on, 35

Transport, of molecules, 126–127

height of, 32–35

Triceps, 7 Vespertilionidae bat, echo location,

movement of, 11, 12 175–176

Turbulent ﬂuid ﬂow, 104–105

Vestibular system, balance maintenance,

blood, 110–111 21 T wave, 203

Virtual image, 297

Tympanic membrane, 162, 168, 169–170,

Viscosity, and Poiseuille’s law, 103–104 175

Viscous friction, 24, 103, Vision, 214–215

astigmatic, 227, 228, 229

Ultrasonic

hyperopic, 227, 228, 229

diathermy, 178

image quality, 218–219

ﬂow meter, 178

myopic, 227, 228, 229

waves, 177–178

nervous system and, 226–227

Ultrasound imaging, 177–178

presbyopic, 217, 229

Unit

range, 229–230

calorie, 119

threshold of, 225–226

coulomb, 287

Vitreous humor, 216

diopter, 219

Vocal cord, 176

dyne, 285

Voltage, 289

farads, 291

and current sources, 292

henry, hertz, 163

Walking, 50

kilocalorie, 284

center of mass motion in, 56–57

mho, 291

on injured hip, 17

newton, 5

simple harmonic motion, 50–51

of energy, 286

speed, 52–53

of force, 285

Water

of length, 285

content of food, 148

of mass, 285

density of, and ﬂoating, 87–88

of power, 286

elimination from body, 148

of pressure, 285

index of refraction, 220

pascal (Pa), 83

insect locomotion on, 93–95

poise, 103, 104

latent heat of vaporization, 155

radian, 276

mean free path of molecules in, 124

siemen, 291

osmosis, 129

torr, 83

sea, 89

Uranium, isotopes of, 257

soil, sound and, 166

Vein, 105

speciﬁc heat, 119

blood pressure in, 109

speed of sound in, 164

pulmonary, 105

surface tension, 89

Velocity

viscosity, 104

angular, 276

Wave, See also Sound

maximum, 54, 78–79

deﬁned, 162 Index

Wave (cont.)

heat converted into, 139–140

diﬀraction, 168

implication of second law of thermody

fundamental and harmonic, 171, 172

namics, 138

interference, 166–167

muscular movement, 42 P, 203

Worm

reﬂection and refraction, 165–166

hydrostatic forces in moving, 84–86

standing, 166–167

movement of, 84 T, ultrasonic, 177–178

X-ray, 243, 249–250

wavelength, 164

computerized tomography, 250–251,

Weight, 274 257

loss, 155

of lungs, 250

Whiplash injury, Work

Young’s modulus, 62

chemical energy and, 42

of resilin, 79–80

deﬁned, 43, 282

rupture strength for materials and, 65

This page intentionally left blank This page intentionally left blank This page intentionally left blank This page intentionally left blank This page intentionally left blank <h1>Document Outline</h1> <li>Front Cover</li> <li>Title: Physics in Biology and Medicine</li> <li>ISBN 0123694116</li> <li>Table of Contents (with page links) <ul> <li>1 Static Forces</li> <li>2 Friction</li> <li>3 Translational Motion</li> <li>4 Angular Motion</li> <li>5 Elasticity and Strength of Materials</li> <li>6 Insect Flight</li> <li>7 Fluids</li> <li>8 The Motion of Fluids</li> <li>9 Heat and Kinetic Theory</li> <li>10 Thermodynamics</li> <li>11 Heat and Life</li> <li>12 Waves and Sound</li> <li>13 Electricity</li> <li>14 Electrical Technology</li> <li>15 Optics</li> <li>16 Atomic Physics</li> <li>17 Nuclear Physics</li> <li>Appendices, Bibliography, Answers to Exercises, Index</li> </ul> </li> <li>Preface</li> <li>Abbreviations</li> <li>Chapter 1. Static Forces <ul> <li>1.1 Equilibrium and Stability</li> <li>1.2 Equilibrium Considerations for the Human Body</li> <li>1.3 Stability of the Human Body under the Action of an External Force</li> <li>1.4 Skeletal Muscles</li> <li>1.5 Levers</li> <li>1.6 The Elbow</li> <li>1.7 The Hip</li> <li>1.8 The Back</li> <li>1.9 Standing Tip-Toe on One Foot</li> <li>1.10 Dynamic Aspects of Posture</li> <li>Exercises</li> </ul> </li> <li>Chapter 2. Friction <ul> <li>2.1 Standing at an Incline</li> <li>2.2 Friction at the Hip Joint</li> <li>2.3 Spine Fin of a Catfish</li> <li>Exercises</li> </ul> </li> <li>Chapter 3. Translational Motion <ul> <li>3.1 Vertical Jump</li> <li>3.2 Effect of Gravity on the Vertical Jump</li> <li>3.3 Running High Jump</li> <li>3.4 Range of a Projectile</li> <li>3.5 Standing Broad Jump</li> <li>3.6 Running Broad Jump (Long Jump)</li> <li>3.7 Motion through Air</li> <li>3.8 Energy Consumed in Physical Activity</li> <li>Exercises</li> </ul> </li> <li>Chapter 4. Angular Motion <ul> <li>4.1 Forces on a Curved Path</li> <li>4.2 A Runner on a Curved Track</li> <li>4.3 Pendulum</li> <li>4.4 Walking</li> <li>4.5 Physical Pendulum</li> <li>4.6 Speed of Walking and Running</li> <li>4.7 Energy Expended in Running</li> <li>4.8 Alternate Perspectives on Walking and Running</li> <li>4.9 Carrying Loads</li> <li>Exercises</li> </ul> </li> <li>Chapter 5. Elasticity and Strength of Materials <ul> <li>5.1 Longitudinal Stretch and Compression</li> <li>5.2 A Spring</li> <li>5.3 Bone Fracture: Energy Considerations</li> <li>5.4 Impulsive Forces</li> <li>5.5 Fracture Due to a Fall: Impulsive Force Considerations</li> <li>5.6 Airbags: Inflating Collision Protection Devices</li> <li>5.7 Whiplash Injury</li> <li>5.8 Falling from Great Height</li> <li>5.9 Osteoarthritis and Exercise</li> <li>Exercises</li> </ul> </li> <li>Chapter 6. Insect Flight <ul> <li>6.1 Hovering Flight</li> <li>6.2 Insect Wing Muscles</li> <li>6.3 Power Required for Hovering</li> <li>6.4 Kinetic Energy of Wings in Flight</li> <li>6.5 Elasticity of Wings</li> <li>Exercises</li> </ul> </li> <li>Chapter 7. Fluids <ul> <li>7.1 Force and Pressure in a Fluid</li> <li>7.2 Pascal’s Principle</li> <li>7.3 Hydrostatic Skeleton</li> <li>7.4 Archimedes’ Principle</li> <li>7.5 Power Required to Remain Afloat</li> <li>7.6 Buoyancy of Fish</li> <li>7.7 Surface Tension</li> <li>7.8 Soil Water</li> <li>7.9 Insect Locomotion on Water</li> <li>7.10 Contraction of Muscles</li> <li>7.11 Surfactants</li> <li>Exercises</li> </ul> </li> <li>Chapter 8. The Motion of Fluids <ul> <li>8.1 Bernoulli’s Equation</li> <li>8.2 Viscosity and Poiseuille’s Law</li> <li>8.3 Turbulent Flow</li> <li>8.4 Circulation of the Blood</li> <li>8.5 Blood Pressure</li> <li>8.6 Control of Blood Flow</li> <li>8.7 Energetics of Blood Flow</li> <li>8.8 Turbulence in the Blood</li> <li>8.9 Arteriosclerosis and Blood Flow</li> <li>8.10 Power Produced by the Heart</li> <li>8.11 Measurement of Blood Pressure</li> <li>Exercises</li> </ul> </li> <li>Chapter 9. Heat and Kinetic Theory <ul> <li>9.1 Heat and Hotness</li> <li>9.2 Kinetic Theory of Matter</li> <li>9.3 Definitions</li> <li>9.4 Transfer of Heat</li> <li>9.5 Transport of Molecules by Diffusion</li> <li>9.6 Diffusion through Membranes</li> <li>9.7 The Respiratory System</li> <li>9.8 Surfactants and Breathing</li> <li>9.9 Diffusion and Contact Lenses</li> <li>Exercises</li> </ul> </li> <li>Chapter 10. Thermodynamics <ul> <li>10.1 First Law of Thermodynamics</li> <li>10.2 Second Law of Thermodynamics</li> <li>10.3 Difference between Heat and Other Forms of Energy</li> <li>10.4 Thermodynamics of Living Systems</li> <li>10.5 Information and the Second Law</li> <li>Exercises</li> </ul> </li> <li>Chapter 11. Heat and Life <ul> <li>11.1 Energy Requirements of People</li> <li>11.2 Energy from Food</li> <li>11.3 Regulation of Body Temperature</li> <li>11.4 Control of Skin Temperature</li> <li>11.5 Convection</li> <li>11.6 Radiation</li> <li>11.7 Radiative Heating by the Sun</li> <li>11.8 Evaporation</li> <li>11.9 Resistance to Cold</li> <li>11.10 Heat and Soil</li> <li>Exercises</li> </ul> </li> <li>Chapter 12. Waves and Sound <ul> <li>12.1 Properties of Sound</li> <li>12.2 Some Properties of Waves</li> <li>12.3 Hearing and the Ear</li> <li>12.4 Bats and Echoes</li> <li>12.5 Sounds Produced by Animals</li> <li>12.6 Acoustic Traps</li> <li>12.7 Clinical Uses of Sound</li> <li>12.8 Ultrasonic Waves</li> <li>Exercises</li> </ul> </li> <li>Chapter 13. Electricity <ul> <li>13.1 The Nervous System</li> <li>13.2 Electricity in Plants</li> <li>13.3 Electricity in the Bone</li> <li>13.4 Electric Fish</li> <li>Exercises</li> </ul> </li> <li>Chapter 14. Electrical Technology <ul> <li>14.1 Electrical Technology in Biological Research</li> <li>14.2 Diagnostic Equipment</li> <li>14.3 Physiological Effects of Electricity</li> <li>14.4 Control Systems</li> <li>14.5 Feedback</li> <li>14.6 Sensory Aids</li> <li>Exercises</li> </ul> </li> <li>Chapter 15. Optics <ul> <li>15.1 Vision</li> <li>15.2 Nature of Light</li> <li>15.3 Structure of the Eye</li> <li>15.4 Accommodation</li> <li>15.5 Eye and the Camera</li> <li>15.6 Lens System of the Eye</li> <li>15.7 Reduced Eye</li> <li>15.8 Retina</li> <li>15.9 Resolving Power of the Eye</li> <li>15.10 Threshold of Vision</li> <li>15.11 Vision and the Nervous System</li> <li>15.12 Defects in Vision</li> <li>15.13 Lens for Myopia</li> <li>15.14 Lens for Presbyopia and Hyperopia</li> <li>15.15 Extension of Vision</li> <li>Exercises</li> </ul> </li> <li>Chapter 16. Atomic Physics <ul> <li>16.1 The Atom</li> <li>16.2 Spectroscopy</li> <li>16.3 Quantum Mechanics</li> <li>16.4 Electron Microscope</li> <li>16.5 X-rays</li> <li>16.6 X-ray Computerized Tomography</li> <li>16.7 Lasers</li> <li>Exercises</li> </ul> </li> <li>Chapter 17. Nuclear Physics <ul> <li>17.1 The Nucleus</li> <li>17.2 Magnetic Resonance Imaging</li> <li>17.3 Radiation Therapy</li> <li>17.4 Food Preservation by Radiation</li> <li>17.5 Isotopic Tracers</li> <li>17.6 Laws of Physics and Life</li> <li>Exercises</li> </ul> </li> <li>Appendix A. Basic Concepts in Mechanics <ul> <li>A.1 Speed and Velocity</li> <li>A.2 Acceleration</li> <li>A.3 Force</li> <li>A.4 Pressure</li> <li>A.5 Mass</li> <li>A.6 Weight</li> <li>A.7 Linear Momentum</li> <li>A.8 Newton’s Laws of Motion</li> <li>A.9 Conservation of Linear Momentum</li> <li>A.10 Radian</li> <li>A.11 Angular Velocity</li> <li>A.12 Angular Acceleration</li> <li>A.13 Relations between Angular and Linear Motion</li> <li>A.14 Equations for Angular Momentum</li> <li>A.15 Centripetal Acceleration</li> <li>A.16 Moment of Inertia</li> <li>A.17 Torque</li> <li>A.18 Newton’s Laws of Angular Motion</li> <li>A.19 Angular Momentum</li> <li>A.20 Addition of Forces and Torques</li> <li>A.21 Static Equilibrium</li> <li>A.22 Work</li> <li>A.23 Energy</li> <li>A.24 Forms of Energy</li> <li>A.25 Power</li> <li>A.26 Units and Conversions</li> </ul> </li> <li>Appendix B. Review of Electricity <ul> <li>B.1 Electric Charge</li> <li>B.2 Electric Field</li> <li>B.3 Potential Difference or Voltage</li> <li>B.4 Electric Current</li> <li>B.5 Electric Circuits</li> <li>B.6 Voltage and Current Sources</li> <li>B.7 Electricity and Magnetism</li> </ul> </li> <li>Appendix C. Review of Optics <ul> <li>C.1 Geometric Optics</li> <li>C.2 Converging Lenses</li> <li>C.3 Images of Extended Objects</li> <li>C.4 Diverging Lenses</li> <li>C.5 Lens Immersed in a Material Medium</li> </ul> </li> <li>Bibliography</li> <li>Answers to Numerical Exercises</li> <li>Index (with page links) <ul> <li>A</li> <li>B</li> <li>C</li> <li>D</li> <li>E</li> <li>F</li> <li>G</li> <li>H</li> <li>I</li> <li>J</li> <li>K</li> <li>L</li> <li>M</li> <li>N</li> <li>O</li> <li>P</li> <li>Q</li> <li>R</li> <li>S</li> <li>T</li> <li>U</li> <li>V</li> <li>W</li> <li>X,Y</li> </ul> </li> </body></html>

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