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Physics for Health Sciences Chapter Exam Questions - 1470 Verified Questions

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Physics for Health Sciences

Chapter Exam Questions

Course Introduction

Physics for Health Sciences is designed to introduce students to the fundamental principles of physics with a focus on applications relevant to the health and medical fields. The course covers topics such as mechanics, fluid dynamics, thermodynamics, waves, optics, electricity, and radiation, emphasizing how these concepts underpin technologies and procedures in diagnostics, treatment, and patient care. Through problem-solving, laboratory work, and real-world examples, students gain the scientific foundation necessary to understand modern healthcare technologies and to pursue further studies in health-related disciplines.

Recommended Textbook

College Physics Strategic Approach with Mastering Physics 2nd Edition by Randall D. Knight

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Page 2

Chapter 1: Representing Motion

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Sample Questions

Q1) A weight lifter can bench press 171 kg.How many milligrams (mg)is this?

A)1.71 × 10<sup>8</sup> mg

B)1.71 × 10<sup>9</sup> mg

C)1.71 × 10<sup>7</sup> mg

D)1.71 × 10<sup>6</sup> mg

Answer: A

Q2) Your car gets 34.7 mi/gal on a trip.How many kilometers/liter did it get? (3.79 = 1 gal;1 mi = 1.61 km)

A)14.7 km/l

B)9.16 km/l

C)55.9 km/l

D)32.4 km/l

Answer: A

Q3) A person on a diet loses 1.6 kg in a week.How many micrograms/second (µg/s)are lost?

A)2.6 × 10<sup>3</sup> g/s

B)1.6 × 10<sup>5</sup> g/s

C)44 g/s

D)6.4 × 10<sup>4</sup> g/s

Answer: A

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Chapter 2: Motion in One Dimension

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Sample Questions

Q1) A sports car can go from rest to 32 m/s in 3.88 s.The same car can come to a full stop from that speed in 3.96 s.What is the ratio of starting to stopping accelerations?

A)-1.0

B)1.0

C)-0.98

D)0.98

Answer: A

Q2) An object is dropped from rest into a pit,and accelerates due to gravity at roughly 10 m/s2.It hits the ground in 5 seconds.A rock is then dropped from rest into a second pit,and hits the ground in 10 seconds.How much deeper is the second pit,compared to the first pit? Neglect air resistance.

A)four times deeper

B)two times deeper

C)three times deeper

D)five times deeper

Answer: A

Q3) What quantity is measured by your speedometer (be as specific as possible)?

Answer: Your speedometer tells you the instantaneous speed of your car.

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4

Chapter 3: Vectors and Motion in Two Dimensions

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Sample Questions

Q1) You walk 53 m to the north,then turn 60° to your right and walk another 45 m.Determine the direction of your displacement vector.Express your answer as an angle relative to east.

A)63° N of E

B)50° N of E

C)57° N of E

D)69° N of E

Answer: A

Q2) The magnitude of the displacement vector from A to B can never be less than the distance from A to B,but it can be greater than that distance.

A)True

B)False

Answer: False

Q3) What is the minimum number of vectors (none of which have the same magnitude)for which it is theoretically possible that the sum of those vectors can be equal to zero?

Answer: It is possible with three (or more)vectors.Three is the minimum number for which the condition may be satisfied.

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Chapter 4: Forces and Newtons Laws of Motion

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Sample Questions

Q1) When decelerating quickly in a car,you feel as if you are being thrown forward in your seat.Which one of Newton's Laws most directly explains this effect? Explain your reasoning.

Q2) A child pulls on a wagon handle at an angle 37° above the horizontal with a force of 45 N.If the wagon accelerates at 8.1 m/s<sup>2</sup> horizontally,what is the mass of the wagon? Assume frictional forces are negligible.

A)4.4 kg

B)5.6 kg

C)3.1 kg

D)3.7 kg

Q3) A ball is thrown vertically upward,reaches a highest point,and comes back down.At the top of its path,what forces,if any,act on the ball? Explain your answer.

A)no forces

B)only a downward force

C)only an upward force

D)an upward and a downward force,opposing and equal

Q4) Three children pull on a toy in three different directions,yet the toy does not move.Explain how this could be possible.

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Page 6

Chapter 5: Applying Newtons Laws

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Sample Questions

Q1) A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle.The coefficients of static and kinetic friction between the hockey puck and the metal ramp are µs = 0.40 and µk = 0.30,respectively.The puck's initial speed is 16 m/s.What vertical height does the puck reach above its starting point?

A)8.6 cm

B)17 cm

C)13 cm

D)4.2 cm

Q2) You lean against a 200 kg cabinet.The coefficient of static friction between the cabinet and floor is 0.95.Will the cabinet move? Support your answer.

Q3) Dick and Jane stand on a platform of negligible weight,as shown in the figure.Dick weighs 500 N and Jane weighs 400 N.Jane is supporting some of her weight on the end of the rope she is holding.What is the downward force she is exerting on the platform?

A)0

B)50 N

C)100 N

D)240 N

E)300 N

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7

Chapter 6: Circular Motion,orbits,and Gravity

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Sample Questions

Q1) If a highway curve is properly banked and posted at 45 mph,it is a good idea to drive somewhat below this speed if your tires are bald or if the road is icy.

A)True

B)False

Q2) In the table,the mass of Ekapluto is closest to:

A)1 × 10<sup>22</sup> kg

B)3 × 10<sup>22</sup> kg

C)1 × 10<sup>23</sup> kg

D)3 × 10<sup>23</sup> kg

E)1 × 10<sup>24</sup> kg

Q3) If you stood on a planet having a mass four times higher than Earth's mass,and a radius two times longer than Earth's radius,you would weigh

A)the same as you do on Earth.

B)two times more than you do on Earth.

C)two times less than you do on Earth.

D)four times more than you do on Earth.

Q4) How is it possible for someone to remain in her seat (without any straps)while upside down on a loop-the-loop roller coaster?

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Chapter 7: Rotational Motion

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Sample Questions

Q1) A potter's wheel (a solid,uniform disk)of mass 7.0 kg and radius 0.65 m spins about its central axis.A 2.1 kg lump of clay is dropped onto the wheel at a distance 0.41 m from the axis.Calculate the rotational inertia of the system.

A)1.8 kg m<sup>2</sup>

B)1.5 kg m<sup>2</sup>

C)0.40 kg m<sup>2</sup>

D)2.5 kg m<sup>2</sup>

Q2) A 95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of 15 N · m.What is the angle (assumed to be less than 90°)between the wrench handle and the direction of the applied force?

A)18°

B)14°

C)22°

D)25°

Q3) There must be equal amounts of mass on either side of the center of mass.

A)True

B)False

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Chapter 8: Equilibrium and Elasticity

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Sample Questions

Q1) A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15 degrees above the horizontal.The tension in this wire is greater than ma.

A)True

B)False

Q2) In the figure,the Achilles tendon exerts a force F = 720 N.What is the torque it exerts about the ankle joint?

A)12.2 N m

B)16.2 N m

C)21.2 N m

D)25.9 N m

E)36.0 N m

Q3) A stone rolls down a sloping hillside.The normal force that the surface of the hill exerts on the stone is equal to the stone's weight.

A)True

B)False

Q4) Do all points on a rigid,rotating body have the same angular acceleration? Support your answer.

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10

Chapter 9: Momentum

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Sample Questions

Q1) A child swings a 0.38 kg ball in a circle on a string that is 1.3 m long.If the ball makes 1.2 rev/s,what is the magnitude of the ball's angular momentum?

A)4.8 kgm<sup>2</sup>/s

B)0.8 kgm<sup>2</sup>/s

C)3.8 kgm<sup>2</sup>/s

D)5.3 kgm<sup>2</sup>/s

Q2) Three cars,Car X,Car Y,and Car Z,begin accelerating from rest,at the same time.Car X is more massive than Car Y,which is more massive than Car Z.The net force exerted on each car is identical.After 10 seconds,which car has the most amount of momentum?

A)They all have the same amount of momentum.

B)Car X

C)Car Y

D)Car Z

Q3) As a tile falls from the roof of a building to the ground its momentum is conserved.

A)True

B)False

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Chapter 10: Energy and Work

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Sample Questions

Q1) A cannon recoils after it fires a shell.If you measure the range of the shell,can you find the energy released by the gunpowder?

Q2) Joe and Bill throw identical balls vertically upward.Joe throws his ball with an initial speed of twice as high as Bill's ball.The maximum height of Joe's ball will be

A)four times that of Bill's ball.

B)two times that of Bill's ball.

C)equal to that of Bill's ball.

D)eight times that of Bill's ball.

E)roughly 1.3 times that of Bill's ball.

Q3) A helicopter descends vertically to land with a speed of 4.0 m/s.If the shock absorbers have an initial length of 0.50 m,they compress to 79% of their original length and the air in the tires absorbs 21% of the initial energy as heat,what is the ratio of the spring constant to the helicopter's mass? Assume one landing gear in the craft.

A)1.1 kN/kg-m

B)1.1 N/kg-m

C)11 N/kg-m

D)0.11 kN/kg-m

Q4) Is energy conserved during a two-car collision?

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Page 12

Chapter 11: Using Energy

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Sample Questions

Q1) A Carnot engine operates between two reservoirs with unknown temperatures.If the Carnot engine operates at 43% efficiency,what is the ratio of the kelvin temperatures of the reservoirs,T<sub>c</sub>/T<sub>h</sub>?

A)0.57

B)0.0021

C)0.0016

D)0.42999999

Q2) A fluid in an insulated,flexible bottle is heated by a high resistance wire and expands.If 9 kJ of heat is applied to the system and it does 5 kJ of work,how much does the internal energy change?

A)4 kJ

B)14 kJ

C)-4 kJ

D)45 kJ

Q3) A Carnot engine operating between heat reservoirs at 10°C and 40°C has an efficiency of 75%.

A)True

B)False

Q4) Is liberating heat through combustion a reversible or an irreversible process?

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Chapter 12: Thermal Properties of Matter

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Sample Questions

Q1) 148.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

A)92 s

B)5.3 s

C)22 s

D)410,000 s

Q2) The amount of heat needed to raise the temperature of one mole of an ideal gas by 1.0 K at constant volume is the same for all monatomic gases.

A)True

B)False

Q3) If the root mean square speed of gas molecules is doubled,then both its pressure and its absolute temperature will also be doubled.

A)True

B)False

Q4) 52 g of methane (CH<sub>4</sub>)contain 3.25 moles of this gas.

A)True

B)False

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14

Chapter 13: Fluids

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Sample Questions

Q1) Water flows through a pipe having a varying width.More water flows per second through the wide section than through the narrow section because there is more room for it to flow.

A)True

B)False

Q2) The density of material at the center of a neutron star is approximately 1.00 × 10<sup>18</sup> kg/m<sup>3</sup>.Calculate the mass of a cube of this material that is 1.76 microns on each side.One micron is equal to 1 × 10<sup>-6</sup> m.

A)5.45 kg

B)4.74 kg

C)6.16 kg

D)6.70 kg

Q3) Calculate the pressure exerted on the ground by a 79 kgperson standing on one foot.Assume that the bottom of the person's foot is 13 cm wide and 28 cm long.

A)2.1 × 10<sup>4</sup> Pa

B)2.2 × 10<sup>3 </sup>Pa

C)4.8 × 10<sup>4</sup> Pa

D)5.3 × 10<sup>4</sup> Pa

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Chapter 14: Oscillations

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Sample Questions

Q1) A 0.12 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 570 N/m.The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the x-axis (horizontal).The displacement of the block at time t = 0.20 s is closest to:

A)0.01 m

B)-0.01 m

C)0.08 m

D)-0.08 m

E)0.1 m

Q2) A mass attached to a very light spring executes simple harmonic motion.If you want to double its total energy,you should

A)double the amplitude of vibration while changing nothing else.

B)double the force constant of the spring while changing nothing else.

C)double both the amplitude and force constant.

D)double the mass while changing nothing else.

E)double both the mass and amplitude of vibration.

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Page 16

Chapter 15: Traveling Waves and Sound

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Sample Questions

Q1) The sound from a truck moving at 17.00 m/s reflects from a cliff and is heard by an observer on the truck.What is the change in frequency for a wave with initial wavelength = 0.1500 m?

A)245 Hz

B)2281 Hz

C)2066 Hz

D)2400 Hz

Q2) A weight W is hanging from a light vertical string.If a second weight W is added without stretching the string,the speed of pulses on this string will now be twice as great as it originally was.

A)True

B)False

Q3) For a sound wave in air of frequency 3500 Hz and average intensity 1 W/m<sup>2</sup> (pain threshold)what is the maximum change in pressure (pressure amplitude)of the wave?

A)28.6 N/m<sup>2</sup>

B)816 N/m<sup>2</sup>

C)20.2 N/m<sup>2</sup>

D)3.18 × 10<sup>-6 </sup>N/m<sup>2</sup>

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Page 17

Chapter 16: Superposition and Standing Waves

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Sample Questions

Q1) In Situation 16.1,the frequency of the sound produced by the pipe,in SI units,is closest to:

A)210

B)280

C)350

D)430

E)500

Q2) Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator,whose frequency range is 1595 Hz to 2158 Hz.A point P is located 4.7 m from one loudspeaker and 3.6 m from the other.The speed of sound is 344 m/s.The frequency produced by the oscillator,for which destructive interference occurs at point P,in SI units,is closest to:

A)2033

B)2127

C)2095

D)2064

E)2001

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Chapter 17: Wave Optics

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Sample Questions

Q1) In a double slit interference pattern produced by light of wavelength ,the dark spots occur at points for which the path difference between the light from the two slits is equal to m /2,where m = 1,2,3,....

A)True

B)False

Q2) Two radio antennas are 130 m apart on a north-south line.The two antennas radiate in phase at a frequency of 3.6 MHz.All radio measurements are made far from the antennas.The smallest angle,reckoned east of north from the antennas,at which constructive interference of two radio waves occurs,is closest to:

A)50°

B)55°

C)45°

D)40°

E)35°

Q3) A diffraction pattern of a single slit is compared to the diffraction pattern from a circular aperture of diameter r = w.Are they similar,equal?

Q4) What is the difference between diffraction and interference?

Q5) How wide is a single slit that gives its first minimum at 90°?

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Chapter 18: Ray Optics

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Sample Questions

Q1) A screen and a converging lens of focal length f are arranged to have an image of the moon fall on the screen.What is the distance between the lens and the screen?

A)infinity

B)f

C)2f

D)f/2

Q2) A fish appears to be 2.00 m below the surface of a pond when viewed almost directly above by a fisherman.What is the actual depth of the fish? (n<sub>water</sub> = 1.33)

A)2.66 m

B)0.67 m

C)1.5 m

D)0.38 m

Q3) When moving a convex lens toward and away from your eye it reaches a point where the entire lens appears a single color.What is this point? Why?

Q4) What experiment could you quickly do to detect the difference between a real diamond and an identically shaped fake?

Q5) Why shouldn't you spray water on your roses at noon?

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Chapter 19: Optical Instruments

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Sample Questions

Q1) The image of a tree on a 35 mm color slide is 1.7 mm high.It is to be projected onto a screen 8.0 m from the slide,and is to appear 559 mm high.(a)What focal length lens (in meters)is needed? (b)What is the distance in meters between the lens and the slide? (c)What is the magnification of the system?

A)(a)0.02 m (b)0.02 m

(c)329

B)(a)0.02 m (b)7.98 m

(c)0.00

C)(a)0.02 m (b)-0.02 m

(c)0.00

D)(a)0.02 m (b)-8.02 m

(c)0.00

Q2) In Situation 19.2,the distance between the object and the focal point of the objective,in mm,is closest to:

A)0.13

B)0.18

C)0.23

D)0.28

E)0.33

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Page 21

Chapter 20: Electric Fields and Forces

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Q1) What is the electric field strength at x = 0 m,y = 0 m produced by two electrons,one at x = 0.0001 m,y = 0 m and the other at x = -0.0001 m,y = 0 m? (The value of k is 9.0 × 10<sup>9</sup> N·m<sup>2</sup>/C<sup>2</sup>. )

A)0 N/C

B)1.8 × 10<sup>-19</sup> N/C

C)2.88 × 10<sup>-19</sup> N/C

D)5.76 × 10<sup>-19</sup> N/C

Q2) The more closely electric field lines are packed together,the stronger the field.

A)True

B)False

Q3) A metal sphere is insulated electrically and is given a charge.If 25 electrons are added to the sphere in giving a charge,how many Coulombs are added to the sphere?

A)- 4.0 × 10-18 C

B)- 4.0 × 10-20 C

C)- 40 C

D)- 25 C

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Chapter 21: Electric Potential

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Q1) A small object carries a charge of 10.0 C.If the object is so small that it can be regarded as a point charge,what is the energy density at a distance of 2.0 m from the charge? (The value of k is 9.0 \(\times\) 10<sup>9</sup> N·m<sup>2</sup>/C<sup>2</sup>. )

A)2.2 mJ/m<sup>3</sup>

B)4.5 mJ/m<sup>3</sup>

C)9.0 mJ/m<sup>3</sup>

D)18 mJ/m<sup>3</sup>

Q2) If an object is at zero potential,it must be uncharged.

A)True

B)False

Q3) A 1.0 F capacitor has a potential difference of 6.0 V applied across its plates.If the potential difference across its plates is increased to 8.0 V,how much additional energy does the capacitor store?

A)14 J

B)28 J

C)2.0 J

D)4.0 J

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Chapter 22: Current and Resistance

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Q1) A tube of mercury with resistivity 9.84 × 10<sup>-7 </sup> ·m has a 23.0 N/C electric field inside the column of mercury.How much current is flowing,if the diameter of the tube is ?

A)18 A

B)180 A

C)29 A

D)280 A

Q2) The charge carriers in metals are electrons,but this is not necessarily true for other types of material.

A)True

B)False

Q3) If there is an electric field inside of a conductor,then current must be flowing through this conductor.

A)True

B)False

Q4) Lightening is a discharge of electrons that commonly is greater than is needed to neutralize a positive charge.A series of strokes,each in the opposite direction of the previous stroke,occur to overcome this excessive discharge.Why do all of these strokes follow the same path,causing a flickering effect?

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Chapter 23: Circuits

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Q1) A 10.0 V battery is connected across two resistors in series.If the resistors have resistances of 840.0 and 590.0 ,what is the voltage drop across the 590.0 resistor?

A)4.1 V

B)5.9 V

C)14 V

D)7.0 V

Q2) The potential across the terminals of a store-bought 1.5 V AAA battery always remains at 1.5 V unless the battery has gone dead.

A)True

B)False

Q3) Of voltmeters and ammeters,which is/are connected in series?

Q4) In a discharging RC circuit,it takes one time constant for the capacitor to discharge completely.

A)True

B)False

Q5) Why is it appropriate that electromotive force be measured in volts?

Q6) The high potential end of a resistor is the end at which the current enters it.

A)True

B)False

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Chapter 24: Magnetic Fields and Forces

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Q1) Two long,parallel bars carry equal currents in opposite directions.The magnetic fields due to these two currents cancel each other midway between the two bars.

A)True

B)False

Q2) A wire carrying a current is shaped in the form of a circular loop of radius 4.0 mm.If the magnetic field strength at its center is 1.1 mT with no external magnetic fields contributing to it,what is the magnitude of the current that flows through the wire?

A)7.0 A

B)28 A

C)14 A

D)17 A

Q3) A metal wire is bent into a square and carries a uniform current throughout it.The net magnetic field at the center of this square is zero.

A)True

B)False

Q4) The net magnetic field inside a conductor must be zero.

A)True

B)False

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Chapter 25: Electromagnetic Induction and Electromagnetic Waves

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Q1) In the figure,a C-shaped conductor is in a uniform magnetic field B,which is increasing.The polarity of the induced emf in terminals X and Y is:

A)X and Y are at the same potential

B)X is positive and Y is negative

C)Y is positive and X is negative

Q2) A 2.0 m conductor is formed into a square and placed in the horizontal xy-plane.A magnetic field is oriented 30.0º above the horizontal with a strength of 9.0 T.What is the magnetic flux through the conductor?

A)1.1 T m<sup>2</sup>

B)1.9 T m<sup>2</sup>

C)2.3 T m<sup>2</sup>

D)18 T m<sup>2</sup>

Q3) Find the wavelength (in nm)of a 5.83 eV photon.

A)213 nm

B)181 nm

C)234 nm

D)253 nm

Q4) By how much are the electric and magnetic fields out of phase in an electromagnetic wave?

Page 27

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Chapter 26: Ac Electricity

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Sample Questions

Q1) In an AC circuit consisting of a resistor and capacitor in series with each other,the sum of the peak voltages across the resistor and across the capacitor must add up to the emf of the AC source.

A)True

B)False

Q2) The reactance of a capacitor is 7.0 k at a frequency of 0.30 kHz.What is the capacitance?

A)0.076 F

B)0.48 F

C)3.0 F

D)0.107 F

Q3) A series RLC circuit has a peak current of 1.0 A with a frequency of 66 kHz.If the resistance of the circuit is 51 k the capacitance of the circuit is 13 F,and the inductance of the circuit is 30 H,determine the average power of the circuit over one cycle.

A)26,000 W

B)77,000 W

C)7700 W

D)4100 W

Q4) If a circuit doubles its peak voltage,what happens to its rms voltage?

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Chapter 27: Relativity

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Sample Questions

Q1) Adding heat to an object will increase its mass because the added heat energy is equivalent to mass.

A)True

B)False

Q2) Explain why it is impossible for an object to travel at the speed of light.

Q3) Assume that a typical city consumes electrical energy at a rate of 2.0 × 10<sup>-9</sup> W.How many kilograms of matter would have to be converted entirely into energy in order to keep this city running for 21 weeks?

A)0.28 kg

B)0.32 kg

C)0.40 kg

D)0.48 kg

Q4) A particle is moving at about 0.86 c.By what percentage is the Newtonian expression for momentum in error? (The percentage error is the difference between the erroneous and correct expressions,relative to the correct one. )

A)49%

B)40%

C)55%

D)62%

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Chapter 28: Quantum Physics

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Sample Questions

Q1) A photocathode whose work function is 2.9 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm.The range of the wavelength band in this white light illumination for which photoelectrons are not produced,in nm,is closest to:

A)430 to 700

B)400 to 480

C)430 to 480

D)400 to 430

E)480 to 700

Q2) Increasing the kinetic energy of an electron increases its de Broglie wavelength.

A)True

B)False

Q3) The maximum kinetic energy of photoelectrons from a metal is equal to the work function of that metal.

A)True

B)False

Q4) Typical photoelectric work functions are in the range of a few joules.

A)True

B)False

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Chapter 29: Atoms and Molecules

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Q1) The shortest wavelength of a photon that can be emitted by a hydrogen atom,for which the initial state is n = 12,is closest to:

A)92 nm

B)82 nm

C)72 nm

D)62 nm

E)52 nm

Q2) Consider an atom with the electron configuration 1s<sup>2</sup>2s<sup>2</sup>2p<sup>6</sup>3s<sup>2</sup>3p<sup>6</sup>.Which of the following is an accurate statement concerning this atom?

A)The atomic number of this atom is Z = 11.

B)This atom is in an excited state.

C)This atom has a non-zero angular momentum.

D)This atom is most likely to give rise to an ion with charge +2e.

E)This atom would probably be very inert chemically.

Q3) All atoms of a given element contain exactly the same number of protons in their nucleus,but they may have different numbers of neutrons.

A)True

B)False

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Page 31

Chapter 30: Nuclear Physics

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Sample Questions

Q1) In massive stars,three helium atoms fuse together,forming a carbon nucleus.This reaction heats the core of the star.The net mass of the three helium nuclei must therefore be

A)higher than that of the carbon nucleus.

B)less than that of the carbon nucleus.

C)the same as that of the carbon nucleus (mass is always conserved).

Q2) The primary reason very large nuclei are unstable is due to A)the cumulative repulsive force amongst the protons.

B)the cumulative attractive force between the protons and the orbiting electrons.

C)the repulsive force between the neutrons and the protons.

Q3) The material used in nuclear bombs is <sup>239</sup>Pu,with a half-life of about 20,000 years.How long must we wait for a buried stockpile of this substance to decay to 4% of its original <sup>239</sup>Pu mass?

A)93 thousand years

B)64 thousand years

C)45 thousand years

D)0.80000001 thousand years

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Page 32

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