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PHYF144 Tutorial Department of Engineering Sciences and Mathematics, COE

1

Chapter 1: Temperature

2. The temperature difference between the inside and

outside of an automobile engine is 450°C. Express

this temperature difference on (a) the Fahrenheit

scale and (b) the Kelvin scale.

4. The melting point of gold is 1064 °C, and its boiling

point is 2660 °C. (a) Express these temperatures in

Kelvin. (b) Compute the difference between these

temperatures in Celsius degrees and Kelvin.

7. A thin brass ring of inner diameter 10.00 cm at 20.0

°C is warmed and slipped over an aluminum rod

of diameter 10.01 cm and at 20.0 °C. Assuming the

average coefficient of linear expansion are

constant, (a) to what temperature must this

combination be cooled to separate the parts?

Explain whether this separation is attainable. (b)

What if? What if the aluminum rod were 10.02 cm

in diameter?

11. A hollow aluminum cylinder 20.0 cm deep has an

internal capacity of 2.000 L at 20.0°C. It is filled

with turpentine and then slowly warmed to

80.0°C. (a) How much turpentine overflows? (b) If

the cylinder is then cooled back to 20.0 °C, how far

below the cylinder’s rim does the turpentine’s

surface recede?

12. At 20.0°C, an aluminum ring has inner diameter

of 5.0000 cm and a brass rod has a diameter of

5.0500 cm. (a) if only the ring is warmed, what

temperature must it reach so that it will just slip

over the rod? (b) What if? If both the ring and the

rod are warmed together, what temperature must

they both reached so that the ring barely slips over

the rod? Would this latter process work? Explain.

13. A volumetric flask made of Pyrex is calibrated at

20.0°C. It is filled to the 100-mL mark with 35.0°C

acetone. (a) What is the volume of the acetone

when it cools to 20.0°C? (b) How significant is the

change in volume of the flask?

30. The density of gasoline is 730 kg/m3 at 0°C. Its

average coefficient of volume expansion is 9.60 ×

10-4 (°C)-1. Assume 1.00 gal of gasoline occupies

0.00380 m3. How many extra kilograms of gasoline

would you get if you bought 10.0 gal of gasoline

at 0°C rather than a 20.0°C from a pump that is

not temperature compensated?

31. A mercury thermometer is constructed as

shown in Figure P19.31. The capillary tube has

a diameter of 0.00400 cm, and the bulb has a

diameter of 0.250 cm. Ignoring the expansion of

the glass, find the change in the height of the

mercury column that occurs with a

temperature change of 30.0°C.

Figure P19.31

43. Two concrete spans of a 250-m-long bridge are

placed end to end so that no room is allowed

for expansion (Fig. P19.43a). If a temperature

increase of 20.0°C occurs, what is the height y

to which the spans rise when they buckle (Fig.

P19.43b)?

Figure P19.43


2

Chapter 2: The First Law of Thermodynamics

24. (a) Determine the work done on a fluid that

expands from i to f as indicated in Figure P20.24.

(b) What If? How much work is performed on the

fluid if it is compressed from f to i along the same

path?

Figure P20.24

25. An ideal gas is enclosed in a cylinder with a

movable piston on top of it. The piston has a mass

of 8 000 g and an area of 5.00 cm2 and is free to

slide up and down, keeping the pressure of the gas

constant. How much work is done on the gas as

the temperature of 0.200 mol of the gas is raised

from 20.0°C to 300°C?

27. One mole of an ideal gas is heated slowly so that

it goes from the PV state (P0, V0), to (3P0, 3V0), in

such a way that the pressure is directly

proportional to the volume. (a) How much work is

done on the gas in the process? (b) How is the

temperature of the gas related to its volume during

this process?

28. A gas is compressed at a constant pressure of

0.800 atm from 9.00 L to 2.00 L. In the process, 400 J

of energy leaves the gas by heat. (a) What is the

work done on the gas? (b) What is the change in its

internal energy?

30. A gas is taken through the cyclic process

described in Figure P20.30. (a) Find the net energy

transferred to the system by heat during one

complete cycle. (b) What If? If the cycle is

reversed—that is, the process follows the path

ACBA—what is the net energy input per cycle by

heat?

Figure P20.30

32. A sample of an ideal gas goes through the

process shown in Figure P20.32. From A to B,

the process is adiabatic; from B to C, it is

isobaric with 100 kJ of energy entering the

system by heat. From C to D, the process is

isothermal; from D to A, it is isobaric with 150

kJ of energy leaving the system by heat.

Determine the difference in internal energy

Eint,B – Eint,A.

Figure P20.32

35. An ideal gas initially at 300 K undergoes an

isobaric expansion at 2.50 kPa. If the volume

increases from 1.00 m3 to 3.00 m3 and 12.5 kJ is

transferred to the gas by heat, what are (a) the

change in its internal energy and (b) its final

temperature?

43. A bar of gold is in thermal contact with a bar

of silver of the same length and area (Fig.

P20.43). One end of the compound bar is

maintained at 80.0°C while the opposite end is

at 30.0°C. When the energy transfer reaches

steady state, what is the temperature at the

junction?

Figure P20.43


3

44. A thermal window with an area of 6.00 m2 is

constructed of two layers of glass, each 4.00 mm

thick, and separated from each other by an air

space of 5.00 mm. If the inside surface is at 20.0°C

and the outside is at –30.0°C, what is the rate of

energy transfer by conduction through the

window?

47. The surface of the Sun has a temperature of about

5 800 K. The radius of the Sun is 6.96 108 m.

Calculate the total energy radiated by the Sun

each second. Assume that the emissivity is 0.965.


4

Chapter 3: The Kinetic Theory of Gases

3. A sealed cubical container 20.0 cm on a side

contains three times Avogadro's number of

molecules at a temperature of 20.0°C. Find the force

exerted by the gas on one of the walls of the

container.

7. (a) How many atoms of helium gas fill a balloon

having a diameter of 30.0 cm at 20.0°C and 1.00

atm? (b) What is the average kinetic energy of the

helium atoms? (c) What is the root-mean-square

speed of the helium atoms?

9. A cylinder contains a mixture of helium and argon

gas in equilibrium at 150°C. (a) What is the average

kinetic energy for each type of gas molecule? (b)

What is the root-mean-square speed of each type of

molecule?

10. A 5.00-L vessel contains nitrogen gas at 27.0C

and 3.00 atm. Find (a) the total translational kinetic

energy of the gas molecules and (b) the average

kinetic energy per molecule.

13. A 1.00-mol sample of hydrogen gas is heated at

constant pressure from 300 K to 420 K. Calculate (a)

the energy transferred to the gas by heat, (b) the

increase in its internal energy, and (c) the work

done on the gas.

18. A vertical cylinder with a heavy piston contains

air at 300 K. The initial pressure is 200 kPa and the

initial volume is 0.350 m3. Take the molar mass of

air as 28.9 g/mol and assume that CV = 5R/2. (a)

Find the specific heat of air at constant volume in

units of J/kgC. (b) Calculate the mass of the air in

the cylinder. (c) Suppose the piston is held fixed.

Find the energy input required to raise the

temperature of the air to 700 K. (d) What If?

Assume again the conditions of the initial state and

that the heavy piston is free to move. Find the

energy input required to raise the temperature to

700 K.

21. A 1.00-mol sample of an ideal monatomic gas is at

an initial temperature of 300 K. The gas undergoes

an isovolumetric process acquiring 500 J of energy

by heat. It then undergoes an isobaric process

losing this same amount of energy by heat.

Determine (a) the new temperature of the gas and

(b) the work done on the gas.

24. During the compression stroke of a certain

gasoline engine, the pressure increases from 1.00

atm to 20.0 atm. If the process is adiabatic and

the fuel-air mixture behaves as a diatomic ideal

gas, (a) by what factor does the volume change

and (b) by what factor does the temperature

change? (c) Assuming that the compression

starts with 0.016 0 mol of gas at 27.0C, find the

values of Q, W, and Eint that characterize the

process.

29. A 4.00-L sample of a diatomic ideal gas with

specific heat ratio 1.40, confined to a cylinder, is

carried through a closed cycle. The gas is

initially at 1.00 atm and at 300 K. First, its

pressure is tripled under constant volume.

Then, it expands adiabatically to its original

pressure. Finally, the gas is compressed

isobarically to its original volume. (a) Draw a PV

diagram of this cycle. (b) Determine the volume

of the gas at the end of the adiabatic expansion.

(c) Find the temperature of the gas at the start of

the adiabatic expansion. (d) Find the

temperature at the end of the cycle. (e) What

was the net work done on the gas for this cycle?

31. How much work is required to compress 5.00

mol of air at 20.0°C and 1.00 atm to one tenth of

the original volume (a) by an isothermal

process? (b) by an adiabatic process? (c) What is

the final pressure in each of these two cases?


5

Chapter 4: Fluid Mechanics

3. A 50.0-kg woman balances on one heel of a pair of

high-heeled shoes. If the heel is circular and has a

radius of 0.500 cm, what pressure does she exert

on the floor?

4. The four tires of an automobile are inflated to a

gauge pressure of 200 kPa. Each tire has an area of

0.024 0 m2 in contact with the ground. Determine

the weight of the automobile.

6. (a) Calculate the absolute pressure at an ocean

depth of 1 000 m. Assume the density of seawater

is 1 024 kg/m3 and that the air above exerts a

pressure of 101.3 kPa. (b) At this depth, what force

must the frame around a circular submarine

porthole having a diameter of 30.0 cm exert to

counterbalance the force exerted by the water?

14. The tank in Figure P14.14 is filled with water 2.00

m deep. At the bottom of one side wall is a

rectangular hatch 1.00 m high and 2.00 m wide,

which is hinged at the top of the hatch. (a)

Determine the force the water exerts on the hatch.

(b) Find the torque exerted by the water about the

hinges.

22. (a) A light balloon is filled with 400 m3 of helium.

At 0C, the balloon can lift a payload of what

mass? (b) What If? In Table 14.1, observe that the

density of hydrogen is nearly one-half the density

of helium. What load can the balloon lift if filled

with hydrogen?

Figure P14.14

29.A cube of wood having an edge dimension of 20.0

cm and a density of 650 kg/m3 floats on water. (a)

What is the distance from the horizontal top

surface of the cube to the water level? (b) How

much lead weight has to be placed on top of the

cube so that its top is just level with the water?

30. A spherical aluminum ball of mass 1.26 kg

contains an empty spherical cavity that is

concentric with the ball. The ball just barely

floats in water. Calculate (a) the outer radius

of the ball and (b) the radius of the cavity.

35.A plastic sphere floats in water with 50.0

percent of its volume submerged. This same

sphere floats in glycerin with 40.0 percent of

its volume submerged. Determine the

densities of the glycerin and the sphere.

39. A large storage tank, open at the top and filled

with water, develops a small hole in its side at

a point 16.0 m below the water level. If the rate

of flow from the leak is 2.50 10–3 m3/min,

determine (a) the speed at which the water

leaves the hole and (b) the diameter of the

hole.

40. A village maintains a large tank with an open

top, containing water for emergencies. The

water can drain from the tank through a hose

of diameter 6.60 cm. The hose ends with a

nozzle of diameter 2.20 cm. A rubber stopper

is inserted into the nozzle. The water level in

the tank is kept 7.50 m above the nozzle. (a)

Calculate the friction force exerted on the

stopper by the nozzle. (b) The stopper is

removed. What mass of water flows from the

nozzle in 2.00 h? (c) Calculate the gauge

pressure of the flowing water in the hose just

behind the nozzle.


6

Chapter 5: Oscillatory Motion

13. A 1.00-kg object is attached to a horizontal spring.

The spring is initially stretched by 0.100 m, and

the object is released from rest there. It proceeds

to move without friction. The next time the speed

of the object is zero is 0.500 s later. What is the

maximum speed of the object?

19. A 50.0-g object connected to a spring with a force

constant of 35.0 N/m oscillates on a horizontal,

frictionless surface with amplitude of 4.00 cm.

Find (a) the total energy of the system and (b) the

speed of the object when the position is 1.00 cm.

Find (c) the kinetic energy and (d) the potential

energy when the position is 3.00 cm.

23. A particle executes simple harmonic motion with

an amplitude of 3.00 cm. At what position does

its speed equal one half of its maximum speed?

32. A simple pendulum is 5.00 m long. (a) What is the

period of small oscillations for this pendulum if it

is located in an elevator accelerating upward at

5.00 m/s2? (b) What is its period if the elevator is

accelerating downward at 5.00 m/s2? (c) What is

the period of this pendulum if it is placed in a

truck that is accelerating horizontally at 5.00

m/s2?

53. A large block P executes horizontal simple

harmonic motion as it slides across a frictionless

surface with a frequency f = 1.50 Hz. Block B rests

on it, as shown in Figure P15.53, and the

coefficient of static friction between the two is s

= 0.600. What maximum amplitude of oscillation

can the system have if block B is not to slip?

Figure P15.53 Problems 53 and 54.

54. A large block P executes horizontal simple

harmonic motion as it slides across a frictionless

surface with a frequency f. Block B rests on it, as

shown in Figure P15.53, and the coefficient of

static friction between the two is s. What

maximum amplitude of oscillation can the

system have if the upper block is not to slip?

63. A simple pendulum with a length of 2.23 m

and a mass of 6.74 kg is given an initial speed

of 2.06 m/s at its equilibrium position. Assume

it undergoes simple harmonic motion, and

determine its (a) period, (b) total energy, and

(c) maximum angular displacement.

67. A ball of mass m is connected to two rubber

bands of length L, each under tension T, as in

Figure P15.67. The ball is displaced by a small

distance y perpendicular to the length of the

rubber bands. Assuming that the tension does

not change, show that (a) the restoring force is

–(2T/L)y and (b) the system exhibits simple

harmonic motion with an angular frequency

2T / mL .

Figure P15.67

71. A block of mass m is connected to two springs

of force constants k1 and k2 as shown in

Figures P15.71a and P15.71b. In each case, the

block moves on a frictionless table after it is

displaced from equilibrium and released.

Show that in the two cases the block exhibits

simple harmonic motion with periods

Figure P15.71

(a) T 2m k1 k2

k1k2

(b) T 2m

k1 k2


7

Chapter 6: Wave Motion

2. Ocean waves with a crest-to-crest distance of 10.0

m can be described by the wave function y(x, t) =

(0.800 m) sin[0.628(x - vt)], where v = 1.20 m/s. (a)

Sketch y(x, t) at t = 0. (b) Sketch y(x, t) at t = 2.00 s.

Note that the entire wave form has shifted 2.40 m

in the positive x direction in this time interval.

7. A sinusoidal wave is traveling along a rope. The

oscillator that generates the wave completes 40.0

vibrations in 30.0 s. Also, a given maximum

travels 425 cm along the rope in 10.0 s. What is the

wavelength?

9. A wave is described by y = (2.00 cm) sin (kx - t),

where k = 2.11 rad/m, = 3.62 rad/s, x is in meters,

and t is in seconds. Determine the amplitude,

wavelength, frequency, and speed of the wave.

15. (a) Write the expression for y as a function of x

and t for a sinusoidal wave traveling along a rope

in the negative x direction with the following

characteristics: A = 8.00 cm, = 80.0 cm, f = 3.00

Hz, and y(0, t) = 0 at t = 0. (b) What If? Write the

expression for y as a function of x and t for the

wave in part (a) assuming that y(x, 0) = 0 at the

point x = 10.0 cm.

18. A transverse sinusoidal wave on a string has a

period T = 25.0 ms and travels in the negative x

direction with a speed of 30.0 m/s. At t = 0, a

particle on the string at x = 0 has a transverse

position of 2.00 cm and is traveling downward

with a speed of 2.00 m/s. (a) What is the

amplitude of the wave? (b) What is the initial

phase angle? (c) What is the maximum transverse

speed of the string? (d) Write the wave function

for the wave.

22. Transverse waves with a speed of 50.0 m/s are to

be produced in a taut string. A 5.00-m length of

string with a total mass of 0.060 0 kg is used.

What is the required tension?

27. Transverse waves travel with a speed of 20.0 m/s

in a string under a tension of 6.00N. What tension

is required for a wave speed of 30.0 m/s in the

same string?

31. A 30.0-m steel wire and a 20.0-m copper wire,

both with 1.00-mm diameters, are connected end

to end and stretched to a tension of 150 N. How

long does it take a transverse wave to travel

the entire length of the two wires?

39. A sinusoidal wave on a string is described by

the equation y = (0.15 m) sin (0.80x - 50t) where

x and y are in meters and t is in seconds. If the

mass per unit length of this string is 12.0 g/m,

determine (a) the speed of the wave, (b) the

wavelength, (c) the frequency, and (d) the

power transmitted to the wave

49. The wave function for a traveling wave on a

taut string is (in SI units)

y(x,t) = (0.350 m) sin(10 t – 3 x + /4)

(a) What are the speed and direction of travel of

the wave? (b) What is the vertical position of an

element of the string at t = 0, x = 0.100 m? (c)

What are the wavelength and frequency of the

wave? (d) What is the maximum magnitude of

the transverse speed of the string?


8

Chapter 7: Standing wave

5. Two sinusoidal waves are described by the wave

functions

y1 = (5.00 m) sin[(4.00x – 1 200t)] and

y2 = (5.00 m) sin[(4.00x – 1 200t – 0.250)]

where x, y1, and y2 are in meters and t is in

seconds. (a) What is the amplitude of the

resultant wave? (b) What is the frequency of the

resultant wave?

11. Two sinusoidal waves in a string are defined by

the functions

y1 = (2.00 cm) sin(20.0x – 32.0t) and

y2 = (2.00 cm) sin(25.0x – 40.0t)

where y and x are in centimeters and t is in

seconds. (a) What is the phase difference between

these two waves at the point x = 5.00 cm at t =

2.00 s? (b) What is the positive x value closest to

the origin for which the two phases differ by

at t = 2.00 s? (This is where the two waves

add to zero.)

14. Two waves in a long string are given by

y1 0.015 0 m cos

x

2 40t

and

y2 0.015 0 m cos

x

2 40t

where y1, y2, and x are in meters and t is in

seconds. (a) Determine the positions of the nodes

of the resulting standing wave. (b) What is the

maximum transverse position of an element of

the string at the position x = 0.400 m?

17 Two sinusoidal waves combining in a medium are

described by the wave functions

y1 = (3.0 cm) sin(x + 0.60t) and

y2 = (3.0 cm) sin(x – 0.60t)

where x is in centimeters and t is in seconds.

Determine the maximum transverse position of an

element of the medium at (a) x = 0.250cm, (b) x =

0.500 cm, and (c) x = 1.50 cm. (d) Find the three

smallest values of x corresponding to antinodes.

22. A vibrator, pulley, and hanging object are

arranged as in Figure P18.21, with a compound

string, consisting of two strings of different

masses and lengths fastened together end-to-end.

The first string, which has a mass of 1.56 g and a

length of 65.8 cm, runs from the vibrator to the

junction of the two strings. The second string runs

from the junction over the pulley to the suspended

6.93-kg object. The mass and length of the string

from the junction to the pulley are, respectively,

6.75 g and 95.0 cm. (a) Find the lowest

frequency for which standing waves are

observed in both strings, with a node at the

junction. The standing wave patterns in the

two strings may have different numbers of

nodes. (b) What is the total number of nodes

observed along the compound string at this

frequency, excluding the nodes at the vibrator

and the pulley?

Figure P18.21 Problems 21 and 22.

27. A cello A-string vibrates in its first normal

mode with a frequency of 220 Hz. The

vibrating segment is 70.0 cm long and has a

mass of 1.20 g. (a) Find the tension in the

string. (b) Determine the frequency of

vibration when the string vibrates in three

segments.

31. A standing-wave pattern is observed in a thin

wire with a length of 3.00 m. The equation of

the wave is

y = (0.002 m) sin( x)cos(100 t)

where x is in meters and t is in seconds. (a)

How many loops does this pattern exhibit? (b)

What is the fundamental frequency of

vibration of the wire? (c) What If? If the

original frequency is held constant and the

tension in the wire is increased by a factor of

9, how many loops are present in the new

pattern?

63. Two wires are welded together end to end.

The wires are made of the same material, but

the diameter of one is twice that of the other.

They are subjected to a tension of 4.60 N. The

thin wire has a length of 40.0 cm and a linear

mass density of 2.00 g/m. The combination is

fixed at both ends and vibrated in such a way

that two antinodes are present, with the node

between them being right at the weld. (a)

What is the frequency of vibration? (b) How

long is the thick wire?


9

67. Two waves are described by the wave functions

y1(x, t) = 5.0 sin(2.0x – 10t) and

y2(x, t) = 10 cos(2.0x – 10t)

where y1, y2, and x are in meters and t is in

seconds. Show that the wave resulting from their

superposition is also sinusoidal. Determine the

amplitude and phase of this sinusoidal wave.

69. A 12.0-kg object hangs in equilibrium from a

string with a total length of L = 5.00 m and a

linear mass density of = 0.00100 kg/m. The

string is wrapped around two light, frictionless

pulleys that are separated by a distance of d =

2.00 m (Fig. P18.69a). (a) Determine the tension in

the string. (b) At what frequency must the string

between the pulleys vibrate in order to form the

standing wave pattern shown in Figure P18.69b?

Figure P18.69

Chapter 8: The Nature of Light and the Laws

of Geometric Optics

3. In an experiment to measure the speed of light

using the apparatus of Fizeau (see Fig. 35.2), the

distance between light source and mirror was

11.45 km and the wheel had 720 notches. The

experimentally determined value of c was 2.998

× 108 m/s. Calculate the minimum angular speed

of the wheel for this experiment.

Figure 35.2

6. The two mirrors illustrated in Figure P35.6

meet at a right angle. The beam of light in the

vertical plane P strikes mirror 1 as shown. (a)

Determine the distance the reflected light beam

travels before striking mirror 2. (b) In what

direction does the light beam travel after being

reflected from mirror 2?

Figure P35.6

12. The wavelength of red helium–neon laser

light in air is 632.8 nm. (a) What is its frequency?

(b) What is its wavelength in glass that has an

index of refraction of 1.50? (c) What is its speed

in the glass?

18. An opaque cylindrical tank with an open top

has a diameter of 3.00 m and is completely filled

with water. When the afternoon Sun reaches an

angle of 28.0° above the horizon, sunlight ceases


10

to illuminate any part of the bottom of the tank.

How deep is the tank?

21. When the light illustrated in Figure P35.21 passes

through the glass block, it is shifted laterally by the

distance d. Taking n = 1.50, find the value of d.

Figure P35.21

35. The index of refraction for violet light in silica

flint glass is 1.66, and that for red light is 1.62. What

is the angular dispersion of visible light passing

through a prism of apex angle 60.0° if the angle of

incidence is 50.0°? (See Fig. P35.35.)

Figure P35.35

38. Determine the maximum angle θ for which the

light rays incident on the end of the pipe in Figure

P35.38 are subject to total internal reflection along

the walls of the pipe. Assume that the pipe has an

index of refraction of 1.36 and the outside medium

is air.

Figure P35.38

49. A small underwater pool light is 1.00 m below

the surface. The light emerging from the water

forms a circle on the water surface. What is the

diameter of this circle?

59. The light beam in Figure P35.59 strikes surface

2 at the critical angle. Determine the angle of

incidence θ1.

Figure P35.59

61. A light ray of wavelength 589 nm is incident

at an angle θ on the top surface of a block of

polystyrene, as shown in Figure P35.61. (a) Find

the maximum value of θ for which the refracted

ray undergoes total internal reflection at the left

vertical face of the block. What If? Repeat the

calculation for the case in which the polystyrene

block is immersed in (b) water and (c) carbon

disulfide.

Figure P35.61


11

Chapter 9: Image Formation

2. In a church choir loft, two parallel walls are 5.30

m apart. The singers stand against the north wall.

The organist faces the south wall, sitting 0.800 m

away from it. To enable her to see the choir, a flat

mirror 0.600 m wide is mounted on the south wall,

straight in front of her. What width of the north

wall can she see? Suggestion: Draw a topview

diagram to justify your answer.

6. A periscope (Figure P36.6) is useful for viewing

objects that cannot be seen directly. It finds use in

submarines and in watching golf matches or

parades from behind a crowd of people. Suppose

that the object is a distance p1 from the upper

mirror and that the two flat mirrors are separated

by a distance h. (a) What is the distance of the final

image from the lower mirror? (b) Is the final image

real or virtual? (c) Is it upright or inverted? (d)

What is its magnification? (e) Does it appear to be

left–right reversed?

Figure P36.6

14. (a) A concave mirror forms an inverted image

four times larger than the object. Find the focal

length of the mirror, assuming the distance

between object and image is 0.600 m. (b) A convex

mirror forms a virtual image half the size of the

object. Assuming the distance between image and

object is 20.0 cm, determine the radius of curvature

of the mirror.

16. An object 10.0 cm tall is placed at the zero mark

of a meter stick. A spherical mirror located at some

point on the meter stick creates an image of the

object that is upright, 4.00 cm tall, and located at

the 42.0-cm mark of the meter stick. (a) Is the

mirror convex or concave? (b) Where is the mirror?

(c) What is the mirror’s focal length?

23. A glass sphere (n = 1.50) with a radius of 15.0 cm

has a tiny air bubble 5.00 cm above its center. The

sphere is viewed looking down along the extended

radius containing the bubble. What is the apparent

depth of the bubble below the surface of the

sphere?

27. A goldfish is swimming at 2.00 cm/s toward

the front wall of a rectangular aquarium. What

is the apparent speed of the fish measured by an

observer looking in from outside the front wall

of the tank? The index of refraction of water is

1.33.

33. The nickel’s image in Figure P36.33 has twice

the diameter of the nickel and is 2.84 cm from

the lens. Determine the focal length of the lens.

Figure P36.33

36. The projection lens in a certain slide

projector is a single thin lens. A slide 24.0 mm

high is to be projected so that its image fills a

screen 1.80 m high. The slide-to-screen distance

is 3.00 m. (a) Determine the focal length of the

projection lens. (b) How far from the slide

should the lens of the projector be placed in

order to form the image on the screen?

37. An object is located 20.0 cm to the left of a

diverging lens having a focal length f = –32.0 cm.

Determine (a) the location and (b) the

magnification of the image. (c) Construct a ray

diagram for this arrangement.


12

Chapter 10: Interference of Light Waves

1. A laser beam ( = 632.8 nm) is incident on two slits

0.200 mm apart. How far apart are the bright

interference fringes on a screen 5.00 m away from

the double slits?

3. Two radio antennas separated by 300 m as shown

in Figure P37.3 simultaneously broadcast identical

signals at the same wavelength. A radio in a car

traveling due north receives the signals. (a) If the

car is at the position of the second maximum, what

is the wavelength of the signals? (b) How much

farther must the car travel to encounter the next

minimum in reception? (Note: Do not use the

small-angle approximation in this problem.)

4. In a location where the speed of sound is 354 m/s, a

2 000-Hz sound wave impinges on two slits 30.0

cm apart. (a) At what angle is the first maximum

located? (b) What If ? If the sound wave is

replaced by 3.00-cm microwaves, what slit

separation gives the same angle for the first

maximum? (c) What If ? If the slit separation is

1.00 m, what frequency of light gives the same

first maximum angle?

7. Two narrow, parallel slits separated by 0.250 mm

are illuminated by green light ( = 546.1 nm). The

interference pattern is observed on a screen 1.20 m

away from the plane of the slits. Calculate the

distance (a) from the central maximum to the first

bright region on either side of the central

maximum and (b) between the first and second

dark bands.

8. Light with wavelength 442 nm passes through a

double-slit system that has a slit separation d =

0.400 mm. Determine how far away a screen must

be placed in order that a dark fringe appear

directly opposite both slits, with just one bright

fringe between them.

10. Two slits are separated by 0.320 mm. A beam

of 500-nm light strikes the slits, producing an

interference pattern. Determine the number of

maxima observed in the angular range –30.0o <

< 30.0o.

16. The intensity on the screen at a certain point in

a doubleslit interference pattern is 64.0% of the

maximum value. (a) What minimum phase

difference (in radians) between sources

produces this result? (b) Express this phase

difference as a path difference for 486.1-nm

light.

17. In Figure 37.5, let L = 120cm and d = 0.250cm.

The slits are illuminated with coherent 600-nm

light. Calculate the distance y above the central

maximum for which the average intensity on

the screen is 75.0% of the maximum.

Figure 37.5

19. Two narrow parallel slits separated by 0.850

mm are illuminated by 600-nm light, and the

viewing screen is 2.80 m away from the slits.

(a) What is the phase difference between the

two interfering waves on a screen at a point

2.50 mm from the central bright fringe? (b)

What is the ratio of the intensity at this point to

the intensity at the center of a bright fringe?

55. Measurements are made of the intensity

distribution in a Young’s interference pattern

(see Fig. 37.7). At a particular value of y, it is

found that I/Imax = 0.810 when 600-nm light is

used. What wavelength of light should be used

to reduce the relative intensity at the same

location to 64.0% of the maximum intensity?


13

Chapter 11 Modern Physics

Section 40.1, 40.2, 40.3: Introduction to Quantum

Physics

6. A sodium-vapor lamp has a power output of 10.0

W. Using 589.3 nm as the average wavelength of

this source, calculate the number of photons

emitted per second.

7. Calculate the energy, in electron volts, of a photon

whose frequency is (a) 620 THz, (b) 3.10 GHz, (c)

46.0 MHz. (d) Determine the corresponding

wavelengths for these photons and state the

classification of each on the electromagnetic

spectrum.

9. An FM radio transmitter has a power output of 150

kW and operates at a frequency of 99.7 MHz. How

many photons per second does the transmitter

emit?

13. Molybdenum has a work function of 4.20 eV. (a)

Find the cutoff wavelength and cutoff frequency

for the photoelectric effect. (b) What is the stopping

potential if the incident light has a wavelength of

180 nm?

14. Electrons are ejected from a metallic surface with

speeds ranging up to 4.60 × 105 m/s when light with

a wavelength of 625 nm is used. (a) What is the

work function of the surface? (b) What is the cutoff

frequency for this surface?

17. Two light sources are used in a photoelectric

experiment to determine the work function for a

particular metal surface. When green light from a

mercury lamp (λ = 546.1 nm) is used, a stopping

potential of 0.376 V reduces the photocurrent to

zero. (a) Based on this measurement, what is the

work function for this metal? (b) What stopping

potential would be observed when using the

yellow light from a helium discharge tube (λ =

587.5 nm)?

21. Calculate the energy and momentum of a photon

of wavelength 700 nm.

22. X-rays having an energy of 300 keV undergo

Compton scattering from a target. The scattered

rays are detected at 37.0° relative to the incident

rays. Find (a) the Compton shift at this angle, (b)

the energy of the scattered x-ray, and (c) the

energy of the recoiling electron.

Section 42.3: Bohr’s Model of the Hydrogen

Atom

5. For a hydrogen atom in its ground state, use the

Bohr model to compute (a) the orbital speed of

the electron, (b) the kinetic energy of the

electron, and (c) the electric potential energy of

the atom.

8. How much energy is required to ionize

hydrogen (a) when it is in the ground state? (b)

when it is in the state for which n = 3?

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