PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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.
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?
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)?
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.
Figure P19.43
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?
56. A steel wire and a copper wire, each of
diameter 2.000 mm, are joined end to end. At
40.0°C, each has unstretched length of 2.000 m.
The wires are connected between two fixed
supports of 4.000 m apart on a tabletop. The
steel wire extend from x=-2.000 m to x= 0, the
copper wire extend from x= 0 to x= 2.000 m,
and the tension is negligible. The temperature
is then lowered to 20.0°C. At this lower
temperature, find the tension in the wire and
the x coordinate of the junction between the
wires. (Refer to Table 12.1 and 19.1)
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?
1
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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 P20.30
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 P20.24
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?
Figure P20.32
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?
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?
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?
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
2
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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.
3
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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 27.0C, find the
values of Q, W, and  Eint that characterize the
process.
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?
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?
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 27.0C
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.
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?
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/kgC. (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.
4
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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.
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?
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.
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.
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.
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?
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.
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 0C, 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?
5
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
Chapter 5: Oscillatory Motion
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.
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?
66. A block of mass M is connected to a spring of
mass m and oscillates in simple harmonic
motion on a horizontal, frictionless track (Fig.
P15.66). The force constant of the spring is k
and the equilibrium length is  . Assume that
all portions of the spring oscillate in phase and
that the velocity of a segment dx is
proportional to the distance x from the fixed
end; that is, vx = (x/  )v. Also, note that the
mass of a segment of the spring is dm =
(m/  )dx. Find (a) the kinetic energy of the
system when the block has a speed v, and (b)
the period of oscillation.
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?
Figure P15.66
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 .
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.
Figure P15.67
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
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.
maximum amplitude of oscillation can the
system have if the upper block is not to slip?
6
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
Show that in the two cases the block exhibits
simple harmonic motion with periods
(a)
T  2
(b)
T  2
m k1  k 2 
k 1 k2
m
k1  k 2
Figure P15.71
7
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
long does it take a transverse wave to travel
the entire length of the two wires?
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.
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
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?
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)
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.
(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?
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
8
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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?
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.)
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.
14. Two waves in a long string are given by
x
y 1  0.015 0 m cos  40t  and
2

x
y 2  0.015 0 m cos   40t 
2

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 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?
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?
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,
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
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
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)
Chapter 8: The Nature of Light and the Laws
of Geometric Optics
3.
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
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.
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 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 P18.69
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
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
to illuminate any part of the bottom of the tank.
How deep is the tank?
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?
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.
59. The light beam in Figure P35.59 strikes surface
2 at the critical angle. Determine the angle of
incidence θ1.
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 P35.59
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 P35.35
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 P35.61
Figure P35.38
11
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
Chapter 9: Image Formation
2.
6.
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.
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.
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.
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 P36.33
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.
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.
72. Figure P36.72 shows a thin converging lens
for which the radii of curvature are R1 = 9.00 cm
and R2 = –11.0 cm. The lens is in front of a
concave spherical mirror with the radius of
curvature R = 8.00 cm. (a) Assume its focal
points F1 and F2 are 5.00 cm from the center of
the lens. Determine its index of refraction. (b)
The lens and mirror are 20.0 cm apart, and an
object is placed 8.00 cm to the left of the lens.
Determine the position of the final image and its
magnification as seen by the eye in the figure.
(c) Is the final image inverted or upright?
Explain.
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?
Figure P36.72
12
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
Chapter 10: Interference of Light Waves
directly opposite both slits, with just one bright
fringe between them.
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?
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.
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.)
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.
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
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?
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.
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?
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
13
PHYF144 Tutorial
Department of Engineering Sciences and Mathematics, COE
Section 42.3: Bohr’s Model of the Hydrogen
Atom
Chapter 11 Modern Physics
Section 40.1, 40.2, 40.3: Introduction to Quantum
Physics
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.
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.
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?
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 × 10 5 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.
14