CHAPTER 2: Describing Motion: Kinematics in One Dimension
Problems
[The Problems at the end of each Chapter are ranked I, II, or III according to estimated difficulty, with (I) Problems being easiest.
Level III are meant as challenges for the best students. The Problems are arranged by Section, meaning that the reader should have
read up to and including that Section, but not only that Section — Problems often depend on earlier material. Finally, there is a set of
unranked “General Problems” not arranged by Section number.]
2–1 to 2–3
3.
7.
9.
Speed and Velocity
(I) If you are driving 110 km h along a straight road and you look to the side for 2.0 s, how far do you travel during this
inattentive period?
(II) You are driving home from school steadily at 95 km h for 130 km. It then begins to rain and you slow to 65 km h. You
arrive home after driving 3 hours and 20 minutes. (a) How far is your hometown from school? (b) What was your average
speed?
(II) A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. Calculate (a) the average speed
and (b) the average velocity, in m s .
2–5 and 2–6 Motion at Constant Acceleration
21.
27.
(I) A car accelerates from 13 m s to 25 m s in 6.0 s. What was its acceleration? How far did it travel in this time? Assume
constant acceleration.
(II) A car traveling 85 km h strikes a tree. The front end of the car compresses and the driver comes to rest after traveling 0.80
m. What was the average acceleration of the driver during the collision? Express the answer in terms of “g’s,” where
1.00 g  9.80 m s 2 .
2–7
35.
37.
39.
*2–8
Falling Objects [neglect air resistance]
(I) Estimate (a) how long it took King Kong to fall straight down from the top of the Empire State Building (380 m high), and
(b) his velocity just before “landing”?
(II) A ballplayer catches a ball 3.0 s after throwing it vertically upward. With what speed did he throw it, and what height did it
reach?
(II) A helicopter is ascending vertically with a speed of 5.20 m s . At a height of 125 m above the Earth, a package is dropped
from a window. How much time does it take for the package to reach the ground? [Hint: The package’s initial speed equals the
helicopter’s.]
Graphical Analysis
*49. (I) Figure 2–29 shows the velocity of a train as a function of time. (a) At what time was its velocity greatest? (b) During what
periods, if any, was the velocity constant? (c) During what periods, if any, was the acceleration constant? (d) When was the
magnitude of the acceleration greatest?
*50. (II) The position of a rabbit along a straight tunnel as a function of time is plotted in Fig. 2–28. What is its instantaneous
velocity (a) at t  10.0 s and (b) at t  30 .0 s? What is its average velocity (c) between t  0 and t  5.0 s, (d) between
t  25.0 s and t  30 .0 s, and (e) between t  40.0 s and t  50 .0 s?
*51. (II) In Fig. 2–28, (a) during what time periods, if any, is the velocity constant? (b) At what time is the velocity greatest? (c) At
what time, if any, is the velocity zero? (d) Does the object move in one direction or in both directions during the time shown?
*54. (II) In Fig. 2–29, estimate the distance the object traveled during (a) the first minute, and (b) the second minute.
*55. (II) Construct the v vs. t graph for the object whose displacement as a function of time is given by Fig. 2–28.
*56. (II) Figure 2–36 is a position versus time graph for the motion of an object along the x axis. Consider the time interval from A to
B. (a) Is the object moving in the positive or negative direction? (b) Is the object speeding up or slowing down? (c) Is the
acceleration of the object positive or negative? Now consider the time interval from D to E. (d) Is the object moving in the
positive or negative direction? (e) Is the object speeding up or slowing down? (f) Is the acceleration of the object positive or
negative? (g) Finally, answer these same three questions for the time interval from C to D.
CHAPTER 3: Kinematics in Two Dimensions; Vectors
Problems
3–2 to 3–4
1.
5.
Vector Addition
(I) A car is driven 215 km west and then 85 km southwest. What is the displacement of the car from the point of origin
(magnitude and direction)? Draw a diagram.
(II) Graphically determine the resultant of the following three vector displacements: (1) 34 m, 25º north of east; (2) 48 m, 33º
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9.
east of north; and (3) 22 m, 56º west of south.
(II) An airplane is traveling 735 km h in a direction 41.5º west of north (Fig. 3–31). (a) Find the components of the velocity
vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h?
3–5 and 3–6
Projectile Motion (neglect air resistance)
17. (I) A tiger leaps horizontally from a 6.5-m-high rock with a speed of 3.5 m s . How far from the base of the rock will she land?
19. (II) A fire hose held near the ground shoots water at a speed of 6.8 m s. At what angle(s) should the nozzle point in order that
the water land 2.0 m away (Fig. 3–33)? Why are there two different angles? Sketch the two trajectories.
21. (II) A ball is thrown horizontally from the roof of a building 45.0 m tall and lands 24.0 m from the base. What was the ball’s
initial speed?
27. (II) The pilot of an airplane traveling 180 km h wants to drop supplies to flood victims isolated on a patch of land 160 m below.
The supplies should be dropped how many seconds before the plane is directly overhead?
31. (II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65 .0 m s at an angle of 37.0º
with the horizontal, as shown in Fig. 3–35. (a) Determine the time taken by the projectile to hit point P at ground level. (b)
Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point
P, find (c) the horizontal and the vertical components of its velocity, (d) the magnitude of the velocity, and (e) the angle made by
the velocity vector with the horizontal. (f) Find the maximum height above the cliff top reached by the projectile.
32. (II) A shotputter throws the shot with an initial speed of 15 .5 m s at a 34.0º angle to the horizontal. Calculate the horizontal
distance traveled by the shot if it leaves the athlete’s hand at a height of 2.20 m above the ground.
*3–8 Relative Velocity
*39. (II) A boat can travel 2.30 m s in still water. (a) If the boat points its prow directly across a stream whose current is 1.20 m s,
what is the velocity (magnitude and direction) of the boat relative to the shore? (b) What will be the position of the boat, relative
to its point of origin, after 3.00 s? (See Fig. 3–30.)
*41. (II) An airplane is heading due south at a speed of 600 km h. If a wind begins blowing from the southwest at a speed of
100 km h (average), calculate: (a) the velocity (magnitude and direction) of the plane relative to the ground, and (b) how far
from its intended position will it be after 10 min if the pilot takes no corrective action. [Hint: First draw a diagram.]
*42. (II) In what direction should the pilot aim the plane in Problem 41 so that it will fly due south?
*45. (II) A motorboat whose speed in still water is 2.60 m s must aim upstream at an angle of 28.5º (with respect to a line
perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current? (b) What is the
resultant speed of the boat with respect to the shore? (See Fig. 3–28.)
CHAPTER 4: Dynamics: Newton’s Laws of Motion
Questions
3.
4.
6.
16.
If the acceleration of an object is zero, are no forces acting on it? Explain.
Only one force acts on an object. Can the object have zero acceleration? Can it have zero velocity? Explain.
If you walk along a log floating on a lake, why does the log move in the opposite direction?
A person exerts an upward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by
stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.
17. When you stand still on the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up
into the air?
Problems
4–4 to 4–6
3.
5.
7.
9.
Newton’s Laws, Gravitational Force, Normal Force
(I) How much tension must a rope withstand if it is used to accelerate a 960-kg car horizontally along a frictionless surface at
1.20 m s 2 ?
(II) A 20.0-kg box rests on a table. (a) What is the weight of the box and the normal force acting on it? (b) A 10.0-kg box is
placed on top of the 20.0-kg box, as shown in Fig. 4–38. Determine the normal force that the table exerts on the 20.0-kg box and
the normal force that the 20.0-kg box exerts on the 10.0-kg box.
(II) What average force is needed to accelerate a 7.00-gram pellet from rest to 125 m s over a distance of 0.800 m along the
barrel of a rifle?
(II) A 0.140-kg baseball traveling 35 .0 m s strikes the catcher’s mitt, which, in bringing the ball to rest, recoils backward 11.0
cm. What was the average force applied by the ball on the glove?
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
13. (II) An elevator (mass 4850 kg) is to be designed so that the maximum acceleration is 0.0680g. What are the maximum and
minimum forces the motor should exert on the supporting cable?
4–7
Newton’s Laws and Vectors
19. (I) A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from
the other end (Fig. 4–40). Determine the force that the table exerts on the box if the weight hanging on the other side of the
pulley weighs (a) 30.0 N, (b) 60.0 N, and (c) 90.0 N.
23. (II) Arlene is to walk across a “high wire” strung horizontally between two buildings 10.0 m apart. The sag in the rope when she
is at the midpoint is 10.0º as shown in Fig. 4–42. If her mass is 50.0 kg, what is the tension in the rope at this point?
31. (II) Figure 4–49 shows a block mass m1  on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a
second block m2 , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each,
the force (tension) exerted by the cord, and any normal force. (b) Apply Newton’s second law to find formulas for the
acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.
4–8
36.
37.
39.
41.
45.
47.
Newton’s Laws with Friction; Inclines
(I) If the coefficient of kinetic friction between a 35-kg crate and the floor is 0.30, what horizontal force is
required to move the crate at a steady speed across the floor? What horizontal force is required if  k is
zero?
(I) A force of 48.0 N is required to start a 5.0-kg box moving across a horizontal concrete floor. (a) What is
the coefficient of static friction between the box and the floor? (b) If the 48.0-N force continues, the box
accelerates at 0.70 m s 2 . What is the coefficient of kinetic friction?
(I) What is the maximum acceleration a car can undergo if the coefficient of static friction between the
tires and the ground is 0.80?
(II) A 15.0-kg box is released on a 32º incline and accelerates down the incline at 0.30 m s 2 . Find the
friction force impeding its motion. What is the coefficient of kinetic friction?
(II) The coefficient of kinetic friction for a 22-kg bobsled on a track is 0.10. What force is required to push
it down a 6.0º incline and achieve a speed of 60 km h at the end of 75 m?
(II) A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of
kinetic friction is 0.20 and the push imparts an initial speed of 4.0 m s?
2
55. (II) An 18.0-kg box is released on a 37.0º incline and accelerates down the incline at 0.270 m s . Find the friction force
impeding its motion. How large is the coefficient of kinetic friction?
CHAPTER 6: Work and Energy
Questions
3.
6.
7.
8.
Can the normal force on an object ever do work? Explain.
Why is it tiring to push hard against a solid wall even though you are doing no work?
You have two springs that are identical except that spring 1 is stiffer than spring 2 k1  k 2 . On which spring is more work
done (a) if they are stretched using the same force, (b) if they are stretched the same distance?
A hand exerts a constant horizontal force on a block that is free to slide on a frictionless surface (Fig. 6–30). The block starts
from rest at point A, and by the time it has traveled a distance d to point B it is traveling with speed v B . When the block has
traveled another distance d to point C, will its speed be greater than, less than, or equal to 2v B ? Explain your reasoning.
19. Two identical arrows, one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant
frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.
21. When a “superball” is dropped, can it rebound to a height greater than its original height? Explain.
22. Suppose you lift a suitcase from the floor to a table. The work you do on the suitcase depends on which of the following: (a)
whether you lift it straight up or along a more complicated path, (b) the time it takes, (c) the height of the table, and (d) the
weight of the suitcase?
23. Repeat Question 22 for the power needed rather than the work.
24. Why is it easier to climb a mountain via a zigzag trail than to climb straight up?
25. Recall from Chapter 4, Example 4–14, that you can use a pulley and ropes to decrease the force needed to raise a heavy load
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
(see Fig. 6–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy
concepts.
Problems
6–1
3.
Work, Constant Force
(I) A 1300-N crate rests on the floor. How much work is required to move it at constant speed (a) 4.0 m along the floor against a
friction force of 230 N, and (b) 4.0 m vertically?
2
5.
(II) A box of mass 5.0 kg is accelerated by a force across a floor at a rate of 2.0 m s for 7.0 s. Find the net work done on the
box.
7. (II) A lever such as that shown in Fig. 6–35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio
of output force, FO , to input force, FI , is related to the lengths l I and l O from the pivot point by FO FI  l I l O (ignoring
friction and the mass of the lever), given that the work output equals work input.
*13. (II) A spring has k  88 N m . Use a graph to determine the work needed to stretch it from x  3.8 cm to x  5.8 cm, where x is
the displacement from its unstretched length.
6–3
Kinetic Energy; Work-Energy Principle
15. (I) At room temperature, an oxygen molecule, with mass of 5.31 10 26 typically has a KE of about 6.12 10 21 J. How fast is
the molecule moving?
19. (II) An 88-g arrow is fired from a bow whose string exerts an average force of 110 N on the arrow over a distance of 78 cm.
What is the speed of the arrow as it leaves the bow?
6–4 and 6–5
Potential Energy
27.
29.
(I) A 7.0-kg monkey swings from one branch to another 1.2 m higher. What is the change in potential energy?
(II) A 1200-kg car rolling on a horizontal surface has speed v  65 km h when it strikes a horizontal coiled spring and is
brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?
31.
(II) A 55-kg hiker starts at an elevation of 1600 m and climbs to the top of a 3300-m peak. (a) What is the hiker’s change in
potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be more than this? Explain
why.
6–6 and 6–7
Conservation of Mechanical Energy
6–8 and 6–9
Law of Conservation of Energy
33. (I) Jane, looking for Tarzan, is running at top speed 5.3 m s  and grabs a vine hanging vertically from a tall tree in the jungle.
How high can she swing upward? Does the length of the vine affect your answer?
37.
(II) A 65-kg trampoline artist jumps vertically upward from the top of a platform with a speed of 5.0 m s . (a) How fast is he
going as he lands on the trampoline, 3.0 m below (Fig. 6–38)? (b) If the trampoline behaves like a spring with spring stiffness
constant 6.2 10 4 N m , how far does he depress it?
43.
(II) The roller-coaster car shown in Fig. 6–41 is dragged up to point 1 where it is released from rest. Assuming no friction,
calculate the speed at points 2, 3, and 4.
47.
(I) Two railroad cars, each of mass 7650 kg and traveling 95 km h in opposite directions, collide head-on and come to rest.
How much thermal energy is produced in this collision?
49. (II) A ski starts from rest and slides down a 22º incline 75 m long. (a) If the coefficient of friction is 0.090, what is the ski’s
speed at the base of the incline? (b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far
will the ski travel along the level? Use energy methods.
51. (II) You drop a ball from a height of 2.0 m, and it bounces back to a height of 1.5 m. (a) What fraction of its initial energy is lost
during the bounce? (b) What is the ball’s speed just as it leaves the ground after the bounce? (c) Where did the energy go?
6–10
Power
58. (I) How long will it take a 1750-W motor to lift a 315-kg piano to a sixth-story window 16.0 m above?
60. (I) A 1400-kg sports car accelerates from rest to 95 km h in 7.4 s. What is the average power delivered by the engine?
CHAPTER 7:
Linear Momentum
Questions
1.
We claim that momentum is conserved, yet most moving objects eventually slow down and stop. Explain.
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2.
3.
4.
5.
6.
7.
9.
10.
11.
12.
13.
When a person jumps from a tree to the ground, what happens to the momentum of the person upon striking the ground?
When you release an inflated but untied balloon, why does it fly across the room?
It is said that in ancient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice
was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?
How can a rocket change direction when it is far out in space and is essentially in a vacuum?
According to Eq. 7–5, the longer the impact time of an impulse, the smaller the force can be for the same momentum change,
and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which
are intended to inflate during an automobile collision and reduce the possibility of fracture or death.
Cars used to be built as rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that
collapse upon impact. What is the advantage of this new design?
Is it possible for an object to receive a larger impulse from a small force than from a large force? Explain.
A light object and a heavy object have the same kinetic energy. Which has the greater momentum? Explain.
Describe a collision in which all kinetic energy is lost.
At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator.
For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the
water rebounds?
A squash ball hits a wall at a 45º angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball,
(b) of the force on the wall?
Problems
7–1 and 7–2
1.
Momentum and Its Conservation
3.
(I) What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m s ?
(II) A 0.145-kg baseball pitched at 39 .0 m s is hit on a horizontal line drive straight back toward the pitcher at 52 .0 m s . If the
5.
contact time between bat and ball is 3.00  10 3 s, calculate the average force between the ball and bat during contact.
(II) Calculate the force exerted on a rocket, given that the propelling gases are expelled at a rate of 1500 kg s with a speed of
4.0 10 4 m s (at the moment of takeoff).
7. (II) A 12,600-kg railroad car travels alone on a level frictionless track with a constant speed of 18 .0 m s . A 5350-kg load,
initially at rest, is dropped onto the car. What will be the car’s new speed?
12. (II) A 23-g bullet traveling 230 m s penetrates a 2.0-kg block of wood and emerges cleanly at 170 m s . If the block is
stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?
7–3
Collisions and Impulse
15. (II) A golf ball of mass 0.045 kg is hit off the tee at a speed of 45 m s . The golf club was in contact with the ball for
3.5 10 3 s. Find (a) the impulse imparted to the golf ball, and (b) the average force exerted on the ball by the golf club.
18. (II) You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them
into fixed, massive barriers at 50 km h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is
brought to rest. (a) Calculate the average force exerted on the car by the barrier. (b) Calculate the average deceleration of the
car.
20. (II) Suppose the force acting on a tennis ball (mass 0.060 kg) points in the  x direction and is given by the graph of Fig. 7–33
as a function of time. Use graphical methods to estimate (a) the total impulse given the ball, and (b) the velocity of the ball after
being struck, assuming the ball is being served so it is nearly at rest initially.
21. (III) From what maximum height can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air
resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in
breaking the fall). Assume the breaking strength (force per unit area) of bone is 170 10 6 N m , and its smallest cross2
sectional area is 2.5 10 4 m 2 . [Hint: Do not try this experimentally.]
7–4 and 7–5
Elastic Collisions
23. (II) A 0.450-kg ice puck, moving east with a speed of 3.00 m s , has a head-on collision with a 0.900-kg puck initially at rest.
25.
Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?
(II) A 0.060-kg tennis ball, moving with a speed of 2.50 m s , collides head-on with a 0.090-kg ball initially moving away
from it at a speed of 1.15 m s . Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
27. (II) Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–
34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.50 m s and
car B is moving at 3.70 m s , calculate (a) their velocities after the collision, and (b) the change in momentum of each.
30. (III) Take the general case of an object of mass mA and velocity v A elastically striking a stationary v B  0 object of mass
mB head-on. (a) Show that the final velocities v A and v B are given by
 m  mB 
v A ,
   A
vA
 mA  mB 
 2m A 
v A .
v B  
 mA  mB 
(b) What happens in the extreme case when m A is much smaller than mB ? Cite a common example of this. (c) What happens
in the extreme case when m A is much larger than mB ? Cite a common example of this. (d) What happens in the case when
m A  m B ? Cite a common example.
7–6
Inelastic Collisions
31. (I) In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second
32.
33.
35.
36.
projectile causes the the pendulum to swing twice as high, h2  5.2 cm. The second projectile was how many times faster than
the first?
(II) A 28-g rifle bullet traveling 230 m s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the
pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.
(II) (a) Derive a formula for the fraction of kinetic energy lost,  KE KE, for the ballistic pendulum collision of Example 7–10.
(b) Evaluate for m  14.0 g and M  380 g.
(II) A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are
locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction
between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?
(II) A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the
ball make before losing 90% of its energy?
General Problems
65. A 140-kg astronaut (including space suit) acquires a speed of 2.50 m s by pushing off with his legs from an 1800-kg space
71.
75.
79.
80.
81.
capsule. (a) What is the change in speed of the space capsule? (b) If the push lasts 0.40 s, what is the average force exerted on
the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.
A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun.
If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m
before it comes to rest, what was the muzzle speed of the bullet?
The force on a bullet is given by the formula F  580  1.8 105 t over the time interval t  0 to t  3.0 10 3 s. In this
formula, t is in seconds and F is in newtons. (a) Plot a graph of F vs. t for t  0 to t  3.0 ms. (b) Estimate, using graphical
methods, the impulse given the bullet. (c) If the bullet achieves a speed of 220 m s as a result of this impulse, given to it in the
barrel of a gun, what must its mass be?
A block of mass m  2.20 kg slides down a 30.0º incline which is 3.60 m high. At the bottom, it strikes a block of mass
M  7.00 kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the
collision is elastic, and friction can be ignored, determine (a) the speeds of the two blocks after the collision, and (b) how far
back up the incline the smaller mass will go.
In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the
incline, and collide with M again?
The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed


(with respect to the Sun) of 9.6 km s . The mass of Saturn is 5.69 10 26 kg. A spacecraft with mass 825 kg approaches Saturn.
When far from Saturn, it moves in the  x direction at 10.4 km s . The gravitational attraction of Saturn (a conservative force)
acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction.
Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
CHAPTER 8:
Rotational Motion
Questions
4.
5.
6.
7.
Can a small force ever exert a greater torque than a larger force? Explain.

If a force F acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.
Why is it more difficult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you?
A diagram may help you to answer this.
A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a
small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front
sprocket? Why?
Problems
8–4 Torque
22. (I) A 55-kg person riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17
cm. (a) What is the maximum torque she exerts? (b) How could she exert more torque?
23. (I) A person exerts a force of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerted
(a) perpendicular to the door, and (b) at a 45º angle to the face of the door?
24. (II) Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.40 m  N opposes
the motion.
25. (II) Two blocks, each of mass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod
is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.
CHAPTER 10: Fluids
Questions
2.
4.
5.
7.
8.
Airplane travelers sometimes note that their cosmetics bottles and other containers have leaked during a flight. What might
cause this?
Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. Decide what
determines whether your skin is cut — the net force applied to it or the pressure.
A small amount of water is boiled in a 1-gallon metal can. The can is removed from the heat and the lid put on. Shortly
thereafter the can collapses. Explain.
An ice cube floats in a glass of water filled to the brim. What can you say about the density of ice? As the ice melts, will the
glass overflow? Explain.
Will an ice cube float in a glass of alcohol? Why or why not?
Problems
10–2
1.
3.
4.
Density and Specific Gravity
(I) The approximate volume of the granite monolith known as El Capitan in Yosemite National Park (Fig. 10–48) is about
108 m 3 . What is its approximate mass?
(I) If you tried to smuggle gold bricks by filling your backpack, whose dimensions are 60 cm  28 cm 18 cm, what would its
mass be?
(I) State your mass and then estimate your volume. [Hint: Because you can swim on or just under the surface of the water in a
swimming pool, you have a pretty good idea of your density.]
10–3 to 10–6
7.
Pressure; Pascal’s Principle
(I) Estimate the pressure exerted on a floor by (a) one pointed chair leg (60 kg on all four legs) of area  0.020 cm 2 , and (b) a


1500-kg elephant standing on one foot area  800 cm2 .
2
11. (II) The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a “footprint” of 220 cm , estimate
the mass of the car.
12. (II) The maximum gauge pressure in a hydraulic lift is 17.0 atm. What is the largest size vehicle (kg) it can lift if the diameter of
the output line is 28.0 cm?
64. A 2.4-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle
0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a
vein where the gauge pressure is 18 mm-Hg? Answer for the instant just before the fluid starts to move.
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
65. A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process,
the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 3.0 cm, what is the range of
the force that needs to be applied to the pump handle from beginning to end?
68.
A hydraulic lift is used to jack a 970-kg car 12 cm off the floor. The diameter of the output piston is 18 cm,
and the input force is 250 N. (a) What is the area of the input piston? (b) What is the work done in lifting
the car 12 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each
stroke? (d) How many strokes are required to jack the car up 12 cm? (e) Show that energy is conserved
CHAPTER 11: Vibrations and Waves
Questions
2.
5.
7.
8.
14.
15.
19.
20.
Is the acceleration of a simple harmonic oscillator ever zero? If so, where?
How could you double the maximum speed of a simple harmonic oscillator (SHO)?
If a pendulum clock is accurate at sea level, will it gain or lose time when taken to high altitude? Why?
A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch
using only a stopwatch?
Why do the strings used for the lowest-frequency notes on a piano normally have wire wrapped around them?
What kind of waves do you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b)
horizontally parallel to its length?
When a sinusoidal wave crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change
(although the wavelength and velocity do change). Explain why.
If a string is vibrating in three segments, are there any places you could touch it with a knife blade without disturbing the motion?
1 to 11–3 Simple Harmonic Motion
1. (I) If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it travels in one period?
3.
5.
9.
(I) The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car
goes over a bump, what will be the frequency of vibrations?
(II) An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its
frequency if only 0.38 kg hangs from it?
(II) A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m.
Determine (a) the velocity when it passes the equilibrium point, (b) the velocity when it is 0.10 m from
equilibrium, (c) the total energy of the system, and (d) the equation describing the motion of the mass,
assuming that x was a maximum at t  0.
17. (II) At what displacement from equilibrium is the energy of a SHO half KE and half PE?
21. (II) A 300-g mass vibrates according to the equation x  0.38 sin 6.50t, where x is in meters and t is in seconds. Determine (a) the
amplitude, (b) the frequency, (c) the period, (d) the total energy, and (e) the KE and PE when x is 9.0 cm. (f) Draw a careful graph
of x vs. t showing the correct amplitude and period.
22. (II) Figure 11–50 shows two examples of SHM, labeled A and B. For each, what is (a) the amplitude, (b) the frequency, and (c)
the period? (d) Write the equations for both A and B in the form of a sine or cosine.
11–4
Simple Pendulum
28. (I) A pendulum makes 36 vibrations in exactly 60 s. What is its (a) period, and (b) frequency?
29.
(I) How long must a simple pendulum be if it is to make exactly one swing per second? (That is, one
complete vibration takes exactly 2.0 s.)
31. (II) What is the period of a simple pendulum 80 cm long (a) on the Earth, and (b) when it is in a freely
falling elevator?
33. (II) Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust
the length of the pendulum?
11–7 and 11–8
Waves
36. (I) A fisherman notices that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two
crests to be 6.5 m. How fast are the waves traveling?
37. (I) A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m s . How far apart are the wave crests
(compressions)?
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
41. (II) A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take
a pulse to travel from one support to the other?
*43. (II) A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean
11–9
floor directly below 3.0 s later. How deep is the ocean at this point?
Wave Energy
47. (II) The intensity of an earthquake wave passing through the Earth is measured to be 2.0 10 6 J m . at a distance of 48 km from
the source. (a) What was its intensity when it passed a point only 1.0 km from the source? (b) At what rate did energy pass through
an area of 5.0 m 2 at 1.0 km?
*11–10 Intensity Related to A and f
*49.(I) Two waves traveling along a stretched string have the same frequency, but one transports three times the power of the other.
What is the ratio of the amplitudes of the two waves?
11–12 Interference
11–13 Standing Waves; Resonance
52. (I) If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?
53. (I) A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down
from the end? (That is, only two-thirds of the string vibrates as a standing wave.)
2
CHAPTER 12:
Sound
Questions
5. What evidence can you give that the speed of sound in air does not depend significantly on frequency?
6. The voice of a person who has inhaled helium sounds very high-pitched. Why?
11. Standing waves can be said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.”
Explain.
12. In Fig. 12–16, if the frequency of the speakers were lowered, would the points D and C (where destructive and constructive
interference occur) move farther apart or closer together?
13.
Traditional methods of protecting the hearing of people who work in areas with very high noise levels have
consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones
are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it
electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more
noise reduce the sound levels reaching the ears?
14. Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly
different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart?
Explain.
15. Is there a Doppler shift if the source and observer move in the same direction, with the same velocity? Explain.
16. If a wind is blowing, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the
wavelength or velocity changed?
17. Figure 12–32 shows various positions of a child in motion on a swing. A monitor is blowing a whistle in
front of the child on the ground. At which position, A through E, will the child hear the highest frequency
for the sound of the whistle? Explain your reasoning.
Problems
[Unless stated otherwise, assume T  20 º C and vsound  343 m s
12–1
1.
2.
3.
4.
Characteristics of Sound
(I) A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She
hears the echo 2.0 s after shouting. Estimate the length of the lake.
(I) A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor
directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m s (Table 12–1)
and does not vary significantly with depth.
(I) (a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b)
What is the wavelength of a 10-MHz ultrasonic wave?
(II) An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on
another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish, and (b) by the
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
fishermen?
Loudness
*21.(I) A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound
level? (See Fig. 12–6.)
*12–3
*23. (II) Your auditory system can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at (a)
100 Hz, (b) 5000 Hz? (See Fig. 12–6.)
12–4 Sources of Sound: Strings and Air Columns
25. (I) An organ pipe is 112 cm long. What are the fundamental and first three audible overtones if the pipe is (a) closed at one end,
and (b) open at both ends?
27. (I) If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would
be the range of the lengths of pipes required?
33. (II) (a) At T  20 º C, how long must an open organ pipe be to have a fundamental frequency of 294 Hz? (b) If this pipe is filled
with helium, what is its fundamental frequency?
35. (II) A uniform narrow tube 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and
330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?
37. (II) How many overtones are present within the audible range for a 2.14-m-long organ pipe at 20°C (a) if it is open, and (b) if it is
closed?
12–6 Interference; Beats
39. (I) A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one of which is sounding 440
Hz. How far off in frequency is the other string?
40. (I) What is the beat frequency if middle C (262 Hz) and C # (277 Hz) are played together? What if each is played two octaves
lower (each frequency reduced by a factor of 4)?
41.
(I) A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency.
If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz
occurs when they are played simultaneously, estimate the operating frequency of brand X.
42. (II) A guitar string produces 4 beats s when sounded with a 350-Hz tuning fork and 9 beats s when sounded
with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.
12–7 Doppler Effect
49. (I) The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move
with a speed of 30 .0 m s (a) toward the fire engine, and (b) away from it?
50. (I) You are standing still. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m s
(a) toward you, or (b) away from you?
*12–8
Shock Waves; Sonic Boom
*59. (I) (a) How fast is an object moving on land if its speed at 20°C is Mach 0.33? (b) A high-flying jet cruising at 3000 km h
displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?
76. A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop
slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from
the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?
CHAPTER 13:
Temperature and Kinetic Theory
Questions
3. Which is larger, 1 C° or 1 F°?
*4. If system A is in thermal equilibrium with system B, but B is not in thermal equilibrium with system C, what can you say about
5.
6.
7.
8.
the temperatures of A, B, and C?
A flat bimetallic strip consists of aluminum riveted to a strip of iron. When heated, the strip will bend. Which metal will be on the
outside of the curve? [Hint: See Table 13–1.] Why?
In the relation L  L0 T , should L0 be the initial length, the final length, or does it matter? Explain.
The units for the coefficient of linear expansion  are (Cº ) 1 , and there is no mention of a length unit such as meters. Would
the expansion coefficient change if we used feet or millimeters instead of meters? Explain.
Figure 13–27 shows a diagram of a simple thermostat used to control a furnace (or other heating or cooling system). The
bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and
how it can be set at different temperatures.
9. Long steam pipes that are fixed at the ends often have a section in the shape of a U. Why?
10. A flat, uniform cylinder of lead floats in mercury at 0°C. Will the lead float higher or lower when the temperature is raised?
Explain.
11. When a cold mercury-in-glass thermometer is first placed in a hot tub of water, the mercury initially descends a bit and then rises.
Explain.
12. A glass container may break if one part of it is heated or cooled more rapidly than adjacent parts. Explain.
13. The principal virtue of Pyrex glass is that its coefficient of linear expansion is much smaller than that for ordinary glass (Table
13–1). Explain why this gives rise to the increased heat resistance of Pyrex.
14. Will a grandfather clock, accurate at 20ºC, run fast or slow on a hot day (30ºC)? Explain. The clock uses a pendulum supported
on a long, thin brass rod.
15. Freezing a can of soda will cause its bottom and top to bulge so badly the can will not stand up. What has happened?
16. When a gas is rapidly compressed (say, by pushing down a piston), its temperature increases. When a gas expands against a
piston, it cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the
momentum of molecules when they strike the moving piston.
18. Explain in words how Charles’s law follows from kinetic theory and the relation between average kinetic energy and the absolute
temperature.
19. Explain in words how Gay-Lussac’s law follows from kinetic theory.
20. As you go higher in the Earth’s atmosphere, the ratio of N 2 molecules to O 2 molecules increases. Why?
*22. Alcohol evaporates more quickly than water at room temperature. What can you infer about the molecular properties of one
relative to the other?
*23. Explain why a hot humid day is far more uncomfortable than a hot dry day at the same temperature.
*24. Is it possible to boil water at room temperature (20°C) without heating it? Explain.
Problems
13–1
1.
Atomic Theory
(I) How many atoms are there in a 3.4-gram copper penny?
13–2 Temperature and Thermometers
3. (I) (a) “Room temperature” is often taken to be 68°F. What is this on the Celsius scale? (b) The temperature of the filament in a
lightbulb is about 1800°C. What is this on the Fahrenheit scale?
5.
(I) (a) 15° below zero on the Celsius scale is what Fahrenheit temperature? (b) 15° below zero on the
Fahrenheit scale is what Celsius temperature?
13–4 Thermal Expansion
7. (I) A concrete highway is built of slabs 12 m long (20°C). How wide should the expansion cracks between the slabs be (at 20°C)
to prevent buckling if the range of temperature is 30 º C to 50 º C?
10.
(II) To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled
(usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole
1.869 cm in diameter at 20°C. To what temperature must the rivet be cooled if it is to fit in the hole?
13–6 Gas Laws; Absolute Temperature
27. (I) Absolute zero is what temperature on the Fahrenheit scale?
Ideal Gas Law
13–7 and 13–8
3
29. (I) If 3.00 m of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0°C. What is
the volume?
33. (II) A storage tank at STP contains 18.5 kg of nitrogen N 2 . (a) What is the volume of the tank? (b) What is the pressure if an
additional 15.0 kg of nitrogen is added without changing the temperature?
13–9
Ideal Gas Law in Terms of Molecules; Avogadro’s Number
41. (I) Calculate the number of molecules m
3
in an ideal gas at STP.
13–10 Molecular Interpretation of Temperature
47. (I) Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 6000 K.
49. (I) A gas is at 20°C. To what temperature must it be raised to double the rms speed of its molecules?
*13–13 Vapor Pressure; Humidity
*63. (I) What is the dew point (approximately) if the humidity is 50% on a day when the temperature is 25°C?
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*65.(I)
If the air pressure at a particular place in the mountains is 0.72 atm, estimate the temperature at which
water boils.
*67.(I) What is the partial pressure of water on a day when the temperature is 25°C and the relative humidity is
35%?
General Problems
73. A precise steel tape measure has been calibrated at 20°C. At 34°C, (a) will it read high or low, and (b) what will be the
percentage error?
CHAPTER 14: Heat
Questions
1.
2.
3.
4.
6.
7.
8.
9.
17.
18.
19.
21.
24.
26.
29.
30.
What happens to the work done when a jar of orange juice is vigorously shaken?
When a hot object warms a cooler object, does temperature flow between them? Are the temperature changes of the two objects
equal?
(a) If two objects of different temperatures are placed in contact, will heat naturally flow from the object with higher internal
energy to the object with lower internal energy? (b) Is it possible for heat to flow even if the internal energies of the two objects
are the same? Explain.
In warm regions where tropical plants grow but the temperature may drop below freezing a few times in the winter, the
destruction of sensitive plants due to freezing can be reduced by watering them in the evening. Explain.
Why does water in a metal canteen stay cooler if the cloth jacket surrounding the canteen is kept moist?
Explain why burns caused by steam on the skin are often more severe than burns caused by water at 100°C.
Explain why water cools (its temperature drops) when it evaporates, using the concepts of latent heat and internal energy.
Will potatoes cook faster if the water is boiling faster? 17.
Down sleeping bags and parkas are often specified as so many
inches or centimeters of loft, the actual thickness of the garment when it is fluffed up. Explain.
Down sleeping bags and parkas are often specified as so many inches or centimeters of loft, the actual thickness of the garment
when it is fluffed up. Explain.
Microprocessor chips have a “heat sink” glued on top that looks like a series of fins. Why is it shaped like that?
Sea breezes are often encountered on sunny days at the shore of a large body of water. Explain in light of the fact that the
temperature of the land rises more rapidly than that of the nearby water.
A 22°C day is warm, while a swimming pool at 22°C feels cool. Why?
Why is the liner of a thermos bottle silvered (Fig. 14–15), and why does it have a vacuum between its two walls?
Heat loss occurs through windows by the following processes: (1) ventilation around edges; (2) through the frame, particularly if
it is metal; (3) through the glass panes; and (4) radiation. (a) For the first three, what is (are) the mechanism(s): conduction,
convection, or radiation? (b) Heavy curtains reduce which of these heat losses? Explain in detail.
An “emergency blanket” is a thin shiny (metal coated) plastic foil. Explain how it can help to keep an immobile person warm.
Explain why cities situated by the ocean tend to have less extreme temperatures than inland cities at the same latitude.
Problems
14–1
1.
3.
5.
7.
Heat as Energy Transfer
(I) How much heat (in joules) is required to raise the temperature of 30.0 kg of water from 15°C to 95°C?
(II) An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatt-hours? (c)
Your power company charges about a dime per kilowatt-hour. How much would your energy cost per day if you bought it from
the power company? Could you feed yourself on this much money per day?
(II) A water heater can generate 32,000 kJ h. How much water can it heat from 15°C to 50°C per hour?
(II) How many kilocalories are generated when the brakes are used to bring a 1200-kg car to rest from a speed of 95 km h?
14–3 and 14–4
Specific Heat; Calorimetry
9. (I) What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 5.1 kg of the metal from 18.0°C to 31.5°C?
11. (II) A 35-g glass thermometer reads 21.6°C before it is placed in 135 mL of water. When the water and thermometer come to
equilibrium, the thermometer reads 39.2°C. What was the original temperature of the water?
15. (II) How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water initially at 8.0°C? Assume that the part of the pot
which is heated with the water is made of 360 g of aluminum, and that no water boils away.
14–5
Latent Heat
21. (I) How much heat is needed to melt 16.50 kg of silver that is initially at 20°C?
23.
(I) If 2.80  105 J of energy is supplied to a flask of liquid oxygen at
183 º C,
how much oxygen can
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
evaporate?
25. (II) A cube of ice is taken from the freezer at 8.5º C and placed in a 95-g aluminum calorimeter filled with
310 g of water at room temperature of 20.0°C. The final situation is observed to be all water at 17.0°C.
What was the mass of the ice cube?
14–6 to 14–8 Conduction, Convection, Radiation
33. (I) One end of a 33-cm-long aluminum rod with a diameter of 2.0 cm is kept at 460°C, and the other is immersed in water at
22°C. Calculate the heat conduction rate along the rod.
35.
(I) (a) How much power is radiated by a tungsten sphere (emissivity e  0.35 ) of radius 22 cm at a
temperature of 25°C? (b) If the sphere is enclosed in a room whose walls are kept at 5º C, what is the net
flow rate of energy out of the sphere?
41. (II) A 100-W lightbulb generates 95 W of heat, which is dissipated through a glass bulb that has a radius of 3.0 cm and is 1.0 mm
thick. What is the difference in temperature between the inner and outer surfaces of the glass?
CHAPTER 15: The Laws of Thermodynamics
Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
What happens to the internal energy of water vapor in the air that condenses on the outside of a cold glass of water? Is work
done or heat exchanged? Explain.
Use the conservation of energy to explain why the temperature of a gas increases when it is quickly compressed — say, by
pushing down on a cylinder — whereas the temperature decreases when the gas expands.
In an isothermal process, 3700 J of work is done by an ideal gas. Is this enough information to tell how much heat has been
added to the system? If so, how much?
Is it possible for the temperature of a system to remain constant even though heat flows into or out of it? If so, give one or two
examples.
Explain why the temperature of a gas increases when it is adiabatically compressed.
Can mechanical energy ever be transformed completely into heat or internal energy? Can the reverse happen? In each case, if
your answer is no, explain why not; if yes, give one or two examples.
Can you warm a kitchen in winter by leaving the oven door open? Can you cool the kitchen on a hot summer day by leaving the
refrigerator door open? Explain.
Would a definition of heat engine efficiency as e  W QL be useful? Explain.
What plays the role of high-temperature and low-temperature areas in (a) an internal combustion engine, and (b) a steam
engine?
Which will give the greater improvement in the efficiency of a Carnot engine, a 10 C° increase in the high-temperature
reservoir, or a 10 C° decrease in the low-temperature reservoir? Explain.
The oceans contain a tremendous amount of thermal (internal) energy. Why, in general, is it not possible to put this energy to
useful work?
A gas is allowed to expand (a) adiabatically and (b) isothermally. In each process, does the entropy increase, decrease, or stay
the same? Explain.
A gas can expand to twice its original volume either adiabatically or isothermally. Which process would result in a greater
change in entropy? Explain.
Give three examples, other than those mentioned in this Chapter, of naturally occurring processes in which order goes to
disorder. Discuss the observability of the reverse process.
Which do you think has the greater entropy, 1 kg of solid iron or 1 kg of liquid iron? Why?
(a) What happens if you remove the lid of a bottle containing chlorine gas? (b) Does the reverse process ever happen? Why or
why not? (c) Can you think of two other examples of irreversibility?
You are asked to test a machine that the inventor calls an “in-room air conditioner”: a big box, standing in the middle of the
room, with a cable that plugs into a power outlet. When the machine is switched on, you feel a stream of cold air coming out of
it. How do you know that this machine cannot cool the room?
Think up several processes (other than those already mentioned) that would obey the first law of thermodynamics, but, if they
actually occurred, would violate the second law.
Suppose a lot of papers are strewn all over the floor; then you stack them neatly. Does this violate the second law of
thermodynamics? Explain.
The first law of thermodynamics is sometimes whimsically stated as, “You can’t get something for nothing,” and the second law
as, “You can’t even break even.” Explain how these statements could be equivalent to the formal statements.
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*21. Entropy is often called “time’s arrow” because it tells us in which direction natural processes occur. If a movie were run
backward, name some processes that you might see that would tell you that time was “running backward.”
*22. Living organisms, as they grow, convert relatively simple food molecules into a complex structure. Is this a violation of the
second law of thermodynamics?
Problems
15–1 and 15–2
First Law of Thermodynamics
1.
(I) An ideal gas expands isothermally, performing 3.40 10 3 J of work in the process. Calculate (a) the change in internal
energy of the gas, and (b) the heat absorbed during this expansion.
2.
(I) A gas is enclosed in a cylinder fitted with a light frictionless piston and maintained at atmospheric
pressure. When 1400 kcal of heat is added to the gas, the volume is observed to increase slowly from
12.0 m 3 to 18.2 m 3 . Calculate (a) the work done by the gas and (b) the change in internal energy of the gas.
(I) One liter of air is cooled at constant pressure until its volume is halved, and then it is allowed to expand
isothermally back to its original volume. Draw the process on a PV diagram.
3.
4.
5.
10.
(I) Sketch a PV diagram of the following process: 2.0 L of ideal gas at atmospheric pressure are cooled at constant pressure to a
volume of 1.0 L, and then expanded isothermally back to 2.0 L, whereupon the pressure is increased at constant volume until the
original pressure is reached.
(II) A 1.0-L volume of air initially at 4.5 atm of (absolute) pressure is allowed to expand isothermally until the pressure is 1.0
atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating
at constant volume. Draw the process on a PV diagram, including numbers and labels for the axes.
(II) Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume
so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure, from a
volume of 6.8 L to 9.3 L, where the temperature reaches its original value. See Fig. 15–22. Calculate (a)
the total work done by the gas in the process, (b) the change in internal energy of the gas in the process,
and (c) the total heat flow into or out of the gas.
*15. (I) Calculate the average metabolic rate of a person who sleeps 8.0 h, sits at a desk 8.0 h, engages in light activity 4.0 h, watches
television 2.0 h, plays tennis 1.5 h, and runs 0.5 h daily.
15–5
Heat Engines
17. (I) A heat engine exhausts 8200 J of heat while performing 3200 J of useful work. What is the efficiency of this engine?
19.
(I) What is the maximum efficiency of a heat engine whose operating temperatures are 580°C and 380°C?
15–6 Refrigerators, Air Conditioners, Heat Pumps
29. (I) The low temperature of a freezer cooling coil is 15 º C, and the discharge temperature is 30°C. What is the maximum
theoretical coefficient of performance?
31.
(II) A restaurant refrigerator has a coefficient of performance of 5.0. If the temperature in the kitchen
outside the refrigerator is 29°C, what is the lowest temperature that could be obtained inside the
refrigerator if it were ideal?
15–7 Entropy
35. (I) What is the change in entropy of 250 g of steam at 100°C when it is condensed to water at 100°C?
39. (II) A 10.0-kg box having an initial speed of 3.0 m s slides along a rough table and comes to rest. Estimate the total change in
entropy of the universe. Assume all objects are at room temperature (293 K).
*15–12 Energy Resources
*48. (I) Solar cells (Fig. 15–26) can produce about 40 W of electricity per square meter of surface area if directly facing the Sun.
How large an area is required to supply the needs of a house that requires 22 k Wh day? Would this fit on the roof of an
average house? (Assume the Sun shines about 9 h day. )
General Problems
66. Metabolizing 1.0 kg of fat results in about 3.7 10 J of internal energy in the body. (a) In one day, how much fat does the body
7
burn to maintain the body temperature of a person staying in bed and metabolizing at an average rate of 95 W? (b) How long
would it take to burn 1.0-kg of fat this way assuming there is no food intake?
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
68. A dehumidifier is essentially a “refrigerator with an open door.” The humid air is pulled in by a fan and guided to a cold coil,
where the temperature is less than the dew point, and some of the air’s water condenses. After this water is extracted, the air is
warmed back to its original temperature and sent into the room. In a well-designed dehumidifier, the heat is exchanged between
the incoming and outgoing air. This way the heat that is removed by the refrigerator coil mostly comes from the condensation of
water vapor to liquid. Estimate how much water is removed in 1.0 h by an ideal dehumidifier, if the temperature of the room is
25°C, the water condenses at 8°C, and the dehumidifier does work at the rate of 600 W of electrical power.
CHAPTER 16: Electric Charge and Electric Field
Questions
1.
If you charge a pocket comb by rubbing it with a silk scarf, how can you determine if the comb is positively or negatively
charged?
4. A positively charged rod is brought close to a neutral piece of paper, which it attracts. Draw a diagram showing the separation of
charge and explain why attraction occurs.
5. Why does a plastic ruler that has been rubbed with a cloth have the ability to pick up small pieces of paper? Why is this difficult
to do on a humid day?
11. Is the electric force a conservative force? Why or why not? (See Chapter 6.)
14. When determining an electric field, must we use a positive test charge, or would a negative one do as well? Explain.
20. Given two point charges Q and 2Q, a distance l apart, is there a point along the straight line that passes through them where
E  0 when their signs are (a) opposite, (b) the same? If yes, state roughly where this point will be.
21. Consider a small positive test charge located on an electric field line at some point, such as point P in Fig.
16–31a. Is the direction of the velocity and/or acceleration of the test charge along this line? Discuss.
Problems
Coulomb’s Law
16–5 and 16–6
3
[1 mC  10 C, 1 C  10
6
C, 1 nC  10 9 C.]
(I) Calculate the magnitude of the force between two 3.60-C point charges 9.3 cm apart.
3. (I) What is the magnitude of the electric force of attraction between an iron nucleus (q  26e) and its
innermost electron if the distance between them is 1.5 10 12 m?
7. (II) Two charged spheres are 8.45 cm apart. They are moved, and the force on each of them is found to
have been tripled. How far apart are they now?
12. (II) Particles of charge 75,  48, and 85 C are placed in a line (Fig. 16–49). The center one is 0.35 m
from each of the others. Calculate the net force on each charge due to the other two.
16–7 and 16–8 Electric Field, Field Lines
1.
23. (I) What are the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2360 N C
that points due east?
25. (I) A downward force of 8.4 N is exerted on a 8.8 C charge. What are the magnitude and direction of the electric field at this
point?
27. (II) What is the magnitude of the acceleration experienced by an electron in an electric field of 750 N C? How does the
direction of the acceleration depend on the direction of the field at that point?
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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.