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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portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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
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.
6–8 and 6–9
Law of Conservation of Energy
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
 and v B are given by
mB head-on. (a) Show that the final velocities v A
 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
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.
71. 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?


75. The force on a bullet is given by the formula F  580  1.8 10 t over the time interval t  0 to t  3.0 10 3 s. In this
5
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?
79. 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.
80. 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?
81. 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 1026 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.
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
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.
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?
3.
4.
(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.
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
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.
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?
1 to 11–3 Simple Harmonic Motion
1.
3.
5.
9.
(I) If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it travels in one period? [T, f, A]
(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? [k, T, A, m, Fg]
(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? [f, T ]
(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?
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.