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 happens to the truck’s acceleration if its trailer leaks sand

at a constant rate through a hole in its bottom?
19. A large crate is placed on the bed of a truck, but is not
tied down. (a) As the truck accelerates forward, the crate
remains at rest relative to it. What force causes the crate
to accelerate forward? (b) If the driver slams on the
brakes, what could happen to the crate?
20. Draw a free-body diagram for each of the following objects:
(a) a projectile in motion in the presence of air resistance,
(b) a rocket leaving the launch pad with its engines
operating, (c) an athlete running along a horizontal
track.
Section 4.1 Forces
Section 4.2 Newton’s First Law
Section 4.3 Newton’s Second Law
Section 4.4 Newton’s Third Law
1. A 6.0-kg object undergoes an acceleration of 2.0 m/s2.
(a) What is the magnitude of the resultant force acting on
it? (b) If this same force is applied to a 4.0-kg object, what
acceleration is produced?
2. A football punter accelerates a football from rest to a
speed of 10 m/s during the time in which his toe is in
contact with the ball (about 0.20 s). If the football has a
mass of 0.50 kg, what average force does the punter exert
on the ball?
3. The heaviest invertebrate is the giant squid, which is estimated
to have a weight of about 2 tons spread out over its
length of 70 feet. What is its weight in newtons?
4. The heaviest flying bird is the trumpeter swan, which
weighs in at about 38 pounds at its heaviest. What is its
weight in newtons?
5. A bag of sugar weighs 5.00 lb on Earth. What would it
weigh in newtons on the Moon, where the free-fall acceleration
is one-sixth that on Earth? Repeat for Jupiter,
where g is 2.64 times that on Earth. Find the mass of the
bag of sugar in kilograms at each of the three locations.
6. A freight train has a mass of 1.5  107 kg. If the locomotive
can exert a constant pull of 7.5  105 N, how long
does it take to increase the speed of the train from rest to
80 km/h?
7. The air exerts a forward force of 10 N on the propeller of
a 0.20-kg model airplane. If the plane accelerates forward
at 2.0 m/s2, what is the magnitude of the resistive force
exerted by the air on the airplane?
8. A 5.0-g bullet leaves the muzzle of a rifle with a speed of
320 m/s. What force (assumed constant) is exerted on the
bullet while it is traveling down the 0.82-m-long barrel of
the rifle?
9. A Chinook salmon has a maximum underwater speed of
3.0 m/s, and can jump out of the water vertically with a
speed of 6.0 m/s. A record salmon has a length of 1.5 m
and a mass of 61 kg. When swimming upward at constant
speed, and neglecting buoyancy, the fish experiences three
forces: an upward force F exerted by the tail fin, the downward
drag force of the water, and the downward force of
gravity. As the fish leaves the surface of the water, however,
it experiences a net upward force causing it to accelerate
from 3.0 m/s to 6.0 m/s. Assuming that the drag force disappears
as soon as the head of the fish breaks the surface
and that F is exerted until 2/3 of the fish’s length has left
the water, determine the magnitude of F.
10. Consider a solid metal sphere (S) a few centimeters in diameter
and a feather (F). For each quantity in the list that
follows, indicate whether the quantity is the same, greater,
or lesser in the case of S or in that of F? Explain in each
case why you gave the answer you did. Here is the list:
(a) the gravitational force; (b) the time it will take to fall a
given distance in air; (c) the time it will take to fall a given
distance in vacuum; (d) the total force on the object
when falling in vacuum.
11. A boat moves through the water with
two forces acting on it. One is a 2 000-N forward push by
the water on the propellor, and the other is a 1 800-N resistive
force due to the water around the bow. (a) What is
the acceleration of the 1000-kg boat? (b) If it starts from
rest, how far will the boat move in 10.0 s? (c) What will its
velocity be at the end of that time?
12. Two forces are applied to a car in an effort to move it, as
shown in Figure P4.12. (a) What is the resultant of these
two forces? (b) If the car has a mass of 3 000 kg, what
acceleration does it have? Ignore friction.
PROBLEMS
1, 2, 3 = straightforward, intermediate, challenging  = full solution available in Student Solutions Manual/Study Guide
= coached solution with hints available at www.cp7e.com = biomedical application
10°
30°
450 N 400 N
Figure P4.12
13. After falling from rest from a height of 30 m, a 0.50-kg
ball rebounds upward, reaching a height of 20 m. If the
contact between ball and ground lasted 2.0 ms, what average
force was exerted on the ball?
14. The force exerted by the wind on the sails of a sailboat is
390 N north. The water exerts a force of 180 N east. If the
boat (including its crew) has a mass of 270 kg, what are
the magnitude and direction of its acceleration?
Section 4.5 Applications of Newton’s Laws
15. Find the tension in each cable supporting the 600-N cat
burglar in Figure P4.15.
110 Chapter 4 The Laws of Motion
16. Find the tension in the two wires that support the 100-N
light fixture in Figure P4.16.
17. A 150-N bird feeder is supported by three cables as shown
in Figure P4.17. Find the tension in each cable.
37.0°
600 N
40° 40°
100 N
Figure P4.16
Figure P4.15
60° 30°
Bird
food
Figure P4.17
19. Two blocks are fastened to the ceiling of an elevator as in
Figure P4.19. The elevator accelerates upward at
2.00 m/s2. Find the tension in each rope.
20. Two people are pulling a boat through the water as in
Figure P4.20. Each exerts a force of 600 N directed at a
30.0 angle relative to the forward motion of the boat. If
the boat moves with constant velocity, find the resistive
force exerted by the water on the boat. F:
w1 = 220 N
110 N 40° a
w2
Figure P4.18
A
B
D
C
2.00 m/s2 10.0 kg
10.0 kg
Figure P4.19
F 30.0°
30.0°
600 N
600 N
Figure P4.20
21. The distance between two telephone poles is 50.0 m.
When a 1.00-kg bird lands on the telephone wire midway
between the poles, the wire sags 0.200 m. Draw a freebody
diagram of the bird. How much tension does the
bird produce in the wire? Ignore the weight of the wire.
22. You are a judge in a children’s kite-flying contest, and two
children will win prizes for the kites that pull most
strongly and least strongly, respectively, on their strings.
To measure string tensions, you borrow a weight hanger,
some slotted weights, and a protractor from your physics
teacher, and use the following protocol, illustrated in Figure
P4.22: Wait for a child to get her kite well controlled,
hook the hanger onto the kite string about 30 cm from
her hand, pile on weight until that section of string is horizontal,
record the mass required, and record the angle
between the horizontal and the string running up to the
kite. (a) Explain how this method works. As you construct
your explanation, imagine that the children’s parents ask
you about the method, that they might make false assumptions
about your ability without concrete evidence,
18. The leg and cast in Figure P4.18 weigh 220 N (w1).
Determine the weight w2 and the angle  needed so
that no force is exerted on the hip joint by the leg plus
the cast.
Problems 111
and that your explanation is an opportunity to give them
confidence in your evaluation technique. (b) Find the
tension in the string if the mass is 132 g and the angle
is 46.3 .
23. A 5.0-kg bucket of water is raised from a
well by a rope. If the upward acceleration of the bucket is
3.0 m/s2, find the force exerted by the rope on the bucket.
24. A shopper in a supermarket pushes a loaded cart with a horizontal
force of 10 N. The cart has a mass of 30 kg. (a) How
far will it move in 3.0 s, starting from rest? (Ignore friction.)
(b) How far will it move in 3.0 s if the shopper places his
30-N child in the cart before he begins to push it?
25. A 2 000-kg car is slowed down uniformly from 20.0 m/s to
5.00 m/s in 4.00 s. (a) What average force acted on the
car during that time, and (b) how far did the car travel
during that time?
26. Two packing crates of masses 10.0 kg and 5.00 kg are connected
by a light string that passes over a frictionless pulley
as in Figure P4.26. The 5.00-kg crate lies on a smooth
incline of angle 40.0 . Find the acceleration of the 5.00-kg
crate and the tension in the string.
28. An object of mass 2.0 kg starts from rest and slides down
an inclined plane 80 cm long in 0.50 s. What net force is
acting on the object along the incline?
29. A 40.0-kg wagon is towed up a hill inclined at 18.5 with
respect to the horizontal. The tow rope is parallel to the
incline and has a tension of 140 N. Assume that the
wagon starts from rest at the bottom of the hill, and
neglect friction. How fast is the wagon going after moving
80.0 m up the hill?
30. An object with mass m1  5.00 kg rests on a frictionless
horizontal table and is connected to a cable that passes
over a pulley and is then fastened to a hanging object with
mass m2  10.0 kg, as shown in Figure P4.30. Find the acceleration
of each object and the tension in the cable.
27. Assume that the three blocks portrayed in Figure P4.27
move on a frictionless surface and that a 42-N force acts
as shown on the 3.0-kg block. Determine (a) the acceleration
given this system, (b) the tension in the cord
connecting the 3.0-kg and the 1.0-kg blocks, and (c) the
force exerted by the 1.0-kg block on the 2.0-kg block.
31. A train has a mass of 5.22  106 kg and is moving at
90.0 km/h. The engineer applies the brakes, resulting in
a net backward force of 1.87  106 N on the train. The
brakes are held on for 30.0 s. (a) What is the final speed
of the train? (b) How far does the train travel during this
period?
32. (a) An elevator of mass m moving upward has two forces
acting on it: the upward force of tension in the cable and
the downward force due to gravity. When the elevator is
accelerating upward, which is greater, T or w? (b) When
the elevator is moving at a constant velocity upward,
which is greater, T or w? (c) When the elevator is moving
upward, but the acceleration is downward, which
is greater, T or w? (d) Let the elevator have a mass of
1 500 kg and an upward acceleration of 2.5 m/s2. Find T.
Is your answer consistent with the answer to part (a)? (e)
The elevator of part (d) now moves with a constant upward
velocity of 10 m/s. Find T. Is your answer consistent
with your answer to part (b)? (f) Having initially moved
upward with a constant velocity, the elevator begins to accelerate
downward at 1.50 m/s2. Find T. Is your answer
consistent with your answer to part (c)?
33. A 1 000-kg car is pulling a 300-kg trailer. Together, the car
and trailer have an acceleration of 2.15 m/s2 in the forward
direction. Neglecting frictional forces on the trailer,
determine (a) the net force on the car, (b) the net force
on the trailer, (c) the force exerted by the trailer on the
car, and (d) the resultant force exerted by the car on the
road.
34. Two objects with masses of 3.00 kg and 5.00 kg are connected
by a light string that passes over a frictionless pulley,
as in Figure P4.34. Determine (a) the tension in the
string, (b) the acceleration of each object, and (c) the distance
each object will move in the first second of motion
if both objects start from rest.
Figure P4.22
5.00 kg
10.0 kg
40.0°
Figure P4.26
1.0 kg
2.0 kg
3.0 kg
42 N
Figure P4.27
m1
m2
Figure P4.30 (Problems 30, 36, and 45)
112 Chapter 4 The Laws of Motion
Section 4.6 Forces of Friction
35. A dockworker loading crates on a ship finds that a 20-kg
crate, initially at rest on a horizontal surface, requires a
75-N horizontal force to set it in motion. However, after
the crate is in motion, a horizontal force of 60 N is required
to keep it moving with a constant speed. Find the
coefficients of static and kinetic friction between crate
and floor.
36. In Figure P4.30, m1  10 kg and m2  4.0 kg. The coefficient
of static friction between m1 and the horizontal surface
is 0.50, and the coefficient of kinetic friction is 0.30.
(a) If the system is released from rest, what will its acceleration
be? (b) If the system is set in motion with m2 moving
downward, what will be the acceleration of the system?
37. A 1 000-N crate is being pushed across a level floor at a
constant speed by a force of 300 N at an angle of 20.0
below the horizontal, as shown in Figure P4.37a. (a) What
is the coefficient of kinetic friction between the crate and
the floor? (b) If the 300-N force is instead pulling the
block at an angle of 20.0 above the horizontal, as shown
in Figure P4.37b, what will be the acceleration of the
crate? Assume that the coefficient of friction is the same
as that found in (a).
F:
not tied down to the truck and has a coefficient of static
friction of 0.500 with the truck bed. (a) Calculate the minimum
stopping distance for which the load will not slide
forward relative to the truck. (b) Is any piece of data unnecessary
for the solution?
40. A woman at an airport is towing her 20.0-kg suitcase at
constant speed by pulling on a strap at an angle 
 above
the horizontal (Fig. P4.40). She pulls on the strap with a
35.0-N force, and the friction force on the suitcase is
20.0 N. Draw a free-body diagram of the suitcase. (a) What
angle does the strap make with the horizontal? (b) What
normal force does the ground exert on the suitcase?
42. A box of books weighing 300 N is shoved across the floor
of an apartment by a force of 400 N exerted downward at
an angle of 35.2 below the horizontal. If the coefficient
of kinetic friction between box and floor is 0.570, how
long does it take to move the box 4.00 m, starting from
rest?
43. An object falling under the pull of gravity is acted upon
by a frictional force of air resistance. The magnitude of
this force is approximately proportional to the speed of
the object, which can be written as f  bv. Assume that
b  15 kg/s and m  50 kg. (a) What is the terminal
speed the object reaches while falling? (b) Does your answer
to part (a) depend on the initial speed of the object?
Explain.
44. A student decides to move a box of books into her dormitory
room by pulling on a rope attached to the box. She
pulls with a force of 80.0 N at an angle of 25.0 above
the horizontal. The box has a mass of 25.0 kg, and the
3.00 kg
5.00 kg
Figure P4.34
(a) (b)
F F
Figure P4.37
u
Figure P4.40
41. The coefficient of static friction between the 3.00-kg crate
and the 35.0 incline of Figure P4.41 is 0.300. What minimum
force must be applied to the crate perpendicular
to the incline to prevent the crate from sliding down the
incline?
F:
35.0°
3.00 kg
F
Figure P4.41
38. A hockey puck is hit on a frozen lake and starts moving
with a speed of 12.0 m/s. Five seconds later, its speed is
6.00 m/s. (a) What is its average acceleration? (b) What is
the average value of the coefficient of kinetic friction between
puck and ice? (c) How far does the puck travel during
the 5.00-s interval?
39. Consider a large truck carrying a heavy load, such as steel
beams. A significant hazard for the driver is that the load
may slide forward, crushing the cab, if the truck stops
suddenly in an accident or even in braking. Assume, for
example, that a 10 000-kg load sits on the flat bed of a
20 000-kg truck moving at 12.0 m/s. Assume the load is
Problems 113
coefficient of kinetic friction between box and floor is
0.300. (a) Find the acceleration of the box. (b) The student
now starts moving the box up a 10.0 incline, keeping
her 80.0 N force directed at 25.0 above the line of
the incline. If the coefficient of friction is unchanged,
what is the new acceleration of the box?
45. Objects with masses m1  10.0 kg and
m2  5.00 kg are connected by a light string that passes
over a frictionless pulley as in Figure P4.30. If, when the
system starts from rest, m2 falls 1.00 m in 1.20 s, determine
the coefficient of kinetic friction between m1 and the table.
46. A car is traveling at 50.0 km/h on a flat highway. (a) If the
coefficient of friction between road and tires on a rainy
day is 0.100, what is the minimum distance in which the
car will stop? (b) What is the stopping distance when the
surface is dry and the coefficient of friction is 0.600?
47. A 3.00-kg block starts from rest at the top of a 30.0 incline
and slides 2.00 m down the incline in 1.50 s. Find
(a) the acceleration of the block, (b) the coefficient of kinetic
friction between the block and the incline, (c) the
frictional force acting on the block, and (d) the speed of
the block after it has slid 2.00 m.
48. Objects of masses m1  4.00 kg and m2  9.00 kg are connected
by a light string that passes over a frictionless pulley
as in Figure P4.48. The object m1 is held at rest on the
floor, and m2 rests on a fixed incline of 
  40.0 . The objects
are released from rest, and m2 slides 1.00 m down the
incline in 4.00 s. Determine (a) the acceleration of each
object, (b) the tension in the string, and (c) the coefficient
of kinetic friction between m2 and the incline.
49. Find the acceleration reached by each of the two objects
shown in Figure P4.49 if the coefficient of kinetic friction
between the 7.00-kg object and the plane is 0.250.
friction between block and incline is s  0.300, determine
(a) the minimum value of and (b) the normal
force exerted by the incline on the block.
F:
51. The person in Figure P4.51 weighs 170 lb. Each crutch
makes an angle of 22.0 with the vertical (as seen from the
front). Half of the person’s weight is supported by the
crutches, the other half by the vertical forces exerted by
the ground on his feet. Assuming that he is at rest and
that the force exerted by the ground on the crutches acts
along the crutches, determine (a) the smallest possible
coefficient of friction between crutches and ground and
(b) the magnitude of the compression force supported by
each crutch.
40.0°
m2
m1
Figure P4.48
12.0 kg
7.00 kg
37.0°
Figure P4.49
F
θ
Figure P4.50
50. A 2.00-kg block is held in equilibrium on an incline of
angle 
  60.0 by a horizontal force applied in the direction
shown in Figure P4.50. If the coefficient of static
F:
52. A block of mass m  2.00 kg rests on the left edge of
a block of length L  3.00 m and mass M  8.00 kg.
The coefficient of kinetic friction between the two blocks
is k  0.300, and the surface on which the 8.00-kg block
rests is frictionless. A constant horizontal force of magnitude
F  10.0 N is applied to the 2.00-kg block, setting it
22.0° 22.0°
Figure P4.51
(a)
(b)
M
M
F m
L
F m
Figure P4.52
114 Chapter 4 The Laws of Motion
in motion as shown in Figure P4.52a. (a) How long will it
take before this block makes it to the right side of the
8.00-kg block, as shown in Figure P4.52b? (Note: Both
blocks are set in motion when the force is applied.)
(b) How far does the 8.00-kg block move in the process?
Additional Problems
53. In Figure P4.53, the coefficient of kinetic friction between
the two blocks shown is 0.30. The surface of the table and
the pulleys are frictionless. (a) Draw a free-body diagram
for each block. (b) Determine the acceleration of each
block. (c) Find the tension in the strings.
F:
54. The force exerted by the wind on a sailboat is approximately
perpendicular to the sail and proportional to the
component of the wind velocity perpendicular to the sail.
For the 800 kg sailboat shown in Figure P4.54, the proportionality
constant is
Water exerts a force along the keel (bottom) of the boat
that prevents it from moving sideways, as shown in the
figure. Once the boat starts moving forward, water also
exerts a drag force backwards on the boat, opposing the
forward motion. If a 17-knot wind (1 knot  0.514 m/s) is
blowing to the east, what is the initial acceleration of the
sailboat?
Fsail  550
N
m/s vwind⊥
59. A box rests on the back of a truck. The coefficient of static
friction between the box and the bed of the truck is 0.300.
(a) When the truck accelerates forward, what force accelerates
the box? (b) Find the maximum acceleration the truck
can have before the box slides.
60. A 4.00-kg block is pushed along the ceiling with a constant
applied force of 85.0 N that acts at an angle of 55.0
T1
T2
2.0 kg
3.0 kg
10.0 kg
Figure P4.53
30°
E
N
Fkeel
Fsail
Figure P4.54
45.0° 45.0°
60.0 N 60.0 N
Figure P4.55
55. (a) What is the resultant force exerted by the two cables
supporting the traffic light in Figure P4.55? (b) What is
the weight of the light?
56. As a protest against the umpire’s calls, a baseball pitcher
throws a ball straight up into the air at a speed of 20.0
m/s. In the process, he moves his hand through a distance
of 1.50 m. If the ball has a mass of 0.150 kg, find the
force he exerts on the ball to give it this upward speed.
57. A boy coasts down a hill on a sled, reaching a level surface
at the bottom with a speed of 7.0 m/s. If the coefficient of
friction between the sled’s runners and the snow is 0.050
and the boy and sled together weigh 600 N, how far does
the sled travel on the level surface before coming to rest?
58. (a) What is the minimum force of friction required to
hold the system of Figure P4.58 in equilibrium? (b) What
coefficient of static friction between the 100-N block and
the table ensures equilibrium? (c) If the coefficient of kinetic
friction between the 100-N block and the table is
0.250, what hanging weight should replace the 50.0-N
weight to allow the system to move at a constant speed
once it is set in motion?
100 N
50.0 N
Figure P4.58
55.0°
85.0 N
Figure P4.60
Problems 115
with the horizontal, as in Figure P4.60. The block accelerates
to the right at 6.00 m/s2. Determine the coefficient
of kinetic friction between block and ceiling.
61. A frictionless plane is 10.0 m long and inclined at 35.0 .
A sled starts at the bottom with an initial speed of 5.00
m/s up the incline. When the sled reaches the point at
which it momentarily stops, a second sled is released
from the top of the incline with an initial speed vi. Both
sleds reach the bottom of the incline at the same moment.
(a) Determine the distance that the first sled traveled
up the incline. (b) Determine the initial speed of
the second sled.
62. Three objects are connected by light strings as shown in
Figure P4.62. The string connecting the 4.00-kg object
and the 5.00-kg object passes over a light frictionless
pulley. Determine (a) the acceleration of each object and
(b) the tension in the two strings.
64. A 5.0-kg penguin sits on a 10-kg sled, as shown in Figure
P4.64. A horizontal force of 45 N is applied to the sled,
but the penguin attempts to impede the motion by holding
onto a cord attached to a wall. The coefficient of kinetic
friction between the sled and the snow, as well as
that between the sled and the penguin, is 0.20. (a) Draw a
free-body diagram for the penguin and one for the sled,
and identify the reaction force for each force you include.
Determine (b) the tension in the cord and (c) the acceleration
of the sled.
63. A 2.00-kg aluminum block and a 6.00-kg copper block are
connected by a light string over a frictionless pulley. The
two blocks are allowed to move on a fixed steel block
wedge (of angle 
  30.0 ) as shown in Figure P4.63.
Making use of Table 4.2, determine (a) the acceleration
of the two blocks and (b) the tension in the string.
5.00 kg
4.00 kg
3.00 kg
Figure P4.62
θ
Copper
Aluminum
Steel
m1
m2
Figure P4.63
45 N
Figure P4.64
65. Two boxes of fruit on a frictionless horizontal surface are
connected by a light string as in Figure P4.65, where m1 
10 kg and m2  20 kg. A force of 50 N is applied to the
20-kg box. (a) Determine the acceleration of each box
and the tension in the string. (b) Repeat the problem for
the case where the coefficient of kinetic friction between
each box and the surface is 0.10.
66. A high diver of mass 70.0 kg jumps off a board 10.0 m
above the water. If her downward motion is stopped 2.00 s
after she enters the water, what average upward force did
the water exert on her?
67. Two people pull as hard as they can on ropes attached to
a 200-kg boat. If they pull in the same direction, the boat
has an acceleration of 1.52 m/s2 to the right. If they pull
in opposite directions, the boat has an acceleration of
0.518 m/s2 to the left. What is the force exerted by each
person on the boat? (Disregard any other forces on the
boat.)
68. A 3.0-kg object hangs at one end of a rope that is attached
to a support on a railroad car. When the car accelerates to
the right, the rope makes an angle of 4.0 with the vertical,
as shown in Figure P4.68. Find the acceleration of the car.
69. Three blocks of masses 10.0 kg, 5.00 kg, and 3.00 kg are
connected by light strings that pass over frictionless pulleys
as shown in Figure P4.69. The acceleration of the
5.00-kg block is 2.00 m/s2 to the left, and the surfaces are
4.0°
3.0 kg
a
Figure P4.68
T
50 N
m1 m2
Figure P4.65
116 Chapter 4 The Laws of Motion
70. An inquisitive physics student, wishing to combine pleasure
with scientific inquiry, rides on a rollercoaster sitting
on a bathroom scale. (Do not try this yourself on a roller
coaster that forbids loose heavy packages.) The bottom of
the seat in the rollercoaster car is in a plane parallel to
the track. The seat has a perpendicular back and a seat
belt that fits around the student’s chest in a plane parallel
to the bottom of the seat. The student lifts his feet from
the floor, so that the scale reads his weight, 200 lb, when
the car is horizontal. At one point during the ride, the car
zooms with negligible friction down a straight slope inclined
at 30.0 below the horizontal. What does the scale
read at that point?
71. A van accelerates down a hill (Fig. P4.71), going from rest
to 30.0 m/s in 6.00 s. During the acceleration, a toy (m 
0.100 kg) hangs by a string from the van’s ceiling. The acceleration
is such that the string remains perpendicular to
the ceiling. Determine (a) the angle 
 and (b) the tension
in the string.
72. An 80-kg stuntman jumps from a window of a building situated
30 m above a catching net. Assuming that air resistance
exerts a 100-N force on the stuntman as he falls, determine
his velocity just before he hits the net.
73. The parachute on a race car of weight 8 820 N opens at
the end of a quarter-mile run when the car is traveling at
35 m/s. What total retarding force must be supplied by
the parachute to stop the car in a distance of 1 000 m?
74. On an airplane’s takeoff, the combined
action of the air around the engines and wings of an airplane
exerts an 8 000-N force on the plane, directed upward
at an angle of 65.0 above the horizontal. The plane rises
with constant velocity in the vertical direction while continuing
to accelerate in the horizontal direction. (a) What is the
weight of the plane? (b) What is its horizontal acceleration?
77. The board sandwiched between two other boards in Figure
P4.77 weighs 95.5 N. If the coefficient of friction between
the boards is 0.663, what must be the magnitude
of the compression forces (assumed to be horizontal) acting
on both sides of the center board to keep it from
slipping?
78. A magician pulls a tablecloth from under a 200-g mug located
30.0 cm from the edge of the cloth. The cloth exerts
a friction force of 0.100 N on the mug and is pulled
with a constant acceleration of 3.00 m/s2. How far does
the mug move relative to the horizontal tabletop before
the cloth is completely out from under it? Note that the
cloth must move more than 30 cm relative to the tabletop
during the process.
79. An inventive child wants to reach an apple in a tree without
climbing the tree. Sitting in a chair connected to a
rope that passes over a frictionless pulley (Fig. P4.79),
the child pulls on the loose end of the rope with such a
force that the spring scale reads 250 N. The child’s true
weight is 320 N, and the chair weighs 160 N. (a) Show
that the acceleration of the system is upward and find its
magnitude. (b) Find the force the child exerts on the
chair.
10.0 kg
25.0°
T2
5.00 kg
3.00 kg
T1
Figure P4.69
u
u
Figure P4.71
F
Figure P4.76
Figure P4.77
rough. Find (a) the tension in each string and (b) the coefficient
of kinetic friction between blocks and surfaces.
(Assume the same k for both blocks that are in contact
with surfaces.)
75. A 72-kg man stands on a spring scale in an elevator. Starting
from rest, the elevator ascends, attaining its maximum
speed of 1.2 m/s in 0.80 s. The elevator travels with this
constant speed for 5.0 s, undergoes a uniform negative
acceleration for 1.5 s, and then comes to rest. What does
the spring scale register (a) before the elevator starts to
move? (b) during the first 0.80 s of the elevator’s ascent?
(c) while the elevator is traveling at constant speed?
(d) during the elevator’s negative acceleration?
76. A sled weighing 60.0 N is pulled horizontally across snow
so that the coefficient of kinetic friction between sled and
snow is 0.100. A penguin weighing 70.0 N rides on the
sled, as in Figure P4.76. If the coefficient of static friction
between penguin and sled is 0.700, find the maximum
horizontal force that can be exerted on the sled before
the penguin begins to slide off.
Problems 117
80. A fire helicopter carries a 620-kg bucket of water at the
end of a 20.0-m-long cable. Flying back from a fire at a
constant speed of 40.0 m/s, the cable makes an angle of
40.0 with respect to the vertical. Determine the force exerted
by air resistance on the bucket.
81. A bag of cement hangs from three wires as shown in Figure
P4.81. Two of the wires make angles and , respectively,
with the horizontal. (a) Show that, if the system is in
equilibrium, then
(b) Given that w  325 N,  10.0 , and  25.0 , find
the tensions T1, T2, and T3 in the wires.
 
1
T1 
w cos 
2
sin(
1  
2)
 
1
Activities
A.1. There is a simple method for measuring the coefficients of
static and kinetic friction between an object and some surface.
For this investigation, you will need a few coins, your
textbook or some other flat surface that can be inclined, a
A.2. Borrow a spring scale from your instructor and use it to
study some of the properties of the force of friction. (1)
Attach the scale to a block of wood resting on the surface
of a table, and note the force required to start the block
moving. You should each take at least five trials and average
your results. This measured force is the maximum
value of the force of static friction between the block and
surface. (2) Now use the spring scale to measure the force
required to keep the block moving at constant velocity.
Again, perform several trials to find the average value for
this force. The force you find is the force of kinetic friction.
(3) Turn the block so that a side with a different surface
area is in contact with the table. Repeat the preceding
experiments to see if the area of contact between the surfaces
produces different values for the forces of friction.
A.3. Get a bathroom scale and stand on it while riding on an
elevator. Watch carefully what happens to your apparent
weight (the reading on the scale) as the elevator moves
upward or downward as a function of time. What do the
readings on the scale tell you about the acceleration of
the elevator during the ride?
Figure P4.79
w
θ1 θ2
Figure P4.81
Coin
u
Figure A
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