Download Assignment 1 Chapter 5: Linear Forces

Chapter 5: Linear Forces
Assignment 1
Galileo and Inertia (a)
1
A ball is rolling with a velocity of 20 cm/sec and no outside
5
A 50-kg barbell can be lifted at a constant speed by
force acts on it.
exerting a force of 180 N on Planet X.
(a) Draw a free body diagram of the situation.
(a) Draw a free body diagram of the situation.
(b) What will be its velocity after 5 seconds?
(a) What is the acceleration of gravity on Planet X?
(b) If the same barbell is lifted on Earth the same way it
ANSWER
was lifted on planet X, what minimal force is needed?
20 cm/sec
2
ANSWER
(a)
It takes a net force of 50 N to give a body an acceleration of
(b) 3.6 m/s
2
10 m/sec .
2
2
(c) 4.9 x 10 N
(a) Draw a free body diagram of the situation.
(b) What is the mass of the body?
6
A car has a mass of 1600 kg. If a braking force of 500
Newtons is applied to the car while it is in motion, what is
ANSWER
the direction and magnitude of the acceleration it produces?
5.0 kg
ANSWER
3
A shot-putter exerts a net force of 140 N on a shot just
2
-0.312 m/sec
beore it is released from his hand. The shot has an observed
2
acceleration of 19 m/s .
(a) Draw a free body diagram of the situation.
(b) What is the mass of the shot?
7
A 65-kg swimmer steps horizontally off a 10-m tower. The
swimmer comes to a stop 2 m below the surface of the
water.
ANSWER
7.3 kg
(a) Draw a free body diagram of the swimmer in free fall.
(b) Find the swimmer's velocity just before he hits the
water.
4
You’re new motorcycle weighs 2450 N.
(a) Draw the free body diagram of this situation
(b) What is its mass in kilograms?
(c) Draw the free body diagram of the forces on the
swimmer as he enters the water.
(d) Find the net force exerted by the water on the swimmer
as he comes to rest below the surface of the water.
ANSWER
ANSWER
(a)
(b) 250 kg
(a)
(b) 14 m/s,
(c)
(d) 3185 N
Chapter 5: Linear Forces
Assignment 3
Defining Net Force--Newton's Second Law (d)
8
A shopper in a supermarket pushes a loaded 32 kg cart with
10
A 0.150 kg baseball is thrown straight upward with an
a horizontal force of 12 N.
initial speed of 20.0 m/s as it just leaves your hand.
(a) Draw a free body diagram of the situation
(a) Draw a free body diagram of the situation
(b) How far will the cart move in 3.5 s, starting from rest?
(b) Draw a free body diagram of the forces on the ball
(Disregard friction.)
when it reaches half its maximum height?
(c) What is the mass of the child?
(c) What is the force on the ball when it reaches half its
(d) What is the new acceleration of the cart?
maximum height?
(d) How far will the cart move in 3.5 s if the shopper
(d) Draw a free body diagram of the forces on the ball
places an 85 N child in the cart before pushing?
when it reaches its peak?
(e) What is the force on the ball when it reaches its peak?
ANSWER
(Disregard air resistance.)
(a)
ANSWER
(b) 2.3 m
(c) 8.67 kg
(a)
(d)
(b)
(e) 1.8 m
(c) -1.47 N
(d)
9
A 6.0 kg object undergoes an acceleration of 2.0 m/s
2
(e) -1.47 N
(a) Draw a free body diagram of the situation
(b) What is the magnitude of the net external force acting
11
A tow rope is used to pull a 1,750-kg car, giving it an
2
on it?
acceleration of 1.35 m/s .
(c) This same force is applied to a 4.0 kg object. Draw a
(a) Draw a free body diagram of the situation.
free body diagram of the new situation.
(b) What is the net force on the car?
(d) What acceleration is produced?
ANSWER
ANSWER
2,362.5 N
in the direction of the acceleration
(a)
(b) 12 N
(c)
(d) 3.0 m/s
2
Chapter 5: Linear Forces
Assignment 1
Graphing Motion and Force (e)
12
The figure to the left shows the motion of a 20 kg ball.
13
The diagram to the left show the motion of a 2000 kg motor
(a) Calculate the net force during the 0-5 second time
bike during a six second time interval.
interval?
(a) What is the observed accelration during 1-6 second
(b) Calculate the net force during the 5-10 second time
time interval?
interval?
(b) What is the Net Force during the 1-6 second time
(c) Calculate the net force during the 10-15 second time
interval?
interval?
(d) Calculate the net force during the 15-20 second time
interval?
(e) Calculate the net force during the 20-25 second time
interval?
ANSWER
(a)
(b)
ANSWER
14
The graph to the left shows the motion of a runner moving
during an eight second interval.
(a)
(a) What is the observed accelration during 1-6 second
(b)
time interval?
(c)
(b) What is the Net Force during the 1-6 second time
(d)
interval?
(e)
ANSWER
(a)
(b)
Chapter 5: Linear Forces
Assignment 2
Graphing Motion and Force (e)
15
The graph to the left shows the motion of a 5 kg object
17
A single net force of 10 N acts on an object of mass m. The
during a twelve second time interval
particle starts from rest and travels in a straight line a
(a) Calculate the net force during the 0-4 second time
distance of 18 m in 6 s.
interval?
(a) Draw a free body diagram of the situation
(b) Calculate the net force during the 4-8 second time
(b) What is the observed acceleration of the particle?
interval?
(c) Find its mass m.
(c) Calculate the net force during the 8-12 second time
ANSWER
interval?
(a)
(b)
(c) 10 kg
18
David Purley, a racing driver, survived deceleration from
173 km/h to 0.0 km/h over a distance of 0.660 m when his
car crashed. Assume that Purley's mass is 70.0 kg.
(a) Draw a free body diagram of the forces on David
Purley as he crashed into the wall.
ANSWER
(b) What is the observed acceleration on David Purley?
(c) What is the magnitude of the average force acting on
(a)
David Purley during the crash?
(b)
(d) What is David Purley’s weight?
(c)
(c) Compare the crash force to Purley's weight.
ANSWER
16
A net force of 9000 N is used to stop a 1500kg car traveling
at 20 m/s.
(a) Draw a free body diagram of the situation.
(b) What is the observed acceleration of the car?
(c) What braking distance is needed to bring the car to a
halt?
ANSWER
(a)
(b)
(c) 33 m
(a)
2
(b) -1749 m/s
5
(c) -1.22 x 10 N
2
(d) 6.87 x 10 N
(e) 178 times
Chapter 5: Linear Forces
Assignment 5
Kinematics and Force (f)
19
A 7.5 kg bowling ball initially at rest is dropped from the
21
Imagine a landing craft approaching the surface of Callisto,
top of an 11 m building. It hits the ground 1.5 s later.
one of Jupiter’s moons. If the engine provides an upward
(a) Draw a free body diagram of the situation
force (thrust) of 3260 N, the craft descends at a constant
(b) What is the acceleration of the bowling ball?
speed: If the engine provide only 2200 N, the craft
(c) Find the net external force on the falling ball.
accelerates downward at 0.39 m/s .
2
(a) Draw a free body diagram for the forces on the landing
ANSWER
craft for both situations.
(b) What is the weight of the landing craft in the vicinity of
(a)
Callisto's surface?
2
(b) 9.8 m/s
(c) What is the mass of the craft?
(c) 74 N
20
(d) What is the free fall acceleration near the surface of
Callisto?
In the figure below, the 10 kg block is attached to spring
balances calibrated in Newton’s. The system is accelerated
ANSWER
2
upward at the pulley with an acceleration of 5 m/s .
(a) Draw the free body diagram of the forces on the block.
(a)
(b) Give the readings of the balance assuming that the
(b) 3260 N
strings are massless
(c) 2.7 x 10 kg
3
2
(d) -1.2 m/s
22
A spaceship lifts off vertically from the moon, where the
2
free-fall acceleration is 1.6 m/s . An astronaut in the
2
spaceship has an upward acceleration of 1.0 m/s as it lifts
off.
(a) Draw a free body diagram of the forces on the an
astronaut in the spaceship.
(b) What is the force of the spaceship on the astronaut who
ANSWER
(a)
weighs 735 N on Earth?
ANSWER
(b) 74 N
(a)
(b) 195 N
Chapter 5: Linear Forces
Assignment 2
Lifts, Tensions, and Net Forces (g)
23
You need to lower a bundle of old roofing material
25
The parachute on a race car that weighs 8,820 N opens at
weighing 100 Newtons to the ground with a rope that will
the end of a quarter-mile run when the car is traveling 35
snap if the tension in it exceeds 87 Newtons.
m/s.
(a) Draw a free body diagram of the forces on the bundle
(a) Draw the free body diagram of the forces on the car as
of roofing material.
the parachute opens.
(a) What is the net force on on the bundle?
(b) What total retarding force must be supplied by the
(b) What is the observed acceleration on the bundle?
parachute to stop the car in a distance of 1100 m?
(c) How can you avoid snapping the rope during the
descent if you use only one ine?
ANSWER
(d) If the descent is 20 m and you just barely avoid
snapping the rope, with what speed will the bundle hit the
(a)
ground?
(b) -5.0 x 10 N
2
ANSWER
26
Two lifeguards pull on ropes attached to a raft. If they pull
in the same direction, the raft experiences a net external
(a)
force of 334 N to the right. If they pull in opposite
(b)
directions, the raft experiences a net external force of 105 N
(c) lower
to the left.
(d) 7.13 m/s
(a) Draw a free-body diagram representing the raft for each
24
situation.
A 75 kg person escapes from a burning building by jumping
(b) Find the force exerted by each lifeguard on the raft.
from a window 25 m above a catching net. Assume that air
(Disregard any other forces acting on the raft.)
resistance exerts a 95 N force on the person during the fall.
(a) Draw the free body diagram of the forces on the person
as he is falling.
ANSWER
(b) What is the net force on the falling body
(c) What is the observed acceleration of the falling body
(a)
(d) Determine the person's velocity just before he hits the
(b) 114 N;
net.
220 N
ANSWER
27
(a)
(b)
(c)
(d) 20.65 m/s
In a modified "tug-of-war" game, two people pull in
opposite directions, not on a rope, but on a 25-kg block
resting on a smooth surface. The participants exert forces
of 90 N and 92 N.
(a) Draw a free body diagram of the forces on the block
(b) What is the acceleration of the block?
ANSWER
2
0.08 m/s
Chapter 5: Linear Forces
Assignment 2
Lifts, Tensions, and Net Forces (g)
28
A vertical force T is exerted on a 5-kg body near the surface
2
30
Space-shuttle astronauts accelerate 35 m/s during takeoff.
of the earth, as shown in the figure below. For each of the
(a) Draw the free body diagram of the forces on an
following situations draw the free body diagram before you
astronaut seated in the space shuttle.
find the acceleration.
(b) What upward force does a 75 kg astronaut experience
(a) Find the acceleration of the body if T = 5 N.
during an acceleration of this magnitude?
(b) Find the acceleration of the body if T = 10 N.
ANSWER
(c) Find the acceleration of the body if T = 100 N.
(a)
(b) 3360 N
31
Two people pull on a 208 kg boat. If they pull in the same
2
direction the boat has an acceleration of 1.52 m/s . If they
pull in opposite directions, the boat has an acceleration of
2
0.518 m/s to the left.
ANSWER
(a) Draw a free body diagram for each situation.
2
(a) a = -8.81 m/s
(b) What is the magnitude of the force exerted by each
2
(b) a = -7.81 m/s
person on the boat?
2
(c) a = 10.2 m/s
ANSWER
29
A 1000-kg load is being moved by a crane. For each
situation draw a free body diagram before you solve the
(b) 104 N
problem.
(a) Find the tension in the cable that supports the load as it
2
is accelerated upward at 2 m/s .
(b) Find the tension in the cable that supports the load as it
is lifted at constant speed.
(c) Find the tension in the cable that supports the load as it
moves upward but its speed decreases by 2 m/s in each
second.
ANSWER
(a) 11,810 N
(b) 9810 N
(c) T = 7810 N
(a)
211 N
Chapter 5: Linear Forces
Assignment 3
Lifts, Tensions, and Net Forces (g)
32
A boat moves through the water with two forces acting on
35
3
The whale shark is the largest type of fish in the world. Its
4
it. One is a 2.10 x 10 N forward push by the motor, and the
mass can be as large as 2.0 x 10 kg, which is the equivalent
3
other is a 1.80 x 10 N resistive force due to the water.
mass of three average adult elephants. Suppose a crane lifts
(a) Draw the free body diagram of the forces on the motor.
a net with a 2.0 x 10 kg shark off the ground. The net is
(b) What is the net force on the boat?
steadily accelerated from rest over an interval of 0.80 s until
(c) What is the acceleration of the 1200 kg boat?
the net reaches a speed of 1.0 m/s.
(d) If it starts from rest, how far will it move in 10.0 s?
(a) Draw a free body diagram of the forces on the whale
(e) What will its velocity be at the end of this time
shark.
interval?
(b) Calculate the tension in the cable pulling the net.
ANSWER
ANSWER
(a)
(a)
(b)
(b) 2.21 x 10 N
4
5
(c) 0.25 m/s
2
(d) 12.5 m
36
The instruments attached to a weather balloon have a mass
of 5.0 kg. The balloon is released and exerts an upward
(e) 2.5 m/s
force of 98 N on the instruments.
33
A 5.0 kg bucket of water is raised from a well by a rope.
2
(a) Draw a free body diagram of the forces on the weather
The upward acceleration of the bucket is 23.0 m/s .
instruments from the balloon.
(a) Draw a free body diagram of the forces on the bucket
(b) What is the acceleration of the balloon and
(b) What is the net force on the bucket?
instruments?
(c) Find the force exerted by the rope on the bucket of
(c) After the balloon has accelerated for 10 seconds, the
water.
instruments are released. Draw a free body diagram of this
situation
ANSWER
(d) What is the velocity of the instruments at the moment
of their released?
(a)
(d) What net force acts on the instruments at their release?
(b)
(e) When does the direction of instruments velocity first
(c) 164 N
34
A 0.5 mm wire made of carbon and manganese can just
become downward?
ANSWER
barely support the weight of a 70.0 kg person. Suppose this
2
wire is used to lift a 45.0 kg load.
(a) 9.8 m/s , up;
(a) Draw a free body diagram of the forces on the person
(b) 98 m/s, up;
described in the two situations above.
(c) -49 N, down;
(b) What maximum upward acceleration can be achieved
(d)
without breaking the wire?
(e) 10 s
ANSWER
2
5.5 m/s
Chapter 5: Linear Forces
Assignment
Lifts, Tensions, and Net Forces (g)
37
A rubber ball weighs 49 N.
41
The maximum force a grocery sack can withstand and not
(a) What is the mass of the ball?
rip is 250 N. 20 kg of groceries are lifted from the floor to
(b) What is the acceleration of the ball if an upward force
the table with an acceleration of 5 m/s .
of 69 N is applied?
(a) Draw a free body diagram of the forces on the grocery
2
sack
ANSWER
(b) Will the sack hold?
(a) 5.0 kg
ANSWER
2
(b) 4.0 m/s
No, the sack will rip.
38
A small weather rocket weighs 14.7 N.
(a) What is its mass?
42
(b) The rocket is carried up by a balloon is released from
N/cm and compresses the spring 10 cm.
the balloon and fired, and its engine exerts an upward force
(a) What is the weight of the block?
of 10.2 N. What is the acceleration of the rocket?
(b) What is the mass of the block?
ANSWER
ANSWER
(a) 1.50 kg
(a) 20 N
2
(b) -3.00 m/s
39
A block is placed on a spring whose spring constant is 2.0
(b) 2.04 kg
A person fishing hooks a 2.0-kg fish on a line that can only
43
A vertical spring of force constant 400 N/m is attached to a
sustain a maximum of 38 N of force before breaking. At
10-kg block resting on a horizontal surface so that the
one point while reeling in the bass, it fights back with a
spring exerts an upward force on the block. The spring is
force of 40 N.
stretched by 10 cm.
(a) Draw a free body diagram of the forces on the fish.
(a) Draw a free body diagram of the situation.
(b) What is the minimum acceleration with which you must
(b) What force does the spring exert on the block?
play out the line during this time in order to keep the line
(c) What is the force that the surface exerts on the block?
from breaking?
ANSWER
ANSWER
-1 m/s
(a)
2
(b) 40 N
(c) 58.1 N
2
40
A 4500-kg helicopter accelerates upward at 2 m/s .
(a) Draw a free body diagram of the forces on the
helicopter.
(b) What lift force is exerted by the air on the propellers?
44
A 6-kg box slides on a frictionless horizontal surface. It is
pulled by a horizontal spring with force constant of 800
N/m. If the spring is stretched 4 cm from its equilibrium
ANSWER
4
5.3 x 10 N
position, what is the acceleration of the box?
ANSWER
2
5 1/3 m/s
Chapter 5: Linear Forces
Assignment 6
Elastic Forces--Springs (i)
45
A piece cut from a bicycle inner tube is stretched to a total
49
A slingshot consists of a light leather cup attached between
length of 0.7 m long when it carries a load of 25 N. The
two rubber bands.
force constant k is 300 N/m.
(a) If it takes a force of 32 N to stretch the bands 1.2 cm,
(a) How far did the rubber tube stretch when 75 Newton’s
what is the equivalent spring constant of the rubber bands?
of force were added?
(b) How much force is required to pull the cup of this
(b) What was the original length of the tube when no load
slingshot 3.0 cm from its equilibrium position?
was present. (Hint: You need to find the change in x---draw
ANSWER
all three pictures)
3
(a) 2.7 x 10 N/m
ANSWER
(b) 81 N
Hard
(a) .25
50
(b) .616 m
A load of 45 N attached to a spring that is hanging
vertically stretches the spring 0. 14 m. What is the spring
constant?
46
If a mass of 0.55 kg attached to a vertical spring stretches
ANSWER
the spring 2.0-cm from its equilibrium position, what is the
spring constant?
2
3.2 x 10 N/m
ANSWER
270 N/m
51
A pinball machine uses a spring that is compressed 4.0 cm
to launch a ball. If the spring constant is 13 N/m, what is
the force on the ball at the moment the spring is released?
47
A 76 N crate is attached to a spring (k = 450 N/m). How
much displacement is caused by the weight of this crate?
ANSWER
ANSWER
0.52 N
-0. 17
52
In an arcade game, a 0.12 kg disk is shot across a
frictionless horizontal surface by being compressed against
48
A spring of k = 1962 N/m loses its elasticity if stretched
more than 50.0 cm. Suppose the spring described above is
replaced with a spring that stretches 36 cm from its
equilibrium position.
a spring and then released. If the spring has a spring
constant of 230 N/m and is compressed from its equilibrium
position by 6.0 cm, what is the magnitude of the spring
force on the disk at the moment it is released?
(a) What is the spring constant in this case?
(b) Is the second spring stiffer or less stiff than the first
ANSWER
spring?
14 N
ANSWER
(a) 15 N/m
(b) less stiff
Chapter 5: Linear Forces
Assignment 6
Elastic Forces--Springs (i)
53
54
55
Janet wants to find the spring constant of a given spring, so
57
The pygmy shrew has an average mass of 2.0 g. How many
she hangs the spring vertically and attaches a 0.40 kg mass
shrews of average mass must be placed on a spring scale
to the spring's other end. If the spring stretches 3.0 cm from
with a spring constant of 24 N/m to produce 4.0 cm
its equilibrium position, what is the spring constant?
compression?
ANSWER
ANSWER
130 N/m
49 pygmy sherews
In preparing to shoot an arrow, an archer pulls a bow string
58
The largest meteorite of lunar origin reportedly has a mass
back 0.40 m by exerting a force that increases uniformly
of 19 g. If the meteorite produces a compression of 2.24
from 0 to 230 N. What is the equivalent spring constant of
mm when placed on a spring scale, what is the spring
the bow?
constant of the spring?
ANSWER
ANSWER
575 N/m
83 N/m
A child's toy consists of a piece of plastic attached to a
59
Rising 348 m above the ground, La Gran Piedra in Cuba is
2
spring, as shown in the figure. The spring is compressed
the tallest rock on Earth. Suppose an elastic band 2.00 x 10
against the floor a distance of 2.0 cm and released. If the
m long hangs vertically off the top of La Gran Piedra. If the
spring constant is 85 N/m, what is the magnitude of the
band's spring constant is 25.0 N/m, how large must a mass
spring force acting on the toy at the moment it is released?
be if, when it is attached to the band, it causes the band to
stretch all the way to the ground?
ANSWER
377 kg
60
ANSWER
Mauna Kea on the island of Hawaii stands 4200 m above
sea level. However, when measured from the island's seaf
-2
3.20 x 10 N/m, what force would stretch the spring to 1.02
1.7 N
4
x 10 m?
56
A spring of k = 1962 N/m loses its elasticity if stretched
ANSWER
more than 50.0 cm. What is the mass of the heaviest object
the spring can support without being damaged?
ANSWER
2
1.00 x 10 kg
190 N
Chapter 5: Linear Forces
Assignment 6
Elastic Forces--Springs (i)
61
In 1952, a great rainfall hit the island of Reunion in the
64
The largest known crab is a giant spider crab that had a
Indian Ocean. In less than 24 h, 187 kg of rain fell on each
mass of 18.6 kg. The distance from the end of one of this
square meter of soil. If a 187 kg mass is placed on a spring
crab's claws to the end of the other claw measured about 3.7
scale and the platform of the scale is compressed 12.0 cm
m. If this particular giant spider crab were hung from an
before it reaches equilibrium, what is the spring constant of
elastic band so that the elongation of the band was equal to
the spring?
the crab's claw span, what would be the spring constant of
the elastic band?
ANSWER
ANSWER
4
1.53 x 10 N/m
49 N/m
62
The largest ruby in the world may be found in New York.
This ruby is 109 mm long, 91 mm wide, and 58 mm thick,
65
3
The CN Tower in Toronto, Canada, is 553 m tall, making it
making its volume about 575 cm . (By comparison, the
the world's tallest free-standing structure. Suppose an
world's largest diamond, the Star of Africa, has a volume of
unusually long bungee cord is attached to the top of the CN
3
Tower. The equilibrium length of the cord is equal to one-
just over 30 cm .) If this ruby is attached to a vertically
2
hanging spring with a spring constant of 2.00 x 10 N/m so
third the height of the tower. When a test mass of 70.0 kg is
that the spring is stretched 15.8 cm, what is the mass of the
attached, the cord stretches to a length that equals two-
jewel?
thirds of the tower's height. From this information,
determine the spring constant of the bungee cord.
ANSWER
ANSWER
3.22 kg
3.87 N/m
63
The largest tigers, and therefore the largest members of the
cat family, are the Siberian tigers. Male Siberian tigers are
reported to have an average mass of about 389 kg. By
66
A net force of 55 N acts due west on an object. What added
single force on the object produces equilibrium?
contrast, a variety of very small cats that is native to India
have an average adult mass of only 1.5 kg. Suppose this
ANSWER
small cat is placed on a spring scale, causing the spring to
55 N
be extended from its equilibrium position by 1.2 mm. How
due East
far would the spring be extended if a typical male Siberian
tiger were placed on the same scale?
ANSWER
0.31 m
Chapter 5: Linear Forces
Assignment 6
Elastic Forces--Springs (i)
67
A spring is 6 cm long. When it is suspended vertically and
71
Suppose Joe, who weighs 625 N, stands on a bathroom
a 200 g mass is hung from its lower end, its length increases
scale calibrated in Newton’s.
to 7.5 cm.
(a) What force would the scale exert on Joe? In what
(a) What is the constant of the spring?
direction?
(b) What is the tension in the spring if it is stretched to 8.7
(b) If Joe now holds a 50-N cat in his arms, what force
cm?
would the scale exert on him?
(c) After Joe puts down the cat, his father comes up behind
ANSWER
him and lifts upward on his elbows with a 72-N force. What
force does the scale now exert on Joe?
(a) 1.34 N/cm
(b) 3.35 N
68
ANSWER
A spring which obeys Hooke's law is stretched 4 cm by a
(a) 625 N upward
force of 6 N.
(b) 675 N
(a) What is the value of k, the spring constant?
(c) 553 N; upward
(b) How much will the spring be stretched by a force of 1.5
N?
72
A 3.46 kg briefcase is sitting at rest on a level floor.
(a) What is its acceleration?
ANSWER
(b) What is its weight in Newton’s?
(c) What is it’s normal force?
(a) 1.5 N/cm
(b) 1 cm
69
ANSWER
Answer the following questions.
(a) zero
(a) What are the dimensions of Hooke's constant?
(b) 33.9 N
(b) What are the dimensions of the spring constant?
(c) What are the dimensions of the force constant?
73
A man stands on a scale in an elevator that has an upward
acceleration a. The scale reads 960 N. When he picks up a
ANSWER
(a) N/cm
(b) N/cm
20- kg box, the scale reads 1200 N. Find the mass of the
man, his weight, and the acceleration a.
ANSWER
(c) N/cm
m = 80 kg,
70
A 250 g block is placed on top of a vertical spring with a
W = 785 N = 176 lb.,
spring constant k =2.5 N/cm. How much is the spring
a = 2.19 m/s
compressed?
ANSWER
980 c
2
Chapter 5: Linear Forces
Assignment 4
Elevators (k)
74
An elevator weighing 3500 kg. is pulled upward by a cable
2
75
A student stands on a bathroom scale in an elevator at rest
with an acceleration of 1.00 m/s .
on the 64th floor of a building. The scale reads 836 N.
(a) Draw a free body diagram of this situation.
(a) As the elevator moves up, the scale reading increases to
(b) What is the tension in the cable?
935 N, then decreases back to 836 N. Draw a free body
2
(c) The elevator is decelerating at a rate of 1.00 m/s but is
diagram which explains this situation
still moving upward. Draw a free body diagram of this
(b) Find the acceleration of the elevator.
situation
(c) As the elevator approaches the 74th floor, the scale
(d) What is the tension in the elevator cable?
reading drops as low as 782 N. Draw a free body diagram
which explains this situation
ANSWER
(d) What is the acceleration of the elevator?
(e) Using your results from parts a and b, explain which
(a)
(a) 37,835 N
(c)
(b) 30, 835 N.
change in velocity, starting or stopping, would take the
longer time.
(f) Draw the set of free body diagram which shows the
elevator moving down
(g) Explain the changes in the scale you would expect on
the ride back down.
ANSWER
(a)
2
(b) 1.2 m/s ;
(c)
2
(d) - 0.63 m/s ;
(e) stopping, lower acceleration;
(f)
(g) scale reads less than 836 N, reads 836 N, then
Chapter 5: Linear Forces
Assignment 4
Elevators (k)
76
A lamp hangs vertically from a cord in a descending
78
2
A person weighing 490 N stands on a scale in an elevator.
elevator that decelerates at 2.4 m/s .
Draw a free body diagram for each situation.
(a) Draw a free body diagram of this situation.
(a) What does the scale read when the elevator is at rest?
(b) If the tension in the cord is 89 N, what is the lamp's
(b) What is the reading on the scale when the elevator rises
mass?
at a constant velocity?
2
(c) The elevator ascends with an upward acceleration of
(c) The rising elevator slows down at 2.2 m/s as it reaches
2
2.4 m/s
the desired floor. What does the scale read?
(d) What is the tension in the cord?
(d) The elevator descends, accelerating at 2.7 m/s . What
2
does the scale read?
ANSWER
(e) What does the scale read when the elevator descends at
a constant velocity?
(a)
(f) Suppose the cable snapped and the elevator fell freely.
(b) 7.29 kg
What would the scale read?
(c)
(d) 89 N
77
ANSWER
(a) 490 N
Safety engineers estimate that an elevator can hold 20
(b) 490 N
persons of 75-kg average mass. The elevator itself has a
2
(c) 3.8 x 10 N
mass of 500 kg. Tensile strength tests show that the cable
2
(d) 3.6 x 10 N
supporting the elevator can tolerate a maximum force of
(e) 490 N
4
2.96 x 10 N.
(f) 0
(a) Draw a free body diagram of the situation
(b) What is the greatest acceleration that the elevator's
motor can produce without breaking the cable?
79
A 60-kg girl weighs herself by standing on a scale in an
elevator. Draw a free body diagram for each situation.
ANSWER
(a) What does the scale read when the elevator is
descending at a constant rate of 10 m/s,
(a)
(b) What does the scale read when the elevator is
(b) 5 m/s
accelerating downward at 2 m/s , and
2
(c) What does the scale read when the elevator is ascending
at 10 m/s but its speed is decreasing by 2 m/s in each
second?
ANSWER
(a) 588 N
(b) 468 N
(c) Same as part (b)
Chapter 5: Linear Forces
Assignment 6
Friction (l)
80
The largest hydraulic turbines in the world have shafts with
82
5
A 35 kg crate is at rest on the floor. A man attempts to
individual masses that equal 3.18 x 10 kg. Suppose such a
push it across the floor by applying a 110-N force
shaft is delivered to the assembly line on a trailer that is
horizontally.
pulled with a horizontal force of 81.0 kN. If the force of
(a) Take the coefficient of static friction between the crate
friction opposing the motion is 62.0 kN what is the net
and the floor to be 0.37 and show that the crate does not
acceleration of the trailer?
move. (draw a free body diagram of the situation)
(b) What is the maximum magnitude Fs,max of the static
ANSWER
frictional force under the circumstances?
-2
2
(c) Does the crate move?
5.97 x 10 m/s
(d) Suppose next, that a second worker pulls directly
81
A 20.0 kg trunk is pushed across the floor of a moving van
upward on the crate to help out. What is the least pull she
by a horizontal force of 50.0 N. If the trunk moves with a
can exert that will allow the first worker's 110 N push to
constant velocity determine the coefficient of kinetic
move the crate? (hint draw a free body diagram of the
friction between the trunk and the floor.
situation)
(e) If, instead, the second worker pulls horizontally to help
ANSWER
out, what is the least pull she can exert to get the crate
moving? (hint draw a free body diagram of the situation)
0.255
ANSWER
(a) 110 N
(b) 130 N
(c) no
(d) 46 N
(e) 17 N
83
A person applies a 220 N horizontal force to a 55 kg crate
to push it across a level floor. If the coefficient of kinetic
friction is 0.35>
(a) What is the magnitude of the frictional force?
(b) What is the acceleration of the crate?
ANSWER
(a) 190 N
2
(b) 0.56 m/s
Chapter 5: Linear Forces
Assignment 6
Friction (l)
84
In 1994, a commercial automobile accelerated from rest to
88
Cleopatra's Needle, an obelisk given by the Egyptian
96.0 km/h in 3.07 s on a level road. Cars accelerate because
government to Great Britain in the late nineteenth century,
of the force of static friction between their tires and the
is more than 20 m tall and has a mass of roughly 1.89 x 10
road. Using this information, calculate the coefficient of
kg. Suppose the monument is lowered onto its side and
static friction between the tires and the road.
dragged horizontally to a new location. Given that the
5
magnitude of the acceleration of the monument is 0.120
ANSWER
2
m/s and the coefficient of kinetic friction is 0.100,
calculate the magnitude of the force that must be applied to
0.886
the monument in order to move it.
85
Until 1979, the world's easiest driving test was administered
ANSWER
in Egypt. To pass the test, one only needed to drive about
5
6.00 m forward, stop, and drive the same distance in
2.08 x 10 N
reverse. If a car's speed is 12.0 km/h at the end of the 6 m
distance and the braking distance through which the car
89
The heaviest train ever pulled by a single engine had a mass
7
slides is 1.00 m, what is the coefficient of kinetic friction?
of 1.554 x 10 kg and was over 2.00 km long. What force is
needed to pull the train with a constant acceleration of
ANSWER
2
0.200 m/s on a horizontal track? The coefficient of kinetic
friction between the train's wheels and the track is 0.080.
0.567
ANSWER
86
In 1988, a 3,500 kg telephone constructed by a Dutch
7
telecommunications company was demonstrated in the
1.5 x 10 N
Netherlands. Suppose this phone is towed horizontally by a
horizontal force equal to 8,800 N. Given that the coefficient
90
Isaac Newton developed the laws of mechanics. Brian
of kinetic friction is 0.12; calculate the magnitude of the net
Newton put those laws into application when he ran a
acceleration of the telephone.
marathon in about 8.5 h while carrying a bag containing 51
kg of coal. (By doing this, he set a strange but impressive
ANSWER
world record in 1983.) Suppose Brian Newton wants to
remove the bag from the finish line. He drags the bag with a
2
1.3 m/s
horizontal force of 140 N. If the coefficient of kinetic
5
87
A blue whale with a mass of 1.90 x 10 kg was caught in
friction between the bag and the pavement is 0.16, what is
1947. What minimum force would be needed to pull the
the magnitude of the net acceleration of the bag?
whale at a constant velocity along a horizontal ramp if the
ANSWER
coefficient of kinetic friction between the ramp's surface
and the whale were 0.160?
ANSWER
5
2.98 x 10 N
2
1 m/s
Chapter 5: Linear Forces
Assignment 6
Friction (l)
91
A hockey puck is hit on a frozen lake and starts moving
94
The coefficient of static friction between the floor of a truck
with a speed of 12.0 m/s. Exactly 5.00 s later, its speed is
and a box resting on it is 0.30. The truck is traveling at 80
6.00 m/s.
km/h. What is the least distance in which the truck can stop
(a) What is its average acceleration?
if the box is not to slide?
(b) What is the average value of the coefficient of kinetic
ANSWER
friction between puck and ice?
(c) How far does the puck travel during this 5.00 s
83.9
interval?
95
ANSWER
A 25 kg chair initially at rest on a horizontal floor requires a
365 N horizontal force to set it in motion. Once the chair is
(a) -1.2 m/s
in motion, a 327 N horizontal force keeps it moving at a
(b) 0.12
constant velocity.
(c) 45 m
(a) Find the coefficient of static friction between the chair
and the floor.
92
The force that accelerates a car along a flat road is the
(b) Find the coefficient of kinetic friction between the chair
frictional force exerted by the road on the car's tires.
and the floor.
(a) Explain why the acceleration can be greater when the
ANSWER
wheels do not spin.
(b) If a car is to accelerate from 0 to 90 km/h in 12 s at
a) 1.5
constant acceleration, what is the minimum coefficient of
(b) 1.3
friction needed between the road and tires?
96
ANSWER
A railroad flatcar is loaded with crates having a coefficient
of static friction 0.25 with the floor. If the train is moving
(a) Since
s
>
k
at 48 km/h, in how short a distance can the train be stopped
in general, the car's acceleration is
without letting the crate slide?
greater when the wheels do not spin.
(b) 0.212
93
ANSWER
A chair is sliding across a polished floor with an initial
36.28 m
speed of 3 m/s. It comes to rest after sliding 2 m. What is
the coefficient of kinetic friction between the floor and
chair?
97
You have to push with a force of 200 N to slide a
refrigerator across a floor at constant velocity. What is the
force of friction acting on the refrigerator?
ANSWER
ANSWER
0.229
Chapter 5: Linear Forces
Assignment 6
Friction (l)
98
A box weighing 600 N is pushed along a horizontal floor at
constant velocity with a force of 250 N parallel to the floor.
What is the coefficient of kinetic friction between the box
102 If you use a horizontal force of 30.0 N to slide a 12.0-kg
wooden crate across a floor at a constant velocity, what is
the coefficient of sliding friction between crate and floor?
and the floor?
ANSWER
ANSWER
0.255
0.417
99
The coefficient of static friction between the tires of a car
103 A 35 kg box rests on the back of a truck. The coefficient of
static friction between the box and the truck bed is 0.300.
and a horizontal road is m, = 0.6. If the net force on the car
(a) When the truck accelerates forward, what happens to
is the force of static friction exerted by the road,
the box?
(a) What is the maximum acceleration of the car?
(b) Find the maximum acceleration the truck can have
(b) What is the least distance in which the car can stop if it
before the box slides.
is initially traveling at 30 m/s?
ANSWER
ANSWER
(a) If F, > ma, then the box stays in place, but if F, <
(a) 5.89 m/s
2
ma, then the box will slide to the back of the truck
bed.
(b) 76.5 m
2
(b) 2.94 m/s
100 Answer the following questions.
(a) Estimate the maximum acceleration of a car if 40
percent of its weight is on the tires that are powered by the
104 You are driving a 2500.0-kg car at a constant speed of 14.0
m/s along an icy, but straight and level road. While
engine, and if the coefficient of static friction is 0.7.
approaching a traffic light, it turns red. You slam on the
(b) What is the shortest possible time in which this car can
brakes. Your wheels lock, the tires begin skidding, and the
achieve a speed of 100 km/h? Assume the engine has
car slides to a halt in a distance of 25.0 m. What is the
unlimited power.
coefficient of sliding friction (m) between your tires and the
icy roadbed?
ANSWER
(a) 2.75 m/s
2
(b) 10.1 s
101 The braking acceleration for a car based on data in a
2
driver's handbook was -12.2 m/s . If the car has a mass of
925 kg, find the frictional force and state the direction.
ANSWER
4
1.13 x 10 N,
opposite direction of motion
ANSWER
0.4
Chapter 5: Linear Forces
Assignment 6
Friction (l)
105 A sled of mass 50 kg is pulled along snow-covered, flat
ground. The static friction coefficient is 0.30, and the
sliding friction coefficient is 0.10.
108 A 200-kg crate is pushed horizontally with a force of 700
N. If the coefficient of friction is 0.20, calculate the
acceleration of the crate.
(a) What does the sled weigh?
(b) What force will be needed to start the sled moving?
(c) What force is needed to keep the sled moving at a
ANSWER
2
1.5 m/s
constant velocity?
(d) Once moving, what total force must be applied to the
2
sled to accelerate it 3.0 m/s ?
109 A force of 20 N accelerates a 9.0-kg wagon at 2.0 m/s
along the sidewalk
(a) How large is the frictional force?
ANSWER
(b) What is the coefficient of friction?
2
(a) 4.9 x 10 ;
ANSWER
(b) 150 N, static friction;
(c) 49 N, sliding friction;
(a) 2 N
2
(d) 2.0 x 10 N
(b) 0.02 N
106 A bedroom bureau with a mass of 45 kg, including drawers
and clothing, rests on the floor.
(a) If the coefficient of static friction between the bureau
and the floor is 0.45, what is the minimum horizontal force
a person must apply to start the bureau moving?
(b) If the drawers and clothing, with 17.0 kg mass, are
removed before the bureau is pushed, what is the minimum
horizontal force required to start it moving?
ANSWER
(a) 200 N
(b) 120
2
107 A force of 40 N accelerates a 5.0-kg block at 6.0 m/s along
a horizontal surface.
(a) How large is the frictional force?
(b) What is the coefficient of friction?
ANSWER
(a) 10 N
(b) 0.20
2
Chapter 5: Linear Forces
Assignment 6
Friction (l)
110 A museum curator moves artifacts into place on many
different display surfaces. Use the values in the table below
to find Fs, max and Fk for the following situations:
(a) Moving a 145 kg aluminum sculpture across a
112 Although the frictional force between two surfaces may
decrease as the surfaces are smoothed, it will increase if the
surfaces are made extremely smooth and flat. Explain.
ANSWER
horizontal steel platform
(b) Pulling a 15 kg steel sword across a horizontal steel
Because the surfaces are closer together, the
shield
molecules can more easily bond.
(c) Pushing a 227 kg wood bed on a wood floor
(d) Sliding a 0.55 kg glass amulet on a glass display case
113 The graph in the figure shows the relationship between the
applied force and the force of friction.
(a) What is the relationship between the forces at point A?
(b) What is the relationship between the forces at point B?
ANSWER
(a) 867 N
ANSWER
668 N
(a) Fs = Fapplied
(b) 109 N
(b) Fk < Fapplied
83.8 N
(c) 900 N
444 N
(d) 4.9 N
2N
111 A massive metal object on a rough metal surface may
undergo contact welding to that surface. Discuss how this
affects the frictional forces that arise between object and
114 A car is traveling at 50.0 km/h on a flat highway.
(a) If the coefficient of friction between the road and the
tires on a rainy day is 0. 100, what is the minimum distance
needed for the car to stop?
(b) What is the stopping distance when the surface is dry
and the coefficient of friction is 0.600?
ANSWER
surface.
(a) 98.5 m
ANSWER
The frictional forces will increase.
(b) 16.4 m
Chapter 5: Linear Forces
Assignment 6
Friction (l)
115 In order to drag a 100-kg log along the ground at constant
velocity, you have to pull on it with a horizontal force of
118 The largest flowers in the world are the Rafflesia Arnoldii,
found in Malaysia. A single flower is almost a meter across
300 N.
and has a mass up to 11.0 kg. Suppose you cut off a single
(a) What is the resistive force exerted by the ground?
flower and drag it along with a horizontal force of 42.0 N.
(b) What force must you exert if you want to give the log
If the flower's velocity is constant, what is the coefficient of
2
an acceleration of 2 m/s ?
kinetic friction between the flower and the ground?
ANSWER
ANSWER
0.389
(a) 300 N
(b) 500 N
116 A sky diver falls through the air.
(a) As the speed of the sky diver increases, what happens
to the sky diver's acceleration?
(b) What is the acceleration when the sky diver reaches
terminal speed?
ANSWER
(a) As the sky diver's speed increases, the
acceleration decreases because the resistive force
increases with increasing speed
(b) Zero.
117 A 55 kg ice skater, initially at rest on a flat skating rink,
requires a 198 N horizontal force to be set in motion.
However, after the skater is in motion, a horizontal force of
175 N keeps her moving at a constant speed. Find the
coefficients of static and kinetic friction between the skates
and the ice.
ANSWER
0.37;
0.32