Chapter 15: Simple Energy
Transitions
Assignment 1
Defining Kinetic Energy (a)
1
Calculate the kinetic energy of a proton, mass 1.67 x 10-27
kg, traveling at 5.20 x 107 m/s.
6
A 6.0 kg cat runs after a mouse at 10.0 m/s. The 0.100 kg
mouse runs as fast as the cat. A 24 kg dog joins the race
with the same kinetic energy as the cat. What is the dog’s
speed?
Answer
Answer
2.26 x 10-12 Nm
5 m/s
2
A horizontal force of 150 N is used to push a 100.0 kg
packing crate a distance of 6.00 m on a rough horizontal
surface. If the crate moves at constant speed, calculate the
following:
(a) the work done by the force
(b) the coefficient of kinetic friction
7
Answer
1.10 x 109 Nm
Answer
(a) 900 Nm
(b).153
3
Calculate the kinetic energy of an 8.0 x 104 kg airliner
flying at 600.0 km/h.
8
A skier of mass 70.0 kg is pulled up a slope by a motordriven cable.
(a) How much work is required by the motor to pull the
skier 60.0 m up a 350 slope (assumed to be frictionless) at a
constant speed of 2.0 m/s?
(b) What is the kinetic energy of the skiier?
Two bullets have masses of 3.0 g and 6.0 g, respectively.
Both are fired with a speed of 40.0 m/s.
(a) Which bullet has more kinetic energy?
(b) What is the ratio of their kinetic energies?
Answer
(a) the bullet with the greater mass
(b) 2:1
Answer
(a) 23608 Nm
(b) 140 Nm
4
9
A 2.50 x 103 kg car requires 5.0 kJ of work to move from
rest to some final speed. During this time, the car moves
25.0 m.
(a) What is the final speed of the car?
(b) What is the net force exerted on the car?
Answer
Answer
7.61 x 103 Nm
10
(a) 2.0 m/s
(b) 200 N
5
A ski jumper starts from rest 50.0 m above the ground on a
frictionless track, and flies off the track at a 45.00 angle
above the horizontal and at a height of 10.0 m from the
ground. Disregard air resistance.
(a) What is the skier's speed when leaving the track?
(b) What is the maximum height attained?
Answer
(Hard)
(a) 28 m/s
(b) 30 m above ground
Dan Jansen of the United States won a speed-skating
competition at the 1994 Winter Olympics in Calgary,
Canada. He did this by skating 5.00 x 102 m with an
average speed of 50.3 km/h. If his mass was 78.0 kg, what
was his kinetic energy?
A running student has half the kinetic energy that his
younger brother has. The student speeds up by 1.3 m/s, at
which point he has the same kinetic energy as his brother. If
the student's mass is twice as large as his brother's mass,
what were the original speeds of both the student and his
brother?
Answer
Hard
3.2 m/s
6.4 m/s
11
The fastest auto race in the United States is the Busch Clash
at Daytona, Florida. In 1987, the winner's average speed
was about 318 km/h. If the kinetic energy of the winning
car was 3.80 MJ, what was the mass of the car and its
driver?
Answer
974 kg
Chapter 15: Simple Energy
Transitions
Assignment 1
Defining Kinetic Energy (a)
12
The male polar bear is the largest land-dwelling predator.
Its height when standing on its hind legs is more than 3 m
and its mass, which is usually around 500 kg, can be as
large as 680 kg. In spite of this bulk, a running polar bear
can reach speeds of 56.0 km/h.
(a) What is the kinetic energy of a running polar bear,
using the maximum values for its mass and speed?
(b) In 1994, Leroy Burrell of the United States set what
was then a new world record for the men's 100 m run. He
ran the 1.00 x 102 m distance in 9.85 s. What is the ratio of
the polar bear's kinetic energy to the kinetic energy of
Leroy Burrell? Leroy Burrell’s mass at the time was 75 kg.
16
A car traveling at 50.0 km/h skids a distance of 35 m after
its brakes lock.
(a) Estimate how far it will skid if its brakes lock when its
initial speed is 100.0 km/h.
(b) What happens to the car's kinetic energy as it comes to
rest?
Answer
(Hard)
(a) 140 m
(b) Kinetic Energy chanded to Thermal Energy
Answer
(a) 8.2 x 104 Nm
(b) 21.3 to 1
13
17
A 10.0 kg shopping cart is pushed from rest by a 250.0 N
force against a 50.0 N friction force over a 10.0 m distance
(a) How much work is done by each force on their cart?
(b) How much kinetic energy has the cart gained?
(c) What is the cart’s final speed?
Answer
How can the work-energy theorem explain why the force of
sliding firction usually reduces the kinetic energy of a
particle?
Answer
Work done by friction equals the chance in
mechanical enrgy so the particle’s speed ecreases
18
(a) 2.5 x 103Nm
-5 x 102 Nm
2. x 103 Nm
(b) 2 x 103 Nm
(c) 20 m/s
A 70.0 kg base runner begins his slide into second base
while moving at a speed of 4.0 m/s The coefficient of
friction between his clothes and Earth is 0.70. He slides so
that his speed is zero just as he reaches the base.
(a) How much mechanical energy is lost due to friction
acting on the runner?
(b) How far does he slide?
Answer
14
A 2.0 x 103 kg car moves down a level highway under the
actions of two forces. One is a 1,140 N forward force
exerted on the wheels by the road. The other is a 950 N
resistive force exerted on the car by the air. Use the workkinetic energy theorem to find the speed of the car after it
has moved a distance of 20.0 m, assuming the car starts
from rest.
(a) -560 J
(b) 1.16 m
19
Answer
1.9 m/s
A 4.0 kg mass moving at 5.0 m/sec?
(a) What is its kinetic energy
(b) If the mass was accelerated to this speed from rest by a
force of 20 N, over how long a distance did it act?
Answer
(a) 50 Nm
(b) 2.5 m
15
A force of 30.0 N pushes a 1.5-kg cart, initially at rest, a
distance of 2.8 m along a frictionless surface.
(a) Find the work done on the cart.
(b) What is its change in kinetic energy?
(c) What is the cart's final velocity?
Answer
(a) 84 Nm
(b) 84 Nm
(c) 10.5 m/s
20
A freely falling body starting from rest falls 4.9 m during
the first second and acquires a speed of 9.8 m/s.
(a) If the body has a mass of 1.0 kg what is its kinetic
energy at the end of the first second?
(b) What work does it take to raise the body to its previous
position?
Answer
(a) 48.02 Nm
(b) 48.02 Nm
Chapter 15: Simple Energy
Transitions
Assignment 2
Work-Kinetic Energy Theory (d)
21
22
The speed of an automobile of mass 1600 kg increases
uniformly from 20 m/sec to 30 m/sec
(a) What is the increase in kinetic energy
(b) If the acceleration increases uniformly over a distance
of 50 m, what force is accelerating the automobile?
Answer
A rifle can shoot a 4.20-g bullet at a speed of 965 m/s.
(a) Find the kinetic energy of the bullet.
(b) What work is done on the bullet if it starts from rest?
(c) If the work is done over a distance of 0.75 m, what is
the average force on the bullet?
(d) If the bullet comes to rest by pushing 1.5 cm into metal,
what is the magnitude and direction of the average force it
exerts?
(a) 400,000
(b) 8000
Answer
26
(a) 1955 Nm
(b) 1955 Nm
(c) 2608 N
(d) 130,333 N
A .22 caliber bullet of mass 0.0026 kg is shot into a massive
wooden target at 320 m/sec. It penetrates 0.08 m into the
target. What is the average force exerted on the bullet by
the wood? (Use the energy principle, do not find the
acceleration).
27
Answer
1664 N
23
It is not uncommon during the service of a professional
tennis player for the racquet to exert an average force of
150.0 N on the ball. If the ball has a mass of 0.060 kg and is
in contact with the strings of the racquet for 0.030 s, what is
the kinetic energy of the ball as it leaves the racquet?
Assume the ball starts from rest.
Answer
Hard
Answer
(a )-345 Nm
(b) -345 Nm
(c) 34.5 m
28
168.75 N.m
24
In the 1950s, an experimental train that had a mass of 2.50
x 104 kg was powered across level track by a jet engine that
produced a thrust of 5.00 x 105 N for a distance of 500 m.
(a) Find the work done on the train.
(b) Find the change in kinetic energy.
(c) Find the final kinetic energy of the train if it started
from rest.
(d) Find the final speed of the train if there was no friction.
Answer
A 14,700 N car is traveling at 25 m/s. The brakes are
suddenly applied and the car slides to a stop. The average
braking force between the tires and the road is 7100 N.
How far will the car slide once the brakes are applied?
Answer
A 2.00 x 103 kg car has a speed of 12.0 m/s. The car then
hits a tree. The tree doesn't move and the car comes to rest.
(a) Find the change in kinetic energy of the car.
(b) Find the amount of work done in pushing in the front of
the car.
(c) Find the size of the force that pushed the front of the car
in 50.0 cm.
Answer
(a) -144,000 Nm
(b) -144.000 Nm
(c) 288,000 N
29
(a) 2.5 x 108 Nm
(b) 2.5 x 108 Nm
(c) 2.5 x 108 Nm
(d) 141 m/s
25
A 15.0-kg cart is moving with a velocity of 7.50 m/s down
a level hallway. A constant force of -10.0 N acts on the cart
and its velocity becomes 3.20 m/s.
(a) What is the change in kinetic energy of the cart?
(b) How much work was done on the cart?
(c) How far did the cart move while the force acted?
Is conservation of mechanical energy likely to hold in these
situations?
(a) a hockey puck sliding on a frictionless surface of ice
(b) a toy car rolling on a carpeted floor
(c) a baseball being thrown into the air
Answer
30
Situated 4,080 m above sea level, La Paz, Bolivia, is the
highest capital in the world. If a car with a mass of 905 kg
is driven to La Paz from a location that is 1860 m above sea
level, what is the increase in potential energy?
66.02 m
Answer
1.97 x 107 J
Chapter 15: Simple Energy
Transitions
Assignment
Defining Gravitational Potential Energy (e)
31
In 1966, a special research cannon built in Arizona shot an
84 kg projectile to a height of 180 km above Earth's
surface. Find the potential energy associated with the
projectile when its altitude equals 10.0 percent of the
maximum height.
36
A person weighing 630 N climbs up a ladder to a height of
5.0 m.
(a) What work does the person do?
(b) What is the increase in the gravitational potential
energy of the person from the ground to this height?
(c) Where does the energy come from to cause this
increase in the gravitational potential energy?
Answer
1.5 x 107 J
32
The highest-caliber cannon ever built (though never used) is
located in Moscow, Russia. The diameter of the cannon's
barrel is about 89 cm, and the cannon's mass is 3.6 x 104 kg.
What potential energy would be associated with this cannon
if it were lifted by airplane to an altitude of 2.5 km above
sea level? Assume that constant free-fall acceleration at this
altitude is the same as at sea level.
Answer
(a) 3150 J
(b) 3150 J
(c) directly from the work done by the person;
indirectly from the chemical energy stored in the
person's body
37
Answer
8.8 x 108 J
33
Answer
In 1987, Stefka Kostadinova from Bulgaria set a new
women's record in high jump. It is known that the ratio of
the potential energy associated with Kostadinova at the top
of her jump to, her mass was 20.482 m2/s2. What was the
height of her record jump?
Answer
A pendulum is constructed from a 7.26 kg bowling ball
hanging on a 2.5 m long rope. The ball is pulled back until
the rope makes a 450 angle with the vertical.
(a) What is the potential energy of the ball?
(b) What reference level did you use in your calculation?
(a) 52 J
(b) the height of the ball when the rope was vertical.
38
A 6.4 kg bowling ball is lifted 2.1 m into a storage rack.
Calculate the increase in the ball's potential energy.
2.09 m
Answer
34
What PE does a 60.0 kg gymnast acquire in climbing 5.00
m up a vertical pole?
Answer
1.3 x 102 J
39
2.94 x 103 j
35
The 200 kg hammer of a pile driver is lifted 10.0 m. Find
the gravitational potential energy of the system when the
hammer is at this height.
A 40.0 kg child is in a swing that is attached to ropes 2.00
m long. Find the gravitational potential energy associated
with the child relative to the child's lowest position under
the following conditions:
(a) when the ropes are horizontal
(b) when the ropes make a 30.00 angle with the vertical
(c) at the bottom of the circular arc
Answer
Answer
(a) 785 J
(b) 105 J
(c) 0.00 J
19,600 joules
40
Ace raised a 12.0-N physics book from a table 75 cm above
the floor to a shelf, 2.15 m above the floor. What was the
change in potential energy?
Answer
16.8 J
Chapter 15: Simple Energy
Transitions
Assignment
Defining Gravitational Potential Energy (e)
41
A 60.0 kg shell is shot from a cannon to a height of 4.0 x
102 m.
(a) What is the gravitational potential energy of the earthshell system when the shell is at this height.
(b) What is the change in potential energy of the system
when the shell falls to a height of 2.00 x 102 m?
44
Answer
(a) 2.4 x 105 joules
(b) 1.2 x 105 joules
42
A 60.0 kg skier is at the top of a slope, as in the figure
below. At the initial point A, the skier is 10.0 m vertically
above the final point B.
(a) Set the zero level for gravitational potential energy at B,
and find the gravitational potential energy of the skier at A
and at B. Then find the difference in potential energy
between these two points.
(b) Repeat this problem with the zero level at point A.
(c) Repeat this problem with the zero level midway down
the slope, at a height of 5.0 m.
When a 50 kg girl walks a distance of 130 m from the
bottom to the top of a hill, her PE increases by 9800 J.
What is the vertical rise of the hill?
Answer
20 m
43
Answer
(Do in Class)
A 65 kg diver is poised at the edge of a 10.0 m high
platform. Calculate the gravitational potential energy
associated with the position of the diver. Assume the zero
level is at the surface of the pool.
(a) 5890 J
0J
5890 J
(b) 0 J
-5890 J
5890 J
(c) 2900 J
-2900 J
5800 J
Answer
6.4 x 103 J
45
A 70.0 kg stuntman is attached to a bungee cord with an
unstretched length of 15.0 m. He jumps off a bridge
spanning a river from a height of 50.0 m. When he finally
stops, the cord has a stretch length of 44.0 m. Treat the
stuntman as a point mass, and disregard the weight of the
bungee cord. Assuming the spring constant of the bungee
cord is 71.8 N/m, what is the total potential energy relative
to the water when the man stops falling?
Answer
3.43 x 104 J
46
The staples inside a stapler are kept in place by a spring
with a relaxed length of 0.115 m. If the spring constant is
51.0 N/m, how much elastic potential energy is stored in the
spring when its length is 0.150 m?
Answer
3.1 x 10-2 Nm
Chapter 15: Simple Energy
Transitions
Assignment 3
Defining Spring Potential Energy (f)
47
A spring with a force constant of 5.2 N/m has a relaxed
length of 2.45 m. When a mass is attached to the end of the
spring and allowed to come to rest, the vertical length of the
spring is 3.57 m. Calculate the elastic potential energy
stored in the spring.
52
An archer pulls the middle of the bowstring back a distance
of 0.30 m. If the force applied is 6.0 N, what potential
energy is stored in the stretched string of the bow?
Answer
Answer
.9 joules
PE = 1/2 kx2
3.3 J
48
49
The force constant of a spring in a child's toy car is 550
N/m. How much elastic potential energy is stored in the
spring if the spring is compressed a distance of 1.2 cm?
53
A pinball bangs against a bumper, giving the ball a speed of
42 cm/s. If the ball has a mass of 50.0 g, what is the ball's
kinetic energy in joules?
Answer
Answer
4.0 x 10-2 Nm
4.4 x 10-3 J
A spring has a force constant of 500.0 N/m. Show that the
energy stored in the spring is as follows:
(a) 0.400 J when the spring is stretched 4.00 cm from
equilibrium
(b) 0.225 J when the spring is compressed 3.00 cm from
equilibrium
(c) zero when the spring is unstretched
54
A 0.250 kg block on a vertical spring with a spring constant
of 5.00 x 103 N/m is pushed downward, compressing the
spring 0. 100 m. When released, the block leaves the spring
and travels upward vertically. How high does it rise above
the point of release?
Answer
Answer
(a) (0.5)(500.0 N/m)
(4.00 x 10-2 m)2 = 0.400 J
(b) (0.5)(500.0 N/m)
(3.00 x 10-2 m)2 = 0.225 J
(c) (0.5)(500.0 N/m)(0 m)2= 0 J
50
10.2 m
55
In 1992, David Engwall of California used a slingshot to
launch a dart with a mass of 62 g. The dart traveled a
horizontal distance of 477 m. Suppose the slingshot had a
spring constant of 3.0 x 104 N/m and was stretched 9.8 cm.
What was the elastic potential energy stored in the slingshot
just before the dart was launched?
Answer
(hard)
0.14 m
56
Answer
1.4 x 102 J
51
Suppose a 51 kg bungee jumper steps off the Royal Gorge
Bridge, in Colorado. The bridge is situated 321 m above the
Arkansas River. The bungee cord's spring constant is 32
N/m, the cord's relaxed length is 104 m, and its length is
179 m when the jumper stops falling. What is the total
potential energy associated with the jumper at the end of the
fall? Assume that the bungee cord has negligible mass.
Answer
16.1 x 104 J
A 0.18 kg ball is placed on a compressed spring on the
floor. The spring exerts an average force of 5.6 N through a
distance of 15 cm as it shoots the ball upward. How high
will the ball travel above the release spring?
A 10.0 kg test rocket is fired vertically from Cape
Canaveral. Its fuel gives it a kinetic energy of 1960 J by the
time the rocket motor burns all of the fuel. What additional
height will the rocket rise?
Answer
20.0 m
Chapter 15: Simple Energy
Transitions
Assignment 4
Conservation of Total Energy (g)
57
When April Moon set a record for flight shooting in 1981,
the arrow traveled a distance of 9.50 x 102 m. Suppose the
arrow had a mass of 65.0 g and that the angle at which the
arrow was launched was 45.00 above the horizontal.
(a) What was the kinetic energy of the arrow at the instant
it left the bowstring?
(b) If the bowstring was pulled back 55.0 cm from its
relaxed position, what was the spring constant of the
bowstring?
(c) Assuming that air resistance is negligible, use the
principle of energy conservation to determine the maximum
height that the arrow reaches.
(d) How does this value compare with the value found by
using the equations for projectile motion?
(e) What was the initial velocity of the arrow?
61
Answer
1.02 m
62
Answer
(hard)
(a) 312 J
(b) 4.00 x 103 N/m
(c) 238 m
(d) 237 m
(e) 98 m/s
58
Starting from rest, a 10.0 kg suitcase slides 3.00 m down a
frictionless ramp inclined at 30.00 from the floor. The
suitcase then slides an additional 5.00 m along the floor
before coming to a stop. following:
(a) Determine the speed of the suitcase at the bottom of the
ramp.
(b) Determine the mechanical energy lost due to friction.
(c) Determine the coefficient of kinetic friction between the
suitcase and the floor.
The largest watermelon ever grown had a mass of 118 kg.
Suppose this watermelon is exhibited on a platform 5.00 m
above the ground. After the exhibition, the watermelon is
allowed to slide to the ground along a smooth ramp. How
high above the ground is the watermelon at the moment its
kinetic energy is 4.61 kJ?
One species of eucalyptus tree, Eucalyptus Regnens, grows
to heights similar to those attained by California redwoods.
One specimen of eucalyptus tree has a measured height of
143.0 m. Suppose a bird sitting on top of this tree drops a
nut. What is the speed of the falling nut at the moment it is
50.0 m above the ground? Do you need to know the, mass
of the nut? Disregard air resistance.
Answer
42.7 m/s
63
In 1989, Michel Menin of France walked a tightrope 3150
m above the ground. Suppose a coin with a mass of 5.00 g
falls from Menin's pocket during his walk What potential
energy is associated with the coin when its speed is 60.0
m/s?
Answer
146 J
Answer
(a) 5.42 m/s
(b) 0.300
(c) 147 J
59
64
A certain motorcycle can attain a speed of 3.00 x 102 km/h.
Suppose a motorcyclist reaches this speed and then drives
the cycle up a hill, turning the engine off at the bottom of
the hill, before beginning the climb. If the motorcyclist
reaches a maximum height of 250.0 m, how much kinetic
energy is dissipated by friction? The combined mass of the
motorcycle and rider is 250.0 kg.
Answer
255, 486 Nm
An archer puts a 0.30-kg arrow to the bow string. A force of
201 N is applied to draw the string back 1.3 m.
(a) Assuming no frictional loss, with what speed does the
arrow leave the bow?
(b) If the arrow is shot straight up, how high does it rise?
Answer
(a) 295 m/s
(b) 44.4 m
65
Bill throws a 10.0-g ball straight down from a height of 2.0
m. The ball strikes the floor at a speed of 7.5 m/s. What was
the initial speed of the ball?
Answer
60
A 0.25-kg ball is dropped from a height of 3.2 m and
bounces to a height of 2.4 m. What is its loss in potential
energy?
Answer
-2.0 J
4.1 m/s
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (g)
66
A 15.0-kg model plane flies horizontally at a constant speed
of 12.5 m/s.
(a) Calculate its kinetic energy.
(b) The plane goes into a dive and levels off 20.4 m closer
to Earth. How much potential energy does it lose during the
dive? Assume no additional drag.
(c) How much kinetic energy does the plane gain during
the dive?
(d) What is its new kinetic energy
(e) What is its new horizontal velocity?
70
A pendulum has a bob whose mass is 1.0 kg. At either of
the highest points of its swing, the bob is 0.10 m higher
than it is at the lowest point of its swing.
(a) How much more potential energy does the bob have at
its highest point than it does at its lowest point?
(b) What is the kinetic energy of the bob when it passes
through the lowest point of its swing?
(c) What is its velocity at that point?
Answer
(a) .98 j
(b) .98 j
(c) 1.4 m/sec
Answer
(a)
(b)
(c)
(d)
(e)
67
3
1.17 x 10 J
3.00 x 103 J
3.00 x 103J
4.17 x 103 J
23.6 m/s
71
A mass of 2.0 kg is dropped from a height of 5.0 m. Make
a table showing its potential and kinetic energies when it is
at each of these distances from the ground:
(a) 5.0 m
(b) 4.0 m
(c) 2.0 m
(d) 0.0 m
A 0.60 kg rubber ball has a speed of 2.0 m/s at point A and
kinetic energy of 7.5 J at point B. Determine the following:
(a) the ball's kinetic energy at A
(b) the ball's speed at B
(c) the total work done on the ball as it moves from A to B
Answer
(a) 1.2 J
(b) 5.0 m/s
(c) 6.3 J
Answer
(a)
(b)
(c)
(d)
68
K=0 P=98
K=19 P=78.4 6
K=58.8 P=39.2
K=98 P=0
72
A particle of mass 522 g starts at rest and slides down a
frictionless track, as shown in the figure below. It leaves the
track horizontally, striking the ground.
(a) At what height above the ground does the ball start to
move?
(b) What is the ball's velocity when it leaves the track?
(c) What is the ball's velocity when it hits the ground?
A ping-pong ball of mass m rolls off the edge of a table that
is l m high. When the ball strikes the floor its speed is 5
m/sec. How fast was it rolling when it left the table? (use
the energy principle.)
Answer
2.36 m/sec
69
A cart of mass 500 kg starts from rest at the top of one hill,
rolls to the bottom, and then ascends a second hill. The
height of the first hill is 30 m and that of the second hill is
10 m. what is the kinetic energy of the cart when it reaches
the top of the second hill? (Neglect friction)
Answer
9.8 x 104 J
Answer
(a) 1.45 m
(b) 1.98 m/s
(c) 5.33 m/s
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (g)
73
A 215 g particle is released from rest at point A inside a
smooth hemispherical bowl of radius 30.0 cm, as shown in
the figure below. Calculate the following:
(a) Calculate the gravitational potential energy at A
relative to B
(b) Calculate the particle's kinetic energy at B
(c) Calculate the particle's speed at B
(d) Calculate the kinetic energy and potential energy at C
77
A pendulum bob, mass 0.5 kg is displaced from the vertical
until it is 0.25 m above its lowest point. Upon release, it
rises to a height of 0.24 m on the other side.
(a) How much energy was lost to friction?
(b) Assuming that half the total frictional loss (due to air
resistance and friction in the pivot) takes place during the
downward swing, with what speed does the bob pass
through the lowest point?
Answer
(a) 0.049 J
(b) 2.19 m/sec
78
Answer
(a)
(b)
(c)
(d)
74
0.633 j
0.633 j
2.43 m/s
0.211 J
0.422 j
Tarzan swings on a 30.0 m long vine initially inclined at an
angle of 37.00 with the vertical.
(a) What is his speed at the bottom of the swing if he starts
from rest?
(b) What is his speed at the bottom of the swing if he
pushes off with a speed of 4.00 m/s?
Answer
(a) 10.9 m/s
(b) 11.6 m/s
75
Tarzan and Jane, whose total mass is 130.0 kg, start their
swing on a 5.0 m long vine when the vine is at an angle of
30.00 with the horizontal. At the bottom of the arc, Jane,
who’s mass is 50.0 kg, releases the vine. What is the
maximum height at which Tarzan can land on a branch after
his swing continues? (Hint: Treat Tarzan's and Jane's
energies as separate quantities.)
Answer
2.5 m
76
Maven's mass is 28 kg. She climbs the 4.8 m ladder of a
slide, and reaches a velocity of 3.2 m/s at the bottom of the
slide. How much work was done by friction on Maven?
Answer
1173 J
A 0.10 kg steel ball drops to the floor from a height of 2.0
m and then rebounds to a height of 1.9 m.
(a) What was the potential energy of the ball at the moment
it was dropped?
(b) What was the kinetic energy of the ball just before it hit
the floor?
(c) What kinetic energy did the ball have just after it hit the
floor?
(d) What is the energy loss?
Answer
(a) 1.96 j
(b) 1.96 j
(c) 1.86 j
79
A 50.0 kg diver steps off a 10.0 m high diving board and
drops straight down into the water. If the diver comes to
rest 5.0 m below the surface of the water, determine the
average resistance force exerted on the diver by the water.
Answer
-15 x 103 N
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (Friction) (k)
80
The figure is a graph of the gravitational potential energy
and kinetic energy of a 75 g yo-yo as it moves up and down
on its string. Use the graph to answer the following
questions.
(a) By what amount does the mechanical energy of the yoyo decrease after 6.0 s?
(b) What is the speed of the yo-yo afte 4.5 s?
(c) What is the maximum height of the yo-yo?
84
During the hammer throw at a track meet, an 8.0 kg
hammer is accidentally thrown straight up. If 784 joules of
work were done on the hammer to give it its vertical
velocity, how high will it rise?
Answer
10 meters
85
An 8000 kg truck moves at 10 m/sec up a hill that makes an
angle of 100 degrees with the horizontal?
(a) What is the KE of the truck?
(b) What is his total energy after the truck has traveled for
5 seconds?
Answer
(a) 4 x 105 j
(b) 1.08 x 105 j
Answer
(a) 100 mj
(b) 3.1 m/s
(c) 0.8 m
81
86
The largest apple ever grown had a mass of about 1.47 kg.
Suppose you hold such an apple in your hand 1.50 m above
the ground. You accidentally drop the apple, then manage
to catch it just before it hits the ground. What are the
kinetic energy and speed of the apple at that moment?
A bird is flying with a speed of 18.0 m/s over water when it
accidentally drops a 2.00 kg fish. Assuming the altitude of
the bird is 5.80 m, and disregarding friction, what is the
speed of the fish when it hits the water?
Answer
20.7 m/s
87
Answer
21.6 J
5.42 m/s
A pendulum 2.0 m long is released from rest when the
support string is at an angle of 25.00 with the vertical. What
is the speed of the bob at the bottom of the swing?
Answer
1.9 m/s
82
A 50.0-kg shell is shot from a cannon at Earth's surface to a
height of 4.00 x 102 m.
(a) What is the gravitational potential energy with respect
to Earth's surface of the Earth-shell system when the shell is
at this height?
(b) What is the change in potential energy of the system
when the shell falls to a height of 2.00 x 102 m?
88
Answer
Answer
(a) at the ball's lowest height;
(b) at its maximum height
(a) 1.96 x 105 j
(b) -9.8 x 104 j
83
An average force of 8.2 N is used to pull a 0.80-kg rock,
stretching a sling shot 43 cm. The rock is shot downward
from a bridge 18 m above a stream. What will be the
velocity of the rock just before it enters the water?
A ball is thrown straight up.
(a) At what position is its kinetic energy at its maximum?
(b) At what position is gravitational potential energy at its
maximum?
89
A 75 kg boy, starting from rest, slides down a 30 degree hill
that is 70 m long. He arrives at the bottom with a speed of
15 m/sec. How much thermal energy has been shared
between the surface of the hill and the seat of his pants?
(Use the energy principle; do not find the acceleration.)
Answer
19.1 m/s
Answer
17,287 Joules
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (Springs) (i)
90
If the spring of a jack-in-the-box is compressed a distance
of 8.0 cm from its relaxed lengtha and then released, what
is the speed of the toy head when the spring returns to it
naturallength? Assume the mass of the toy head is 50.0g,
the spring constant is 80.0 N/m, and the toy head moves
only in the vertical direction. also disregard the mass of the
spring. (Hint: Remember that there are twto forms of
potential energy in the problem.)
94
Answer
2.9 m/s
91
The figure below, a 3.5-kg block is released from a
compressed spring whose spring constant is 640 N/m. After
leaving the spring at the spring's relaxed length, the block
travels over a horizontal surface, with a coefficient of
kinetic friction of 0.25, for a distance of 7.8 m before
coming to rest.
a. How much mechanical energy was dissipated by the
frictional force in bringing the block to rest?
b. What was the maximum kinetic energy of the block?
c. How far was the spring compressed before the block was
released?
An egg of mass 50 g is dropped from a building 20 m high
onto a target consisting of a thick block of foam rubber.
(a) Find the KE of the egg just as it strikes the target.
(b) The egg penetrates 20 cm into the rubber while
stopping. What force is exerted on the egg?
Answer
Answer
(a) 9.8 J
(b) 49 J
92
A runaway truck with failed brakes is barreling down a hill
at a speed of 15 m/s. Fortunately, there is an emergency
escape ramp, at the bottom of the hill. The inclination of the
ramp is 150. How far up the ramp must the truck go before
it comes to a complete stop.
Answer
93
Two snowy peaks are 850 m and 750 m above the valley
between them. A ski run extends down from the top of the
higher peak and then back up to the top of the lower one,
with a total length of 3.2 km and an average slope of 30o
(a) A skier starts from rest on the higher peak. At what
speed will he arrive at the top of the lower peak if he just
coasts without using the poles? Ignore friction.
(b) Approximately what coefficient of kinetic friction
between snow and skis would make him stop just at the top
of the lower peak?
(a) 67 J
(b) 67 J
(c) 0.46 m
95
A spring (k = 200 N/m) is fixed at the top of a friction less
plane that makes an angle of 400 with the horizontal as
shown in the figure. A 1.0 kg mass is projected up the
plane, from an initial position that is 0.60 m from the end of
the uncompressed spring, with an initial kinetic energy of
16 J.
(a) What is the kinetic energy of the mass at the instant it
has compressed the spring 0.20 m?
(b) With what kinetic energy must the mass be projected
up the plane if it is to stop momentarily when it has
compressed the spring by 0.40 m?
Answer
Answer
(a) 44 m/s
(b) 0.036
(a) 7.0 J
(b) 22J
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (Gravity) (h)
96
A 1000-kg roller-coaster car moves from point A, see the
figure to the left, to point B and then to point C.
(a) What is its gravitational PE at B and C relative to point
A? That is, take y = 0 at point A.
(b) What is the change in potential energy when it goes
from B to C?
(c) Repeat parts (a) and (b), but take the reference point (y
= 0) to be at point C.
98
A ball of mass m = 2.60 kg, starting from rest, falls a
vertical distance h = 55.0 cm before striking a vertical
coiled spring, which it compresses (see the figure to the
left) an amount Y = 15.0 cm. Determine the spring constant
of the spring. Assume the spring has negligible mass.
Measure all distances from the point where the ball first
touches the uncompressed spring (y = 0 at this point).
Answer
Answer
97
A pellet of mass 0.100 kg is pressed against a spring inside
a horizontal tube as shown in the figue to the left. The
spring (with spring constant k = 250 N/m) is compressed
6.0 cm and released. If the pellet detaches from the spring
when the latter reaches its normal length (x = 0), what
speed does the pellet acquire?
1584 N/m
99
Assume the height of the first hill in the figure to the left is
40 m. The car is found to reach a vertical height of only 25
m on the second hill before coming to a stop. It traveled a
total distance of 400 m. Estimate the average friction force
(assume constant) on the car. Assume the car has a mass of
1000 kg.
Answer
Answer
367.5 Nm
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (Mixed Systems) (j)
100 A 75-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 to the left (see the figure to the left)?
(b) If the trampoline behaves like a spring of spring
constant 5.2 x 104 N/m, how far does he depress it?
103 A block whose mass m is 5.7 kg slides on a horizontal
frictionless tabletop with a constant speed v of 1.2 m/s. It is
brought momentarily to rest as it compresses a spring in its
path (see the figure to the left). By what distance d is the
spring compressed? The spring constant k is 1500 N/m.
Answer
Answer
101 A roller coaster, shown in the figure to the left, is pulled up
to point A where it, and its screaming occupants, are
released from rest. Assuming no friction, calculate the
speed at points A, B, C, D.
on a
104 A ski jumper starts from rest 50.0 m above the ground
frictionless track, and flies off the track at a 45.00 angle
above the horizontal and at a height of 10.0 m from the
ground. Disregard air resistance.
(a) What is the skier's speed when leaving the track?
(b) What is the maximum height attained?
Answer
105 A ball of mass m = 2.60 kg, starting from rest, falls a
vertical distance h = 55.0 cm before striking a vertical
coiled spring, which it compresses (see the figure to the
left) an amount Y = 15.0 cm. Determine the spring constant
of the spring. Assume the spring has negligible mass.
Measure all distances from the point where the ball first
touches the uncompressed spring (y = 0 at this point).
Answer
A 0
B 24.28 m/s
C 9.89 m/s
D 18.73 m/s
102 Suppose the roller coaster in the figure to the left passes
point A with a speed of 1.70 m/s. If the average force of
friction is equal to one-fifth of its weight, with what speed
will it reach point B? The distance traveled is 45.0 m.
Answer
Answer
20.4 m/s
Chapter 15: Simple Energy
Transitions
Assignment
Conservation of Total Energy (Gravity) (h)
106 A 1000-kg roller-coaster car moves from point A, to the
left, to point B and then to point C. The car is initially
traveling at 15 m/s at position A.
(a) What is its potential energy at A?
(b) What is its kinetic energy at A?
(c) What is its potential energy at position B?
(d) What is the total energy at position B?
(e) What is the speed at position C?
Answer
107 A 1000-kg roller-coaster car moves from point A, to the
left, to point B and then to point C. The car is traveling at
15 m/s at A.
(a)
(b)
(c)
(d)
(e)
What is its potential energy at A
What is its kinetic energy at A?
What is its kinetic energy at position B?
What is its speed at position B
What is its speed at position C?
Answer