Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 5 Work and Energy - all with Video Answers

Educators

Chapter Questions

01:30

Problem 1

Can the speed of an object change if the net work done on it is zero?

David Aplin

Numerade Educator

02:53

Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative.
a. a chicken scratching the ground
b. a person reading a sign
c. a crane lifting a bucket of concrete
d. the force of gravity on the bucket in (c)

David Aplin

Numerade Educator

03:24

Problem 3

Furniture movers wish to load a truck using a ramp from the ground to the rear of the truck. One of the movers claims that less work would be required if the ramp's length were increased, reducing its angle with the horizontal. Is this claim valid? Explain.

David Aplin

Numerade Educator

04:42

Problem 4

A pendulum swings back and forth, as shown at right. Does the tension force in the string do work on the pendulum bob? Does the force of gravity do work on the bob? Explain
your answers. (IMAGE CAMMOT COPY)

David Aplin

Numerade Educator

04:58

Problem 5

The drivers of two identical cars heading toward each other apply the brakes at the same instant. The skid marks of one of the cars are twice as long as the skid marks of the other vehicle. Assuming that the brakes of both cars apply the same force, what conclusions can you draw about the motion of the cars?

David Aplin

Numerade Educator

04:17

Problem 6

When a punter kicks a football, is he doing work on the ball while his toe is in contact with it? Is he doing work on the ball after the ball loses contact with his toe? Are any forces doing work on the ball while the ball is in flight?

David Aplin

Numerade Educator

01:07

Problem 7

A person lifts a $4.5 \mathrm{kg}$ cement block a vertical distance of $1.2 \mathrm{m}$ and then carries the block horizontally a distance of $7.3 \mathrm{m} .$ Determine the work done by the person and by the force of gravity in this process.

S S

Numerade Educator

02:40

Problem 8

A plane designed for vertical takeoff has a mass of $8.0 \times 10^{3} \mathrm{kg} .$ Find the net work done by all forces on the plane as it accelerates upward at $1.0 \mathrm{m} / \mathrm{s}^{2}$ through a distance of $30.0 \mathrm{m}$ after starting from rest.

David Aplin

Numerade Educator

01:39

Problem 9

When catching a baseball, a catcher's glove moves by $10 \mathrm{cm}$ along the line of motion of the ball. If the baseball exerts a force of $475 \mathrm{N}$ on the glove, how much work is done by the ball?

David Aplin

Numerade Educator

08:19

Problem 10

A flight attendant pulls her $70.0 \mathrm{N}$ flight bag a distance of $253 \mathrm{m}$ along a level airport floor at a constant velocity. The force she exerts is $40.0 \mathrm{N}$ at an angle of
$52.0^{\circ}$ above the horizontal. Find the following:
a. the work she does on the flight bag
b. the work done by the force of friction on the flight bag
c. the coefficient of kinetic friction between the flight bag and the floor

David Aplin

Numerade Educator

02:28

Problem 11

A person drops a ball from the top of a building while another person on the ground observes the ball's motion. Each observer chooses his or her own
location as the level for zero potential energy. Will they calculate the same values for:
a. the potential energy associated with the ball?
b. the change in potential energy associated with the ball?
c. the ball's kinetic energy?

Surjit Tewari

Numerade Educator

00:36

Problem 12

Can the kinetic energy of an object be negative? Explain your answer.

S S

Numerade Educator

00:51

Problem 13

Can the gravitational potential energy associated with an object be negative? Explain your answer.

Surjit Tewari

Numerade Educator

01:01

Problem 14

Two identical objects move with speeds of $5.0 \mathrm{m} / \mathrm{s}$ and $25.0 \mathrm{m} / \mathrm{s} .$ What is the ratio of their kinetic
energies?

S S

Numerade Educator

02:08

Problem 15

A satellite is in a circular orbit above Earth's surface. Why is the work done on the satellite by the gravitational force zero? What does the work-kinetic energy theorem predict about the satellite's speed?

Surjit Tewari

Numerade Educator

01:34

Problem 16

A car traveling at $50.0 \mathrm{km} / \mathrm{h}$ skids a distance of $35 \mathrm{m}$ after its brakes lock. Estimate how far it will skid if its brakes lock when its initial speed is $100.0 \mathrm{km} / \mathrm{h}$ What happens to the car's kinetic energy as it comes to rest?

Surjit Tewari

Numerade Educator

01:07

Problem 17

Explain why more energy is needed to walk up stairs than to walk horizontally at the same speed.

Surjit Tewari

Numerade Educator

01:57

Problem 18

How can the work-kinetic energy theorem explain why the force of sliding friction reduces the kinetic energy of a particle?

Surjit Tewari

Numerade Educator

00:56

Problem 19

What is the kinetic energy of an automobile with a mass of $1250 \mathrm{kg}$ traveling at a speed of $11 \mathrm{m} / \mathrm{s} ?$

S S

Numerade Educator

01:52

Problem 20

What speed would a fly with a mass of 0.55 g need in order to have the same kinetic energy as the automobile in item $19 ?$

S S

Numerade Educator

01:45

Problem 21

A $50.0 \mathrm{kg}$ diver steps off a diving board and drops straight down into the water. The water provides an upward average net force of $1500 \mathrm{N}$. If the diver comes to rest $5.0 \mathrm{m}$ below the water's surface, what is the total distance between the diving board and the diver's stopping point underwater?

Surjit Tewari

Numerade Educator

03:05

Problem 22

In a circus performance, a monkey on a sled is given an initial speed of $4.0 \mathrm{m} / \mathrm{s}$ up a $25^{\circ}$ incline. The combined mass of the monkey and the sled is $20.0 \mathrm{kg}$ and the coefficient of kinetic friction between the sled and the incline is $0.20 .$ How far up the incline does the sled move?

Surjit Tewari

Numerade Educator

03:40

Problem 23

A $55 \mathrm{kg}$ skier is at the top of a slope, as shown in the illustration below. At the initial point $\mathbf{A}$, the skier is $10.0 \mathrm{m}$ vertically above the final point $\mathbf{B}.$
a. Set the zero level for gravitational potential energy at $\mathbf{B},$ and find the gravitational potential energy associated with the skier at $\mathbf{A}$ and at $\mathbf{B}$ Then find the difference in potential energy between these two points.
b. Repeat this problem with the zero level at point $\mathbf{A}.$
c. Repeat this problem with the zero level midway down the slope, at a height of $5.0 \mathrm{m}.$ (FIGURE CANNOT COPY)

Surjit Tewari

Numerade Educator

02:10

Problem 24

A $2.00 \mathrm{kg}$ ball is attached to a ceiling by a string. The distance from the ceiling to the center of the ball is $1.00 \mathrm{m},$ and the height of the room is $3.00 \mathrm{m} .$ What is the gravitational potential energy associated with the ball relative to each of the following?
a. the ceiling
b. the floor
c. a point at the same elevation as the ball

Surjit Tewari

Numerade Educator

02:11

Problem 25

A spring has a force constant of $500.0 \mathrm{N} / \mathrm{m} .$ Show that the potential energy stored in the spring is as follows:
a. $0.400 \mathrm{J}$ when the spring is stretched $4.00 \mathrm{cm}$ from equilibrium
b. 0.225 J when the spring is compressed $3.00 \mathrm{cm}$ from equilibrium
c. zero when the spring is unstretched

Surjit Tewari

Numerade Educator

02:07

Problem 26

Each of the following objects possesses energy. Which forms of energy are mechanical, which are nonmechanical, and which are a combination?
a. glowing embers in a campfire
b. a strong wind
c. a swinging pendulum
d. a person sitting on a mattress
e. a rocket being launched into space

Surjit Tewari

Numerade Educator

01:21

Problem 27

Discuss the energy transformations that occur during the pole-vault event shown in the photograph below. Disregard rotational motion and air resistance, (IMAGE CAMMOT COPY)

Surjit Tewari

Numerade Educator

02:35

Problem 28

A strong cord suspends a bowling ball from the center of a lecture hall's ceiling, forming a pendulum. The ball is pulled to the tip of a lecturer's nose at the front of the room and is then released. If the lecturer remains stationary, explain why the lecturer is not struck by the ball on its return swing. Would this person be safe if the ball were given a slight push from its starting position at the person's nose?

Surjit Tewari

Numerade Educator

01:40

Problem 29

Discuss the work done and change in mechanical energy as an athlete does the following:
a. lifts a weight
b. holds the weight up in a fixed position
c. lowers the weight slowly

Surjit Tewari

Numerade Educator

02:46

Problem 30

A ball is thrown straight up. At what position is its kinetic energy at its maximum? At what position is gravitational potential energy at its maximum?

Surjit Tewari

Numerade Educator

02:01

Problem 31

Advertisements for a toy ball once stated that it would rebound to a height greater than the height from which it was dropped. Is this possible?

Surjit Tewari

Numerade Educator

01:43

Problem 32

A weight is connected to a spring that is suspended vertically from the ceiling. If the weight is displaced downward from its equilibrium position and released, it will oscillate up and down. How many forms of potential energy are involved? If air resistance and friction are disregarded, will the total mechanical energy be conserved? Explain.

Surjit Tewari

Numerade Educator

01:00

Problem 33

A child and sled with a combined mass of $50.0 \mathrm{kg}$ slide down a frictionless hill that is 7.34 m high. If the sled starts from rest, what is its speed at the bottom of the hill?

Surjit Tewari

Numerade Educator

03:25

Problem 34

Tarzan swings on a $30.0 \mathrm{m}$ long vine initially inclined at an angle of $37.0^{\circ}$ with the vertical. What is his speed at the bottom of the swing if he does the following?
a. starts from rest
b. starts with an initial speed of $4.00 \mathrm{m} / \mathrm{s}$

Surjit Tewari

Numerade Educator

02:46

Problem 35

If an automobile engine delivers 50.0 hp of power, how much time will it take for the engine to $\operatorname{do} 6.40 \times$ $10^{5}$ J of work? (Hint: Note that one horsepower, $1 \mathrm{hp}$, is equal to $746 \text { watts. })$

Surjit Tewari

Numerade Educator

01:13

Problem 36

Water flows over a section of Niagara Falls at the rate of $1.2 \times 10^{6} \mathrm{kg} / \mathrm{s}$ and falls $50.0 \mathrm{m} .$ How much power is generated by the falling water?

Surjit Tewari

Numerade Educator

03:49

Problem 37

A 215 g particle is released from rest at point $A$ inside a smooth hemispherical bowl of radius
$30.0 \mathrm{cm},$ as shown at right. Calculate the following:
a. the gravitational potential energy at
A relative to B
b. the particle's kinetic energy at $\mathbf{B}$
c. the particle's speed at $\mathbf{B}$
d. the potential energy and kinetic energy at $\mathbf{C}$

Surjit Tewari

Numerade Educator

01:53

Problem 38

A person doing a chin-up weighs $700.0 \mathrm{N},$ disregarding the weight of the arms. During the first $25.0 \mathrm{cm}$ of the lift, each arm exerts an upward force of $355 \mathrm{N}$ on the torso. If the upward movement starts from rest, what is the person's speed at this point?

Surjit Tewari

Numerade Educator

01:14

Problem 39

A $50.0 \mathrm{kg}$ pole vaulter running at $10.0 \mathrm{m} / \mathrm{s}$ vaults over the bar. If the vaulter's horizontal component of velocity over the bar is $1.0 \mathrm{m} / \mathrm{s}$ and air resistance is disregarded, how high was the jump?

Surjit Tewari

Numerade Educator

02:11

Problem 40

An $80.0 \mathrm{N}$ box of clothes is pulled $20.0 \mathrm{m}$ up a $30.0^{\circ}$ ramp by a force of $115 \mathrm{N}$ that points along the ramp. If the coefficient of kinetic friction between the box and ramp is $0.22,$ calculate the change in the box's kinetic energy.

Surjit Tewari

Numerade Educator

03:00

Problem 41

Tarzan and Jane, whose total mass is $130.0 \mathrm{kg},$ start their swing on a $5.0 \mathrm{m}$ long vine when the vine is at an angle of $30.0^{\circ}$ with the horizontal. At the bottom of the arc, Jane, whose 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.)

Surjit Tewari

Numerade Educator

02:10

Problem 42

A $0.250 \mathrm{kg}$ block on a vertical spring with a spring constant of $5.00 \times 10^{3} \mathrm{N} / \mathrm{m}$ is pushed downward, compressing the spring $0.100 \mathrm{m}$. When released, the block leaves the spring and travels upward vertically. How high does it rise above the point of release?

Nishant Kumar

Numerade Educator

03:29

Problem 43

Three identical balls, all with the same initial speed, are thrown by a juggling clown on a tightrope. The first ball is thrown horizontally, the second is thrown at some angle above the horizontal, and the third is thrown at some angle below the horizontal. Disregarding air resistance, describe the motions of the three balls, and compare the speeds of the balls as they reach the ground.

Surjit Tewari

Numerade Educator

02:16

Problem 44

A $0.60 \mathrm{kg}$ rubber ball has a speed of $2.0 \mathrm{m} / \mathrm{s}$ at point A and kinetic energy of $7.5 \mathrm{J}$ at point $\mathrm{B}$. 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 from A to B

Surjit Tewari

Numerade Educator

04:02

Problem 45

Starting from rest, a $5.0 \mathrm{kg}$ block slides $2.5 \mathrm{m}$ down a rough $30.0^{\circ}$ incline in 2.0 s. Determine the following:
a. the work done by the force of gravity
b. the mechanical energy lost due to friction
c. the work done by the normal force between the block and the incline

Surjit Tewari

Numerade Educator

01:09

Problem 46

A skier of mass $70.0 \mathrm{kg}$ is pulled up a slope by a motor-driven cable. How much work is required to pull the skier $60.0 \mathrm{m}$ up a $35^{\circ}$ slope (assumed to be frictionless) at a constant speed of $2.0 \mathrm{m} / \mathrm{s} ?$

Surjit Tewari

Numerade Educator

03:39

Problem 47

An acrobat on skis starts from rest $50.0 \mathrm{m}$ above the ground on a frictionless track and flies off the track at a $45.0^{\circ}$ angle above the horizontal and at a height of $10.0 \mathrm{m} .$ Disregard air resistance.
a. What is the skier's speed when leaving the track?
b. What is the maximum height attained?

Surjit Tewari

Numerade Educator

02:32

Problem 48

Starting from rest, a $10.0 \mathrm{kg}$ suitcase slides $3.00 \mathrm{m}$ down a frictionless ramp inclined at $30.0^{\circ}$ from the floor. The suitcase then slides an additional $5.00 \mathrm{m}$ along the floor before coming to a stop. Determine the following:
a. the suitcase's speed at the bottom of the ramp
b. the coefficient of kinetic friction between the suitcase and the floor
c. the change in mechanical energy due to friction

Surjit Tewari

Numerade Educator

01:26

Problem 49

A light horizontal spring has a spring constant of $105 \mathrm{N} / \mathrm{m} .$ A $2.00 \mathrm{kg}$ block is pressed against one end of the spring, compressing the spring $0.100 \mathrm{m}$. After the block is released, the block moves $0.250 \mathrm{m}$ to the right before coming to rest. What is the coefficient of kinetic friction between the horizontal surface and the block?

Surjit Tewari

Numerade Educator

04:50

Problem 50

A $5.0 \mathrm{kg}$ block is pushed $3.0 \mathrm{m}$ at a constant velocity up a vertical wall by a constant force applied at an angle of $30.0^{\circ}$ with the horizontal, as shown at right. If the coefficient of kinetic friction between the block and the wall is
$0.30,$ determine the following: (FIGURE CANNOT COPY)
a. the work done by the force on the block
b. the work done by gravity on the block
c. the magnitude of the normal force between the block and the wall

Surjit Tewari

Numerade Educator

03:42

Problem 51

A $25 \mathrm{kg}$ child on a $2.0 \mathrm{m}$ long swing is released from rest when the swing supports make an angle of $30.0^{\circ}$ with the vertical.
a. What is the maximum potential energy associated with the child?
b. Disregarding friction, find the child's speed at the lowest position.
c. What is the child's total mechanical energy?
d. If the speed of the child at the lowest position is $2.00 \mathrm{m} / \mathrm{s},$ what is the change in mechanical energy due to friction?

Surjit Tewari

Numerade Educator

04:54

Problem 52

A ball of mass $522 \mathrm{g}$ starts at rest and slides down a frictionless track, as shown in the diagram. It leaves the track horizontally, striking the ground. (GRAPH CANNOT COPY)
a. At what height above the ground does the ball start to move?
b. What is the speed of the ball when it leaves the track?
c. What is the speed of the ball when it hits the ground?

Surjit Tewari

Numerade Educator