Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

Chapter 6

Work and Energy - all with Video Answers

Educators

Chapter Questions

Problem 1

During a tug-of-war, team A pulls on team B by applying a force of $1100 \mathrm{N}$ to the rope between them. The rope remains parallel to the ground. How much work does team A do if they pull team B toward them a distance of $2.0 \mathrm{m} ?$

Adnan Gill

Adnan Gill

Numerade Educator

Problem 2

You are moving into an apartment and take the elevator to the 6 th floor. Suppose your weight is $685 \mathrm{N}$ and that of your belongings is $915 \mathrm{N}$.
(a) Determine the work done by the elevator in lifting you and your belongings up to the 6 th floor $(15.2 \mathrm{m})$ at a constant velocity.
(b) How much work does the elevator do on you alone (without belongings) on the downward trip, which is also made at a constant velocity?

Adnan Gill

Numerade Educator

Problem 3

The brakes of a truck cause it to slow down by applying a retarding force of $3.0 \times 10^{3} \mathrm{N}$ to the truck over a distance of $850 \mathrm{m} .$ What is the work done by this force on the truck? Is the work positive or negative? Why?

Adnan Gill

Numerade Educator

Problem 4

A 75.0 -kg man is riding an escalator in a shopping mall. The escalator moves the man at a constant velocity from ground level to the floor above, a vertical height of $4.60 \mathrm{m}$. What is the work done on the man by (a) the gravitational force and (b) the escalator?

Adnan Gill

Numerade Educator

Problem 5

Suppose in Figure 6.2 that $+1.10 \times 10^{3}$ J of work is done by the force $\mathbf{F}$ (magnitude $=30.0 \mathrm{N}$ ) in moving the suitcase a distance of $50.0 \mathrm{m} .$ At what angle $\theta$ is the force oriented with respect to the ground?

Adnan Gill

Numerade Educator

Problem 6

A person pushes a 16.0-kg shopping cart at a constant velocity for a distance of $22.0 \mathrm{m}$. She pushes in a direction $29.0^{\circ}$ below the horizontal. A $48.0-\mathrm{N}$ frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.

Adnan Gill

Numerade Educator

Problem 7

The drawing shows a plane diving toward the ground and then climbing back upward. During each of these motions, the lift force $\overrightarrow{\mathbf{L}}$ acts perpendicular to the displacement $\overrightarrow{\mathbf{s}},$ which has the same magnitude, $1.7 \times 10^{3} \mathrm{m},$ in each case. The engines of the plane exert a thrust $\mathbf{T},$ which points in the direction of the displacement and has the same magnitude during the dive and the climb. The weight $\overrightarrow{\mathbf{W}}$ of the plane has a magnitude of $5.9 \times 10^{4} \mathrm{N} .$ In both motions, net work is performed due to the combined action of the forces $\overrightarrow{\mathbf{L}}, \overrightarrow{\mathbf{T}},$ and $\overrightarrow{\mathbf{W}}$.
(a) Is more net work done during the dive or the climb? Explain. (b) Find the difference between the net work done during the dive and the climb.

Adnan Gill

Numerade Educator

Problem 8

A person pulls a toboggan for a distance of $35.0 \mathrm{m}$ along the snow with a rope directed $25.0^{\circ}$ above the snow. The tension in the rope is $94.0 \mathrm{N} .$ (a) How much work is done on the toboggan by the tension force? (b) How much work is done if the same tension is directed parallel to the snow?

Adnan Gill

Numerade Educator

Problem 9

As a sailboat sails 52 m due north, a breeze exerts a constant force $\overrightarrow{\mathbf{F}}_{1}$ on the boat's sails. This force is directed at an angle west of due north. A force $\overrightarrow{\mathbf{F}}_{2}$ of the same magnitude directed due north would do the same amount of work on the sailboat over a distance of just $47 \mathrm{m} .$ What is the angle between the direction of the force $\overrightarrow{\mathbf{F}}_{1}$ and due north?

Adnan Gill

Numerade Educator

Problem 10

A55-kg box is being pushed a distance of $7.0 \mathrm{m}$ across the floor by a force $\overrightarrow{\mathbf{P}}$ whose magnitude is $160 \mathrm{N}$. The force $\overrightarrow{\mathbf{P}}$ is parallel to the displacement of the box. The coefficient of kinetic friction is $0.25 .$ Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force.

Sachin Rao

Numerade Educator

Problem 11

A $1.00 \times 10^{2}-\mathrm{kg}$ crate is being pushed across a horizontal floor by a force $\overrightarrow{\mathbf{P}}$ that makes an angle of $30.0^{\circ}$ below the horizontal. The coefficient of kinetic friction is $0.200 .$ What should be the magnitude of $\overrightarrow{\mathbf{P}},$ so that the net work done by it and the kinetic frictional force is zero?

Sachin Rao

Numerade Educator

Problem 12

A $1200-\mathrm{kg}$ car is being driven up a $5.0^{\circ}$ hill. The frictional force is directed opposite to the motion of the car and has a magnitude of $f=$ $524 \mathrm{N} .$ A force $\overrightarrow{\mathbf{F}}$ is applied to the car by the road and propels the car forward. In addition to these two forces, two other forces act on the car:
its weight $\overrightarrow{\mathbf{W}}$ and the normal force $\overrightarrow{\mathbf{F}}_{\mathrm{N}}$ directed perpendicular to the road surface. The length of the road up the hill is $290 \mathrm{m}$. What should be the magnitude of $\overrightarrow{\mathbf{F}},$ so that the net work done by all the forces acting on the car is $+150 \mathrm{kJ} ?$

Adnan Gill

Numerade Educator

Problem 13

A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. The thrust of its engines is $2.3 \times$ $10^{5} \mathrm{N} .$ In being launched from rest it moves through a distance of $87 \mathrm{m}$ and has a kinetic energy of $4.5 \times 10^{7} \mathrm{J}$ at lift-off. What is the work done on the jet by the catapult?

Adnan Gill

Numerade Educator

Problem 14

A golf club strikes a 0.045-kg golf ball in order to launch it from the tee. For simplicity, assume that the average net force applied to the ball acts parallel to the ball's motion, has a magnitude of $6800 \mathrm{N},$ and is in contact with the ball for a distance of $0.010 \mathrm{m}$. With what speed does the ball leave the club?

Sachin Rao

Numerade Educator

Problem 15

It takes $185 \mathrm{kJ}$ of work to accelerate a car from $23.0 \mathrm{m} / \mathrm{s}$ to $28.0 \mathrm{m} / \mathrm{s} .$ What is the car's mass?

Sachin Rao

Numerade Educator

Problem 16

Starting from rest, a $1.9 \times 10^{-4}-\mathrm{kg}$ flea springs straight upward. While the flea is pushing off from the ground, the ground exerts an average upward force of $0.38 \mathrm{N}$ on it. This force does $+2.4 \times 10^{-4} \mathrm{J}$ of work on the flea. (a) What is the flea's speed when it leaves the ground? (b) How far upward does the flea move while it is pushing off? Ignore both air resistance and the flea's weight.

Adnan Gill

Numerade Educator

Problem 17

Go A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 70.3 -kg water-skier has an initial speed of $6.10 \mathrm{m} / \mathrm{s}$. Later, the speed increases to $11.3 \mathrm{m} / \mathrm{s} .$ Determine the work done by the net external force acting on the skier.

Sachin Rao

Numerade Educator

Problem 18

As background for this problem, review Conceptual Example $6 .$ A $7420-\mathrm{kg}$ satellite has an elliptical orbit, as in Figure $6.9 b .$ The point on the orbit that is farthest from the earth is called the apogee and is at the far right side of the drawing. The point on the orbit that is closest to the earth is called the perigee and is at the left side of the drawing. Suppose that the speed of the satellite is $2820 \mathrm{m} / \mathrm{s}$ at the apogee and $8450 \mathrm{m} / \mathrm{s}$ at the perigee. Find the work done by the gravitational force when the satellite moves from (a) the apogee to the perigee and (b) the perigee to the apogee.

Adnan Gill

Numerade Educator

Problem 19

The hammer throw is a track-and-field event in which a $7.3 \mathrm{kg}$ ball (the "hammer"), starting from rest, is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of $29 \mathrm{m} / \mathrm{s} .$ For comparison, a .22 caliber bullet has a mass of $2.6 \mathrm{g}$ and, starting from rest, exits the barrel of a gun at a speed of $410 \mathrm{m} / \mathrm{s}$. Determine the work done to launch the motion of (a) the hammer and (b) the bullet.

Adnan Gill

Numerade Educator

Problem 20

A $16-\mathrm{kg}$ sled is being pulled along the horizontal snow-covered ground by a horizontal force of $24 \mathrm{N}$. Starting from rest, the sled attains a speed of $2.0 \mathrm{m} / \mathrm{s}$ in $8.0 \mathrm{m} .$ Find the coefficient of kinetic friction between the runners of the sled and the snow.

Adnan Gill

Numerade Educator

Problem 21

An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of $4.5 \times 10^{4} \mathrm{kg},$ and the force causes its speed to change from 7100 to $5500 \mathrm{m} / \mathrm{s}$
(a) What is the work done by the force? (b) If the asteroid slows down over a distance of $1.8 \times 10^{6} \mathrm{m},$ determine the magnitude of the force.

Adnan Gill

Numerade Educator

Problem 22

The concepts in this problem are similar to those in Multiple-Concept Example 4, except that the force doing the work in this problem is the tension in the cable. A rescue helicopter lifts a $79-\mathrm{kg}$ person straight up by means of a cable. The person has an upward acceleration of $0.70 \mathrm{m} / \mathrm{s}^{2}$ and is lifted from rest through a distance of $11 \mathrm{m}$. (a) What is the tension in the cable? How much work is done by (b) the tension in the cable and (c) the person's weight? (d) Use the work-energy theorem and find the final speed of the person.

Jaime Munoz

Numerade Educator

Problem 23

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 24

Consult Multiple-Concept Example 5 for insight into solving this problem. A skier slides horizontally along the snow for a distance of $21 \mathrm{m}$ before coming to rest. The coefficient of kinetic friction between the skier and the snow is $\mu_{\mathrm{k}}=0.050 .$ Initially, how fast was the skier going?

Adnan Gill

Numerade Educator

Problem 25

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 26

Under the influence of its drive force, a snowmobile is moving at a constant velocity along a horizontal patch of snow. When the drive force is shut off, the snowmobile coasts to a halt. The snowmobile and its rider have a mass of 136 kg. Under the influence of a drive force of $205 \mathrm{N}$, it is moving at a constant velocity whose magnitude is $5.50 \mathrm{m} / \mathrm{s}$. The drive force is then shut off. Find (a) the distance in which the snowmobile coasts to a halt and (b) the time required to do so.

Adnan Gill

Numerade Educator

Problem 27

The model airplane in Figure 5.6 is flying at a speed of $22 \mathrm{m} / \mathrm{s}$ on a horizontal circle of radius $16 \mathrm{m}$. The mass of the plane is $0.90 \mathrm{kg}$. The person holding the guideline pulls it in until the radius becomes $14 \mathrm{m}$. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Adnan Gill

Numerade Educator

Problem 28

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 29

A 75.0-kg skier rides a 2830-m-long lift to the top of a mountain. The lift makes an angle of $14.6^{\circ}$ with the horizontal. What is the change in the skier's gravitational potential energy?

Sachin Rao

Numerade Educator

Problem 30

Juggles and Bangles are clowns. Juggles stands on one end of a teeter-totter at rest on the ground. Bangles jumps off a platform $2.5 \mathrm{m}$ above the ground and lands on the other end of the teeter-totter, launching Juggles into the air. Juggles rises to a height of $3.3 \mathrm{m}$ above the ground, at which point he has the same amount of gravitational potential energy as Bangles had before he jumped, assuming both potential energies are measured using the ground as the reference level. Bangles' mass is $86 \mathrm{kg}$. What is Juggles' mass?

Adnan Gill

Numerade Educator

Problem 31

A 0.60-kg basketball is dropped out of a window that is 6.1 m above the ground. The ball is caught by a person whose hands are $1.5 \mathrm{m}$ above the ground. (a) How much work is done on the ball by its weight? What is the gravitational potential energy of the basketball, relative to the ground, when it is (b) released and (c) caught? (d) How is the change $\left(\mathrm{PE}_{\mathrm{f}}-\mathrm{PE}_{0}\right)$ in the ball's gravitational potential energy related to the work done by its weight?

Adnan Gill

Numerade Educator

Problem 32

A pole-vaulter just clears the bar at $5.80 \mathrm{m}$ and falls back to the ground. The change in the vaulter's potential energy during the fall is $-3.70 \times 10^{3} \mathrm{J} .$ What is his weight?

Sachin Rao

Numerade Educator

Problem 33

A bicyclist rides $5.0 \mathrm{km}$ due east, while the resistive force from the air has a magnitude of $3.0 \mathrm{N}$ and points due west. The rider then turns around and rides $5.0 \mathrm{km}$ due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of $3.0 \mathrm{N}$ and points due east. (a) Find the work done by the resistive force during the round trip. (b) Based on your answer to part (a), is the resistive force a conservative force? Explain.

Adnan Gill

Numerade Educator

Problem 34

"Rocket Man" has a propulsion unit strapped to his back. He starts from rest on the ground, fires the unit, and accelerates straight upward. At a height of $16 \mathrm{m},$ his speed is $5.0 \mathrm{m} / \mathrm{s} .$ His mass, including the propulsion unit, has the approximately constant value of 136 kg. Find the work done by the force generated by the propulsion unit.

Adnan Gill

Numerade Educator

Problem 35

A 55.0-kg skateboarder starts out with a speed of 1.80 $\mathrm{m} / \mathrm{s}$. He does $+80.0 \mathrm{J}$ of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is $6.00 \mathrm{m} / \mathrm{s} .$ (a) Calculate the change $\left(\Delta \mathrm{PE}=\mathrm{PE}_{\mathrm{f}}-\mathrm{PE}_{0}\right)$ in the gravitational potential energy. (b) How much has the vertical height of the skater changed, and is the skater above or below the starting point?

Sachin Rao

Numerade Educator

Problem 36

A 35-kg girl is bouncing on a trampoline. During a certain interval after she leaves the surface of the trampoline, her kinetic energy decreases to 210 J from 440 J. How high does she rise during this interval? Neglect air resistance.

Adnan Gill

Numerade Educator

Problem 37

A gymnast is swinging on a high bar. The distance between his waist and the bar is $1.1 \mathrm{m},$ as the drawing shows. At the top of the swing his speed is momentarily zero. Ignoring friction and treating the gymnast as if all of his mass is located at his waist, find his speed at the bottom of the swing.

Adnan Gill

Numerade Educator

Problem 38

Go The skateboarder in the drawing starts down the left side of the ramp with an initial speed of $5.4 \mathrm{m} / \mathrm{s} .$ Neglect nonconservative forces, such as friction and air resistance, and find the height $h$ of the highest point reached by the skateboarder on the right side of the ramp.

Sachin Rao

Numerade Educator

Problem 39

A slingshot fires a pebble from the top of a building at a speed of $14.0 \mathrm{m} / \mathrm{s} .$ The building is $31.0 \mathrm{m}$ tall. Ignoring air resistance, find the speed with which the pebble strikes the ground when the pebble is fired (a) horizontally, (b) vertically straight up, and (c) vertically straight down.

Adnan Gill

Numerade Educator

Problem 40

The drawing shows two boxes resting on frictionless ramps. One box is relatively light and sits on a steep ramp. The other box is heavier and rests on a ramp that is less steep. The boxes are released from rest at $A$ and allowed to slide down the ramps. The two boxes have masses of 11 and 44 kg. If A and B are 4.5 and 1.5 m, respectively, above the ground, determine the speed of (a) the lighter box and (b) the heavier box when each reaches B. (c) What is the ratio of the kinetic energy of the heavier box to that of the lighter box at B?

Sachin Rao

Numerade Educator

Problem 41

A 47.0-g golf ball is driven from the tee with an initial speed of $52.0 \mathrm{m} / \mathrm{s}$ and rises to a height of $24.6 \mathrm{m}$. (a) Neglect air resistance and determine the kinetic energy of the ball at its highest point. (b) What is its speed when it is $8.0 \mathrm{m}$ below its highest point?

Adnan Gill

Numerade Educator

Problem 42

Consult Conceptual Example 9 in preparation for this problem. The drawing shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of $13.0 \mathrm{m} / \mathrm{s}$ via path $1 .$ How fast is he moving on path 2 when he releases the rope at a height of $5.20 \mathrm{m}$ above the water? Ignore the effects of air resistance.

Dading Chen

Numerade Educator

Problem 43

The drawing shows a skateboarder moving at $5.4 \mathrm{m} / \mathrm{s}$ along a horizontal section of a track that is slanted upward by $48^{\circ}$ above the horizontal at its end, which is $0.40 \mathrm{m}$ above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height $H$ to which she rises above the end of the track.

Adnan Gill

Numerade Educator

Problem 44

A small lead ball, attached to a 0.75-m rope, is being whirled in a circle that lies in the vertical plane. The ball is whirled at a constant rate of three revolutions per second and is released on the upward part of the circular motion when it is $1.5 \mathrm{m}$ above the ground. The ball travels straight upward. In the absence of air resistance, to what maximum height above the ground does the ball rise?

Sachin Rao

Numerade Educator

Problem 45

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Ajay Singhal

Numerade Educator

Problem 46

A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of $0.75 \mathrm{m}$. With the string hanging vertically, the object is given an initial velocity of $2.0 \mathrm{m} / \mathrm{s}$ parallel to the ground and swings upward on a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle $\theta$ with its initial vertical orientation and then swings back downward. Find the angle $\theta$.

Adnan Gill

Numerade Educator

Problem 47

A semitrailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway-truck ramp that is inclined at an angle of $14.0^{\circ}$ above the horizontal. The semitrailer coasts to a stop after traveling $154 \mathrm{m}$ along the ramp. What was the truck's initial speed? Neglect air resistance and friction.

Adnan Gill

Numerade Educator

Problem 48

The drawing shows two frictionless inclines that begin at ground level $(h=0 \mathrm{m})$ and slope upward at the same angle $\theta .$ One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed $v_{0}$. On the longer track the block slides upward until it reaches a maximum height $H$ above the ground. On the shorter track the block slides upward, flies off the end of the track at a height $H_{1}$ above the ground, and then follows the familiar parabolic trajectory of projectile motion. At the highest point of this trajectory, the block is a height $H_{2}$ above the end of the track. The initial total mechanical energy of each block is the same and is all kinetic energy. The initial speed of each block is $v_{0}=7.00 \mathrm{m} / \mathrm{s},$ and each incline slopes upward at an angle of $\theta=50.0^{\circ} .$ The block on the shorter track leaves the track at a height of $H_{1}=1.25 \mathrm{m}$ above the ground. Find (a) the height $H$ for the block on the longer track and (b) the total height $H_{1}+H_{2}$ for the block on the shorter track.

Jaime Munoz

Numerade Educator

Problem 49

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates. The crest of the second hill is circular, with a radius of $r=36 \mathrm{m}$. Neglect friction and air resistance. What must be the height $h$ of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

Adnan Gill

Numerade Educator

Problem 50

A person starts from rest at the top of a large frictionless spherical surface, and slides into the water below (see the drawing). At what angle $\theta$ does the person leave the surface? (Hint: When the person leaves the surface, the normal force is zero. )

Sachin Rao

Numerade Educator

Problem 51

A projectile of mass 0.750 kg is shot straight up with an initial speed of $18.0 \mathrm{m} / \mathrm{s}$. (a) How high would it go if there were no air resistance? (b) If the projectile rises to a maximum height of only $11.8 \mathrm{m},$ determine the magnitude of the average force due to air resistance.

Adnan Gill

Numerade Educator

Problem 52

A basketball player makes a jump shot. The $0.600-\mathrm{kg}$ ball is released at a height of $2.00 \mathrm{m}$ above the floor with a speed of $7.20 \mathrm{m} / \mathrm{s}$. The ball goes through the net $3.10 \mathrm{m}$ above the floor at a speed of $4.20 \mathrm{m} / \mathrm{s}$. What is the work done on the ball by air resistance, a nonconservative force?

Sachin Rao

Numerade Educator

Problem 53

Starting from rest, a 93-kg firefighter slides down a fire pole. The average frictional force exerted on him by the pole has a magnitude of $810 \mathrm{N},$ and his speed at the bottom of the pole is $3.4 \mathrm{m} / \mathrm{s}$. How far did he slide down the pole?

Adnan Gill

Numerade Educator

Problem 54

A student, starting from rest, slides down a water slide. On the way down, a kinetic frictional force (a nonconservative force) acts on her. The student has a mass of $83.0 \mathrm{kg}$, and the height of the water slide is $11.8 \mathrm{m}$. If the kinetic frictional force does $-6.50 \times 10^{3} \mathrm{J}$ of work, how fast is the student going at the bottom of the slide?

Sachin Rao

Numerade Educator

Problem 55

The (nonconservative) force propelling a $1.50 \times 10^{3}-\mathrm{kg}$ car up a mountain road does $4.70 \times 10^{6} \mathrm{J}$ of work on the car. The car starts from rest at sea level and has a speed of $27.0 \mathrm{m} / \mathrm{s}$ at an altitude of $2.00 \times 10^{2} \mathrm{m}$ above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are nonconservative forces.

Sachin Rao

Numerade Educator

Problem 56

In the sport of skeleton a participant jumps onto a sled (known as a skeleton) and proceeds to slide down an icy track, belly down and head first. In the 2010 Winter Olympics, the track had sixteen turns and dropped $126 \mathrm{m}$ in elevation from top to bottom. (a) In the absence of nonconservative forces, such as friction and air resistance, what would be the speed of a rider at the bottom of the track? Assume that the speed at the beginning of the run is relatively small and can be ignored. (b) In reality, the gold-medal winner (Canadian Jon Montgomery) reached the bottom in one heat with a speed of $40.5 \mathrm{m} / \mathrm{s}$ (about $91 \mathrm{mi} / \mathrm{h}$ ). How much work was done on him and his sled (assuming a total mass of $118 \mathrm{kg}$ ) by nonconservative forces during this heat?

Jaime Munoz

Numerade Educator

Problem 57

In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of $1.7 \mathrm{m} / \mathrm{s}$. However, this speed is inadequate to compensate for the kinetic friction between the puck and the ice. As a result, the puck travels only one-half the distance between the players before sliding to a halt. What minimum initial speed should the puck have been given so that it reached the teammate, assuming that the same force of kinetic friction acted on the puck everywhere between the two players?

Adnan Gill

Numerade Educator

Problem 58

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 59

? 67.0-kg person jumps from rest off a 3.00-m-high tower straight down into the water. Neglect air resistance. She comes to rest $1.10 \mathrm{m}$ under the surface of the water. Determine the magnitude of the average force that the water exerts on the diver. This force is nonconservative.

Sachin Rao

Numerade Educator

Problem 60

At a carnival, you can try to ring a bell by striking a target with a $9.00-\mathrm{kg}$ hammer. In response, a $0.400-\mathrm{kg}$ metal piece is sent upward toward the bell, which is $5.00 \mathrm{m}$ above. Suppose that $25.0 \%$ of the hammer's kinetic energy is used to do the work of sending the metal piece upward. How fast must the hammer be moving when it strikes the target so that the bell just barely rings?

Sachin Rao

Numerade Educator

Problem 61

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Ajay Singhal

Numerade Educator

Problem 62

A person is making homemade ice cream. She exerts a force of magnitude $22 \mathrm{N}$ on the free end of the crank handle on the ice-cream maker, and this end moves on a circular path of radius $0.28 \mathrm{m}$. The force is always applied parallel to the motion of the handle. If the handle is turned once every $1.3 \mathrm{s},$ what is the average power being expended?

Adnan Gill

Numerade Educator

Problem 63

Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by seven-time-winner Lance Armstrong $(m=75.0 \mathrm{kg})$ is $6.50 \mathrm{W}$ per kilogram of his body mass. (a) How much work does he do during a 135 -km race in which his average speed is $12.0 \mathrm{m} / \mathrm{s} ?$ (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule $=2.389 \times 10^{-4}$ nutritional Calories.

Adnan Gill

Numerade Educator

Problem 64

You are working out on a rowing machine. Each time you pull the rowing bar (which simulates the oars) toward you, it moves a distance of $1.2 \mathrm{m}$ in a time of $1.5 \mathrm{s}$. The readout on the display indicates that the average power you are producing is 82 W. What is the magnitude of the force that you exert on the handle?

Adnan Gill

Numerade Educator

Problem 65

A car accelerates uniformly from rest to $20.0 \mathrm{m} / \mathrm{s}$ in $5.6 \mathrm{s}$ along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is $9.0 \times 10^{3} \mathrm{N}$ and (b) the weight of the car is $1.4 \times 10^{4} \mathrm{N}$.

Adnan Gill

Numerade Educator

Problem 66

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An $810-\mathrm{kg}$ helicopter rises from rest to a speed of $7.0 \mathrm{m} / \mathrm{s}$ in a time of $3.5 \mathrm{s}$ During this time it climbs to a height of $8.2 \mathrm{m} .$ What is the average power generated by the lifting force?

Adnan Gill

Numerade Educator

Problem 67

The cheetah is one of the fastest-accelerating animals, because it can go from rest to $27 \mathrm{m} / \mathrm{s}$ (about $60 \mathrm{mi} / \mathrm{h}$ ) in $4.0 \mathrm{s}$. If its mass is $110 \mathrm{kg}$, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower.

Sachin Rao

Numerade Educator

Problem 68

In 2.0 minutes, a ski lift raises four skiers at constant speed to a height of $140 \mathrm{m}$. The average mass of each skier is $65 \mathrm{kg}$. What is the average power provided by the tension in the cable pulling the lift?

Sachin Rao

Numerade Educator

Problem 69

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Ajay Singhal

Numerade Educator

Problem 70

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Ajay Singhal

Numerade Educator

Problem 71

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Ajay Singhal

Numerade Educator

Problem 72

The graph shows how the force component $F \cos \theta$ along the displacement varies with the magnitude $s$ of the displacement. Find the work done by the force. (Hint: Recall how the area of a triangle is related to the triangle's base and height.)

Adnan Gill

Numerade Educator

Problem 73

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 74

The force component along the displacement varies with the magnitude of the displacement, as shown in the graph. Find the work done by the force in the interval from (a) 0 to $1.0 \mathrm{m},$ (b) 1.0 to $2.0 \mathrm{m},$ and (c) 2.0 to $4.0 \mathrm{m}$ (Note: In the last interval the force component is negative, so the work is negative.

Adnan Gill

Numerade Educator

Problem 75

A a net external force is applied to a $6.00-\mathrm{kg}$ object that is initially at rest. The net force component along the displacement of the object varies with the magnitude of the displacement as shown in the drawing. What is the speed of the object at $s=20.0 \mathrm{m} ?$

Jed Brewer

Numerade Educator

Problem 76

A cable lifts a 1200 -kg elevator at a constant velocity for a distance of $35 \mathrm{m} .$ What is the work done by (a) the tension in the cable and (b) the elevator's weight?

Sachin Rao

Numerade Educator

Problem 77

A 2.00-kg rock is released from rest at a height of 20.0 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: $20.0,10.0,$ and $0 \mathrm{m}$

Sachin Rao

Numerade Educator

Problem 78

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 79

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 80

When an $81.0-\mathrm{kg}$ adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by $2.00 \times 10^{3}$ J. By how much does the potential energy of an $18.0-\mathrm{kg}$ child increase when the child climbs a normal staircase to the second floor?

Adnan Gill

Numerade Educator

Problem 81

A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husband's pulling force is directed $58^{\circ}$ above the horizontal, and the wife's pulling force is directed $38^{\circ}$ above the horizontal. The husband pulls with a force whose magnitude is $67 \mathrm{N}$. What is the magnitude of the pulling force exerted by his wife?

Adnan Gill

Numerade Educator

Problem 82

Some gliders are launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average power must the winch supply in order to accelerate a 184 -kg ultralight glider from rest to $26.0 \mathrm{m} / \mathrm{s}$ over a horizontal distance of $48.0 \mathrm{m} ?$ Assume that friction and air resistance are negligible, and that the tension in the winch cable is constant.

Adnan Gill

Numerade Educator

Problem 83

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 84

A 63-kg skier coasts up a snow-covered hill that makes an angle of $25^{\circ}$ with the horizontal. The initial speed of the skier is $6.6 \mathrm{m} / \mathrm{s}$. After coasting $1.9 \mathrm{m}$ up the slope, the skier has a speed of $4.4 \mathrm{m} / \mathrm{s}$. (a) Find the work done by the kinetic frictional force that acts on the skis. (b) What is the magnitude of the kinetic frictional force?

Adnan Gill

Numerade Educator

Problem 85

A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water $5.00 \mathrm{m}$ from the end of the slide in a time of $0.500 \mathrm{s}$ after leaving the slide. Ignoring friction and air resistance, find the height $H$ in the drawing.

Adnan Gill

Numerade Educator

Problem 86

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 87

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 88

A car, starting from rest, accelerates in the $+x$ direction as in the figure. It has a mass of $1.10 \times 10^{3} \mathrm{kg}$ and maintains an acceleration of $+4.60 \mathrm{m} / \mathrm{s}^{2}$ for $5.00 \mathrm{s}$. Assume that a single horizontal force (not shown) accelerates the vehicle. Determine the average power generated by this force.

Sachin Rao

Numerade Educator

Problem 89

The skateboarder in the figure is coasting down a ramp, and there are three forces acting on her: her weight $\overrightarrow{\mathbf{W}}$ (magnitude $=675 \mathrm{N}$ ), a frictional force $\overrightarrow{\mathbf{f}}$ (magnitude $=125 \mathrm{N}$ ) that opposes her motion, and a normal force $\overrightarrow{\mathbf{F}}_{\mathbf{N}}$ (magnitude $=612 \mathrm{N}$ ) Concepts: Part $b$ of the figure shows each force, along with the displacement $\overrightarrow{\mathbf{s}}$ of the skateboarder. By examining these diagrams and without doing any numerical calculations, determine whether the work done by each force is positive, negative, or zero. Provide a reason for each answer. Calculations: Determine the net work done by the
three forces when she coasts for a distance of $9.2 \mathrm{m}$

Jaime Munoz

Numerade Educator

Problem 90

The figure shows a $0.41-\mathrm{kg}$ block sliding from $\mathrm{A}$ to $\mathrm{B}$ along a frictionless surface. When the block reaches $B,$ it continues to slide along the horizontal surface $\mathrm{BC}$ where the kinetic frictional force acts. As a result, the block slows down, coming to rest at C. The kinetic energy of the block at A is $37 \mathrm{J},$ and the heights of $\mathrm{A}$ and $\mathrm{B}$ are 12.0 and 7.0 $\mathrm{m}$ above the ground, respectively. Concepts:
(i) Is the total mechanical energy of the block conserved as the block goes from $A$ to $B ?$ Why or why not?
(ii) When the block reaches point $\mathrm{B},$ has its kinetic energy increased, decreased, or remained the same relative to what it was at A? Give a reason for your answer. (iii) Is the total mechanical energy of the block conserved as the block goes from B to C? Justify your answer. Calculations: (a) What is the value of the kinetic energy of the block when it reaches $\mathrm{B} ?$ (b) How much work does the kinetic frictional force do during the BC segment of the trip?

Jaime Munoz

Numerade Educator

Problem 91

A Makeshift Elevator. While exploring an elaborate tunnel system, you and your team get lost and find yourselves at the bottom of a $450-\mathrm{m}$ vertical shaft. Suspended from a thick rope (near the floor) is a large rectangular bucket that looks like it had been used to transport tools and debris up and down the tunnel. Mounted on the floor near one of the walls is a gasoline engine $(3.5 \mathrm{hp})$ that turns a pulley and rope, and a sign that reads "Emergency Lift." It is clear that the engine is used to drive the bucket up the shaft. On the wall next to the engine is a sign indicating that a full tank of gas will last exactly 15 minutes when the engine is running at full power. You open the engine's gas tank and estimate that it is $1 / 4$ full, and there are no other sources of gasoline. (a) Assuming zero friction, if you send your team's lightest member (who weighs $125 \mathrm{lb}$ ), and the bucket weighs $150 \mathrm{lb}$ when empty, how far up the shaft will the engine take her (and the bucket)? Will it get her out of the mine? (b) Assuming an effective collective friction (from the pulleys, etc.) of $\mu_{\mathrm{eff}}=0.10$ (so that $F_{\mathrm{f}}=\mu_{\mathrm{eff}} M g,$ where $M$ is the total mass of the bucket plus team member), will the engine (with a $1 / 4$ -full tank of gas) lift her to the top of the shaft?

Jaime Munoz

Numerade Educator

Problem 92

A Sledding Contest. You are in a sledding contest where you start at a height of $40.0 \mathrm{m}$ above the bottom of a valley and slide down a hill that makes an angle of $25.0^{\circ}$ with respect to the horizontal. When you reach the valley, you immediately climb a second hill that makes an angle of $15.0^{\circ}$ with respect to the horizontal. The winner of the contest will be the contestant who travels the greatest distance up the second hill. You must now choose between using your flat-bottomed plastic sled, or your "Blade Runner," which glides on two steel rails. The hill you will ride down is covered with loose snow. However, the hill you will climb on the other side is a popular sledding hill, and is packed hard and is slick. The two sleds perform very differently on the two surfaces, the plastic one performing better on loose snow, and the Blade Runner doing better on hard-packed snow or ice. The performances of each sled can be quantified in terms of their respective coefficients of kinetic friction on the two surfaces. For the plastic sled: $\mu=0.17$ on loose snow, and $\mu=0.15$ on packed snow or ice. For the Blade Runner, $\mu=0.19$ on loose snow, and $\mu=0.07$ on packed snow or ice. Assuming the two hills are shaped like inclined planes, and neglecting air resistance, (a) how far does each sled make it up the second hill before stopping? (b) Assuming the total mass of the sled plus rider is $55.0 \mathrm{kg}$ in both cases, how much work is done by nonconservative forces (over the total trip) in each case?

Jaime Munoz

Numerade Educator