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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Chapter 6

Work and Kinetic Energy - all with Video Answers

Educators

Chapter Questions

01:30

Problem 1

An old oaken bucket of mass $6.75 \mathrm{~kg}$ hangs in a well at the end of a rope. The rope passes ovet a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to nise the backet siowly si distance of $4.00 \mathrm{~m}$. (a) How much work
do you do on the becket in pulling it up? (b) How much work does gravity do on the bocket? (c) What is the total work done oa the bucket?

Surjit Tewari
Surjit Tewari
Numerade Educator
06:27

Problem 2

A tow truck pulls a car $5.00$ km along a horizontal roadway using a cable having a tension of $850 \mathrm{~N}$. (a) How much work does the cable do on the car if it pulls horizontally? If it pulls at $35.0^{\circ}$ above the horizoatal? (b) How much work does the cable do on the tow truck in both cascs of part (a)? (c) How much work does gmyity do on the car in part (a)?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:23

Problem 3

A factory worker poshes a $30.0 \mathrm{~kg}$ crate s distance of $4.5 \mathrm{~m}$ along a level dloor at constant velocity by pashing borizontally on it. The coefficient of kinetic friction betwoen the crate and the floor is $0.25 .$ (a) What mugnitude of force must the worker apply?
(b) How much work is done on the crate by this forco?
(c) How much work is done on the crate by friction? (d) How mach work is done on the crate by the normal force? By gravity? (e) What is the total wort done on the crate?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:03

Problem 4

Suppose the worker in Exercise $6.3$ pushes downward at un nngle of $30^{\circ}$ below the horivontal.
(B) What magnitude of force must the worker apply to move the crate at constant velocity?
(b) How mach work is done oa the crate by this force when the crate is pushed a distance of $4.5 \mathrm{~m} ?$ (c) How much work is done on the crate by friction during this dilsplacement? (d) How much work is dope on the crate by the normal force? By gravity? (c) What is the total work done on the crate?

Dominador Tan
Dominador Tan
Numerade Educator
01:36

Problem 5

A $75.0 \mathrm{~kg}$ painter climbs a Indder that is $2.75 \mathrm{~m}$ long leaning against a vertical wall. The Ladder makes an $30.0^{\circ}$ ungle with the wall. (a) How much work does gravity do on the painter? (b) Does the answer to part (a) depend on whether the painter climbs at constant speed or accelerates up the ladder?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:04

Problem 6

Two tugboats pull a disabled supertanker. Each tug exerts $\mathrm{E}$ constant force of $1.80 \times 10^{6} \mathrm{~N}$, one $14^{\circ}$ west of north and the other $14^{\text {" }}$ cast of north, ns they poll the tanloer $0.75 \mathrm{~km}$ toward the north. What is the total wark they do on the supertanker?

Keshav Singh
Keshav Singh
Numerade Educator
05:42

Problem 7

Two blocks are connected by a very Ilght string passing over a massless and frictionless pulley (Figure $6.30$ ). Traveling at constant speed, the $20.0-\mathrm{N}$ block moves $75.0 \mathrm{~cm}$ to the right and the 12.0-N block moves $75.0 \mathrm{~cm}$ downward. During this process, how much work is done (c) on the $12.0-\mathrm{N}$ block by (i) gravity and
(ii) the tension in the string?
(b) On the $20.0-\mathrm{N}$ block by (i) gravity,
(ii) the tension in the string.
(iii) friction, and (iv) the normal force? (c) Find the total work done on each block.

Shoukat Ali
Shoukat Ali
Other Schools
01:21

Problem 8

A loeded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force $\vec{F}=(30 \mathrm{~N}) \hat{\imath}-(40 \mathrm{~N}) \boldsymbol{j}$ to the cart as it undergoes a displacement $\overrightarrow{8}=(-9.0 \mathrm{~m}) \hat{i}-(3.0 \mathrm{~m}) \mathbf{j}$. How much work does the force you apply do on the grocery cart?

NR
Nicholas Rombes
University of California - Los Angeles
03:11

Problem 9

A $0.800-\mathrm{kg}$ hall is tied to the end of a string $1.60 \mathrm{~m}$ long and swung in a vertical circle. (a) During one complete circle, starting any where, calcalate the total work done on the ball by (i) the teusion in the string and (ii) gravity. (b) Repeat part (il) for motion along the semicircle from the lowest to the highest point on the path.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:44

Problem 10

(a) How many joules of kinetic energy does a 750 -kg automobile traveling at a typical highway speed of $65 \mathrm{ml} / \mathrm{h}$ heve?
(b) By what fuctor would its kinetic energy decresse if the car tniveled half as fait? (c) How fast (in mi/h) would the car have to travel to hive half as much kinetic energy us in part (a)?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:18

Problem 11

Meteor Crater. About 50,000 years ago, a metcor crushed into the earth near present-diny Flagstaff, Arizona. Recent (2005) measurcments cstimate that this meteor had a misss of sboot $1.4 \times 10^{8}$ kg (around 150,000 tons) and hit the ground at $12 \mathrm{~km} / \mathrm{s}$.
(a) How mucb kinetic energy did this meteur deliver to the Eround? (b) How does this energy compare to the cnetgy roleased by a $1.0$ meguton nuclear bomb? (A megaton bomb releases the same cacrgy as n million tons of 'TNT, and $1.0$ ton of TNT relcases $4.184 \times 10^{9} \mathrm{~J}$ of energ.)

Surjit Tewari
Surjit Tewari
Numerade Educator
02:33

Problem 12

Some 'Typical Kinetic Energies.
(8) How many joules of kinetic energy does a $75-\mathrm{kg}$ person hive when walking and when running? (b) In the Bolur model of the atom, the ground-state clectroa in hydrogen has an orbital speod of $2190 \mathrm{~km} / \mathrm{s}$. Whit is its kinetic eaergy? (Consalt Appendix $\mathrm{R}$ ) (c) If you drop s $1.0 . \mathrm{kg}$ wcight (ahout 2 lb) from shoulder height, how many joules of kinctic cacrgy will it have when it reaches the ground? (d) Is it reasonable that at $30-\mathrm{kg}$ child could run fast enough to have $100 \mathrm{~J}$ of kinetic eneug?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:57

Problem 13

The mass of a proton is 1856 times the mass of an electron.
(a) $A$ proton is traveling at speed $V$. At what specd (in terms of $V$ ) would an clectron have the same kinetic energy as the proton?
(b) An clectron has kinetic energy $K$. If a proton has the same speed as the electron, what is irs kinetic energy (in terms of $K$ )?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:53

Problem 14

A $4.80-\mathrm{kg}$ watermelon is dropped from rest from the roof of a 25.0-m-tall building and fecls no appreciable air resistance. (a) Culculate the work done by grivity oa the watermelon during its displacement from the roof to the ground. (b) Just before it strikes the ground, what is the watermclon's (i) kinetic eacrgy and (ii) specd?
(c) Which of the answers in parts (a) and (b) would be different if thece were appreciable air resistance?

Vishal Gupta
Vishal Gupta
Numerade Educator
12:32

Problem 15

Use the work-energy theorem to solve each of these priblems. You can use Newton's laws to check your answers. Neglect nir resistance in all cases. (a) $A$ branch falls from the top of a $95.0$ -m-tall redwood tree, starting from rest. How fast is it moving when it reaches the groand? (b) A volcano cjects a boulder diroctly upward $525 \mathrm{~m}$ into the air. How fast was the boulder moving just as it left the volcano? (c) A skier moving at $5.00 \mathrm{~m} / \mathrm{s}$ encouaters a Iong, rough horizontal patch of snow heving coeffcient of kinctic friction $0.220$ with her skis. How far does she travel on this patch before stopping? (d) Suppose the rough potch in part (c) was only $290 \mathrm{~m}$ long? How fast would the skicr. be moving when she reached the cad of the pateh? (c) At the base of a frictionless icy hill that rises at $25,0^{\circ}$ above the horizontal, a toboggan has a speed of $12.0 \mathrm{~m} / \mathrm{s}$ toward the hill. How high vertically above the bate will it go before stopping?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:59

Problem 16

You throw a $20-\mathrm{N}$ rock vertically into the air from ground level. You observe that when it is $15.0 \mathrm{~m}$ above the ground, it is traveling at $25.0 \mathrm{~m} / \mathrm{s}$ upward. Use the work-energy theorem to find (a) the rock's speed just us it left the ground and (b) its meximum belght.

Surjit Tewari
Surjit Tewari
Numerade Educator
04:55

Problem 17

You are a member of an Alpine Rescue Team. You must project a box of supplies up an incline of constant alope angle $\alpha$ so that it reaches a stranded wkier who is a vertical distance $h$ gbove the bottom of the incline. The incline is slippery, but there is some
friction present, with kinetic friction coefficient $\mu_{\mathbf{z}}$. Use the wark-energy theorem to calculate the minimum speed you must give the box at the bottom of the incline so that it will reach the skiec. Express your answer in terms of $g, h, \mu_{k}$, and a.

Guilherme Barros
Guilherme Barros
Numerade Educator
14:47

Problem 18

A mass $m$ slides down a smooth inclined plane from an initial vertical height $h$, muking an angle $\alpha$ with the horizontal. (a) The work done by n force is the sum of the work done by the componcnts of the force. Consider the components of gravity parallel and perpendicular to the surface of the plane. Calculate the work dooe on the mass by each of the components, and use these results to show that the work done by graviry is exactly the same as if the mass bad fallen straight down through the nir from u height $h$.
(b) Use the work-energy theorem to prove that the speed of the mass at the bottom of the incline is the same as if it had becn dropped from height $h$, independent of the angle $\alpha$ of the incline. Explain how this speed can be independent of the slope angle.
(c) Use the results of part (b) to find the speed of a rock that slides down an icy frictionless hill, starting from rest $15.0 \mathrm{~m}$ above the bottom.

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:48

Problem 19

A car is stopped in a distanoe $D$ by a constant friction force that is independent of the car's speed. What is the stopping distance (in terms of $D$ ) (a) if the car's initial speed is triplod, and
(b) if the speed is the sarne as it originally was bat the friction force is tripled? (Solve using the work-ebergy theorem.)

MH
Mohammad Tomal Hossain
Numerade Educator
00:51

Problem 20

A moving electron has kinetic energy $K_{1}$. After a net amount of work $W$ has been done oa it, the clectron is moving one-quarter as fast in the opposite direction. (a) Find $W$ in terms of $K_{1}$.
(b) Does your answer depend on the final direction of the cloctron's mction?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:01

Problem 21

A sled with mass $8.00 \mathrm{~kg}$ moves in a straight line on al frictionless horizontal surface. At one point in its path, its speed is $4.00 \mathrm{~m} / \mathrm{s}$, after it has triveled $250 \mathrm{~m}$ beyond this point, its speed is $6.00 \mathrm{~m} / \mathrm{s}$. Use the work-energy theorem to find the force acting on the sled, assuming that this force is constant and that it acts in the dircction of the sled's motion.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:21

Problem 22

A soceer ball with mass $0.420 \mathrm{~kg}$ is initially moving with speed $2.00 \mathrm{~m} / \mathrm{s}$. A soecer player kicks the ball, exerting a constant force of magnitude $40.0 \mathrm{~N}$ in the same direction as the ball's motion. Over what distance must the playet's foot be in contact with the ball to incrcase the ball's speed to $6.00 \mathrm{~m} / \mathrm{s}$ ?

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:58

Problem 23

A 12 -pack of Omni-Cola (mass $4.30 \mathrm{~kg}$ ) is initially at rest on a horizontal floor. It is then pushed in a straight fine for $1.20 \mathrm{~m}$ by a tnined dog that exerts a horizontal force with magnitude $36.0 \mathrm{~N}$. Use the work-energy theorem to find the final speed of the 12 -pack if (a) there is no friction betwcen the 12 -pack and the floor, and (b) the coefficient of kinctic friction between the 12 -pack and the floor is $0.30$.

Kara Merfeld
Kara Merfeld
Numerade Educator
04:03

Problem 24

A batter hits a baseball with mass $0.145$ kg straight upward with sn initial specd of $25.0 \mathrm{~m} / \mathrm{s}$. (it) How much work has gravity ?one on the bascball when it reaches a height of $20.0 \mathrm{~m}$ above the bat? (b) Use the work-energy theorem to calculate the speed of the baseball at a beight of $20.0 \mathrm{~m}$ above the bat. You can ignore air resistance. (c) Does the saswer to part (b) depend on whether the bascball is moving upward oe downward at a height of $20.0 \mathrm{~m}$ ? Explain.

Narayan Hari
Narayan Hari
Numerade Educator
04:14

Problem 25

A litule red wiugon with mass $7.00 \mathrm{~kg}$ moves in a struight line on frictionless horizontal surface. It has an inirinl speed of $4.00 \mathrm{~m} / \mathrm{s}$ and then is pushed $3.0 \mathrm{~m}$ in the direction of the initinl vclocity by a force with a magnitude of $10.0 \mathrm{~N}$. (a) Use the workenergy theorem to calculate the wagon's final speed. (b) Calculate the scceleration produced by the force. Use this scceleralion in the
kinematic relutionships of Chapter 2 to calculate the wagos's final speed. Compare this result to thit calculated in part (a).

Kara Merfeld
Kara Merfeld
Numerade Educator
04:39

Problem 26

A block of ice with mass $2.00 \mathrm{~kg}$ slides $0.750 \mathrm{~m}$ down an inclined plate that slopes downward at an angle of $36.9^{\circ}$ below the borizontal. If the block of ice starts from rest, what is its final speed? You can ignore friction.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:44

Problem 27

Stopping Distance. A car is traveling on a level roed with speed $v_{0}$ at the instunt when the brakes lock, so that the tires slide rather than roll. (a) Uise the work-enorgy theorem to calculate the minimum stopping distance of the car in terms of $v_{0}, g$, and the coefficient of kinetic friction $\mu_{2}$ between the tires and the road.
(b) By what factor would the minimum stopping distance cbange if
(i) the coefficient of kinetic friction were doubled, or (ii) the initial speed were doubled, or (iii) both the coefficient of kinetic friction and the initial speed were doubled?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:24

Problem 28

To strotch if spring $3.00 \mathrm{~cm}$ frotn its unstretched length, $120 \mathrm{~J}$ of work must be done. (a) Whit is the foroe constant of this spring? (b) What magnitude force is needed to stretch the spring $3.00 \mathrm{~cm}$ from its unstretched length? (c) How moch work must be done to cortipress this spring $4.00$ cm from its unstrecched length, nind what force is needed to stretch it this distanco?

Surjit Tewari
Surjit Tewari
Numerade Educator
05:32

Problem 29

A force of $160 \mathrm{~N}$ stretches a spring $0.050 \mathrm{~m}$ beyond its unstretched length. (a) What magnitude of force is required to stretch the spring $0.015 \mathrm{~m}$ beyond its unstretched length? To compress the spring $0.020 \mathrm{~m}$ ? (b) How much work most be done to stretch the spring $0.015 \mathrm{~m}$ beyond its unstretched length? To compress the spring $0.020 \mathrm{~m}$ from its unstretched length?

Guilherme Barros
Guilherme Barros
Numerade Educator
01:32

Problem 30

A child applies a force $\boldsymbol{F}$ paraliel to the $x$ -axis to $8100 \mathrm{~kg}$ sled moying on the frozen surface of a small pond, As the child controls the spoed of the sled, the $x$ component of the forse she applies varies with the $x$ -coordinnte of the slod as shown in Fig. 6.31. Calculate the work dove by the force $\vec{F}$ when the sled moves (a) from $x=0$ to $x=8.0 \mathrm{~m}$
(b) from
$x=8.0 \mathrm{~m}$ to $x=12.0 \mathrm{~m} ;(\mathrm{c})$ from $x=0$ to $120 \mathrm{~m} .$

Surjit Tewari
Surjit Tewari
Numerade Educator
05:50

Problem 31

Suppose the sled in Exercise $6.30$ is initially at rest at $x=0$. Use the work-energy theorem to find the speed of the slod of
(a) $x=8.0 \mathrm{~m}$ and $(b) x=120 \mathrm{~m}$. You can ignoee friction betwoen the sled and the surface of the pond.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:40

Problem 32

A balky cow is leaving the bern as you try harder and harder to pubh ber back in. In coordinates with the origin at the bam doot, the cow wallss from $x=0$ to $x=6.9 \mathrm{~m}$ as you apply a force with $x$ -component $F_{x}=-[20.0 \mathrm{~N}+(3.0 \mathrm{~N} / \mathrm{m}) x]$. How much work does the force you spply do on the cow during this displacement?

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:39

Problem 33

A 6.0-kg box moving at $3.0 \mathrm{~m} / \mathrm{s}$ on a borizontal, frictionless surfece runs into a light spring of force constant $75 \mathrm{~N} / \mathrm{cm}$. Use the work-ebergy theorem to find the maximum compression of the spring.

Kara Merfeld
Kara Merfeld
Numerade Educator
05:27

Problem 34

Leg Presses. As part of your daily workout, you lie on your buck and push with your feet ugainst a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you conpress the springs. You do $80.0 \mathrm{~J}$ of work when you compress the springs $0.200 \mathrm{~m}$ from their uncompresced length. (a) What magnitude of force must yoe apply to bold the platform in this position? (b) How much
adlirional work mitst you do to move the platform $0.200 \mathrm{~m}$ farther, and what maximam force mnst you gpply?

Vishal Gupta
Vishal Gupta
Numerade Educator
12:13

Problem 35

(a) In Exarnple $6.7$ (Section $6.3$ ) it was calculated that with the air track turned ofl, the glider travels $8.6 \mathrm{~cm}$ before it stops instantaneously. How large would the coefficient of static friction $\mu_{4}$ have to be to keep the glider from springing back to the left?
(b) If the coethcicnt of static friction betwcen the glider and the track is $\mu_{\mathrm{a}}=0.60$, what is the maximum initial speed $v_{1}$ that the glider can be given and stil! remain at rest after it stops instantaneously? With the eir track mamed off, the coeficient of kinetic friction is $\mu_{\mathrm{k}}=0.47 .$

David González Cornejo
David González Cornejo
Numerade Educator
01:33

Problem 36

$\mathrm{A} 4.00 \mathrm{~kg}$ block of ice is placed wgainst al horizontal spring that has foroe constant $k=200 \mathrm{~N} / \mathrm{m}$ and is compressed $0.025 \mathrm{~m}$. The spring is released and accelcrutes the block along a horizontal surface. Yon can ignore friction and the mass of the spring. (a) Calculate the work done on the block by the spring during the motion of the block from its initial position to where the spring has returned to its encompressed length. (b) What is the speed of the block after it leaves the spring?

Surjit Tewari
Surjit Tewari
Numerade Educator
04:15

Problem 37

A force $\boldsymbol{F}$ is applied to a $2.0 \mathrm{~kg}$ madio-controlled model car parallel to the x-axis as it moves along a straight track. 'The $x$ -component of the force varies with the $x$ -coordinate of the car as shown in Fig. 6.32. Calculare the work done by the force $\vec{F}$ when the car moves from (a) $x=0$ to $x=3.0 \mathrm{~m} ;$ (b) $x=3.0 \mathrm{~m}$ to $x=4.0 \mathrm{~m} ;(\mathrm{c}) x=4.0 \mathrm{~m}$ to $x=7.0 \mathrm{~m}$ (d) $x=0$ to $x=7.0 \mathrm{~m}$
(e) $x=7.0 \mathrm{~m}$ to $x=20 \mathrm{~m}$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
15:31

Problem 38

Suppose the $20-\mathrm{kg}$ model car in Exercise $6.37$ is initially at rost at $x=0$ and $F$ is the net force ncting oa it. Use the work-eaergy theorem to find the speed of the car at (a) $x=3.0 \mathrm{~m}$;
(b) $x=4.0 \mathrm{~m} ;$ (c) $x=7.0 \mathrm{~m}$.

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:13

Problem 39

At a waterpark, sleds with riders are sent aloag a slippery. horizontal surface by the release of a large compressed spring. The spring with force coastant $k=40.0 \mathrm{~N} / \mathrm{cm}$ and negligible mass rests on the frictionless horizontal surface. One end is in contuct with a stationary wall. A slod and rider with total mass $70.0 \mathrm{~kg}$ are pushed against the other end, compressing the spring $0.375 \mathrm{~m}$. The sled is then released with yero initial velocity. What is the sled's
(a) returns to its nacompressed length and speed when the spring
(b) is still cormpressed $0.200 \mathrm{~m}$ ?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
05:24

Problem 40

Half of spring. (a) Suppose you cut a massless ideal spring in half. If the full spring had a force oonstant $k$, what is the force constant of each half, in terms of $k$ ? (Hint: Think of the original spring as two equal halves, each producing the same force as the entire spring. Do yoe see why the forces mast be equal? (b) If you cut the spring into three equal segments instead, what is the force constant of each one, in terms of $k ?$

Paul A.
Paul A.
California State Polytechnic University, Pomona
07:20

Problem 41

A small glider is placed sgainst s compressed spring at the bottom of an air track that slopes upward at an angle of $40.0^{\circ}$ above the horizontal. The ghder has mass $0.0900 \mathrm{~kg}$. The spring has $k=640 \mathrm{~N} / \mathrm{m}$ and negligible mass. When the spring is released, the glider travels a maximum distance of $1.80 \mathrm{~m}$ along the air track before sliding back down. Before reaching this maximurm distance, the ghider loses contact with the spring. (a) What tlistance was the spring originally comprossed?
(b) When the glider has traveled along the air track $0.80 \mathrm{~m}$ from its initial position against the compressed spcing, is it still in contact with the spring? What is the kinetic energy of the glider at this point?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
05:54

Problem 42

An ingenious bricklayer builds n device for shooting bricks up to the top of the wail where he is working. He places a brick on a vertical compressed spring with force constant $k=450 \mathrm{~N} / \mathrm{m}$ and negligible mase. When the spring is released, the brick is propelled upward. If the brick has mass $1.80 \mathrm{~kg}$ and is to reach a maximum height of $3.6 \mathrm{~m}$ above its initial position on the corrpressed spriag. what distance must the bricklayer compress the spring initially? (The brick loses contact with the spring when the spring returns to its uncompressed length. Why??

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:02

Problem 43

How many joules of energy does a 100 -watt light bulb use per hour? How fast would a 70 -kg person have to run to have that amount of kinetic energy?

Ryan Mcclanahan
Ryan Mcclanahan
Numerade Educator
02:21

Problem 44

The total consumption of clectrical encrgy in the United States is about $1.0 \times 10^{\circ} \mathrm{J}$ per year. (a) What is the average rate of electrical energy consumption in watts? (b) 'The populution of the United States is about 300 million people. What is the sverage rite of clectrical energy consumption per person? (c) The sun transfers eacrgy to the carth by radiation at a rate of aqpeoximately $1.0 \mathrm{~kW}$ per square meter of rurface. If this energy could be collected and converted to electrical eaergy with $40 \%$ efficiency, how great an area (in square kilometers) would be roquired to collect the electrical energy used in the United States?

Surjit Tewari
Surjit Tewari
Numerade Educator
05:21

Problem 45

Magnetar. On December $27_{0}$ 2004, nstronomers observed the greatest flash of fight ever rocorded from outside the solar system. It came from the highly magnetie neutron ster SGR $1806-20$ (a magnetar). During $0.20 \mathrm{~s}$, this star rclcascd as much cncrgy as our sua does in 250,000 years. If $P$ is the average power output of our sun, what was the average power output (in terms of $P)$ of this magnetar?

Yaqub Khan
Yaqub Khan
Numerade Educator
06:28

Problem 46

A $20.0-\mathrm{kg}$ rock is sliding on a rough, borizontal surface at $8.00 \mathrm{~m} / \mathrm{s}$ and eventually stops due to friction. The coefficicnt of kinetic friction between the rock and the surface is $0.200$. What everege power is produced by friction as the rock stops?

Paul A.
Paul A.
California State Polytechnic University, Pomona
01:42

Problem 47

A tandem (two-person) bicycle team must overcome a force of $165 \mathrm{~N}$ to maintain a speed of $9.00 \mathrm{~m} / \mathrm{s}$. Find the power required per rider, assuming that each contributes equally. Express your answer in watts and in horsepower.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
04:20

Problem 48

When its $75-\mathrm{kW}$ (100-hp) cngine is gcncrating full powor, a small single-engine airplane with mass $700 \mathrm{~kg}$ gains altitude at a rate of $2.5 \mathrm{~m} / \mathrm{s}(150 \mathrm{~m} / \mathrm{min}$, ot $500 \mathrm{f} / \mathrm{min})$. What fraction of the
engine power is being used to make the airplane climb? CIhe remainder is used to overoome the effects of air resistance nnd of incfficicncics in the propeller and caginc.)

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:50

Problem 49

Worling Like a Horse. Your job is to lift 30 -kg crates a vertical distance of $0.90 \mathrm{~m}$ from the ground onto the bed of a truck.
(a) How many erates would you have to loed onto the truck in 1 minute for the avenige power output you use to lift the crates to equal $0.50$ hp? (b) How many crates for an merage power output of $100 \mathrm{~W} ?$

Vishal Gupta
Vishal Gupta
Numerade Educator
03:58

Problem 50

An clevator has muss $600 \mathrm{~kg}$, not including passengem. The clovator is designed to ascend, at constant speod, s. vertical distance of $20.0 \mathrm{~m}$ (five floors) in $160 \mathrm{~s}$, and it is driven by a motor that can provide up to $40 \mathrm{kp}$ to the elevator, What is the muxiroum number of passengens that can ride in the elevator? Assume that an zventge passenger has mass $65.0 \mathrm{~kg}$.

Surjit Tewari
Surjit Tewari
Numerade Educator
03:39

Problem 51

Automotive Power. It is not unusual for a $1000-\mathrm{kg}$ car to get 30 mi/gal when travcling at $60 \mathrm{mi} / \mathrm{h}$ oa a level roed. If this car makes a 200 km trip, (a) how many joules of energy does it codsume, and (b) what is the averge rate of energy consumption during the trip? Note that $1.0 \mathrm{gal}$ of gasoline yields $1.3 \times 10^{4} \mathrm{~J}$ (although this can vary). Consult Appendix E.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:59

Problem 52

The aircraft currier John $F$ Kennedy has mass $7.4 \times 10^{7} \mathrm{~kg}$. When its engines are developing their full power of 280,000 hp. the John $F$. Kennedy travels at its top speed of 35 knots ( $65 \mathrm{~lm} / \mathrm{h}$ ). If $70 \%$ of the power output of the cngines is applied to pushing the ship through the water, what is the magnitude of the force of water resistance that opposes the camier's motion at this speed?

Vishal Gupta
Vishal Gupta
Numerade Educator
06:49

Problem 53

A ski tow opentos on a $15.0^{\circ}$ slope of length $300 \mathrm{~m}$. The rope moves at $12.0 \mathrm{~km} / \mathrm{h}$ and provides power for 50 riders at one time, with an average mass per rider of $700 \mathrm{~kg}$. Estimate the power required to operate the tow.

David González Cornejo
David González Cornejo
Numerade Educator
01:08

Problem 54

A typical flying insect applies an average force equal to twice its welght during each downward stroke while hovering. Thke the mass of the insect to be $10 \mathrm{~g}$, and assume the wings move an average downward distance of $1.0$ cm during each stroke. Assuming 100 downward strokes per second, estimate the average power output of the insect.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:33

Problem 55

Rotating Bar. A thin, uniforn $12.0-\mathrm{kg}$ bar that is $2.00 \mathrm{~m}$ long rotates uniformly sbout a pivot st one end, making $5.00$ coraplete rovolutions every $3.00$ seconds. What is the kinctic energy of this bar? (Hint: Diffcrcnt points in the bar have differcnt speeds. Break the bar up into infinitesimal scgments of mass dm and integrate to add up the kinetic energy of all these segments.)

Surjit Tewari
Surjit Tewari
Numerade Educator
03:49

Problem 56

A Near-Rarth Asteroid. On April 13, 2029 (Friday the $13 \mathrm{th} !$, the steroid 99942 Apophis will pass within $18,600 \mathrm{mi}$ of tbe earth-about 1/13 the distunce to the moonl It has n deasity of $2600 \mathrm{~kg} / \mathrm{m}^{3}$, can be modeled as a sphere $320 \mathrm{~m}$ in diametec, and will be traveling at $12.6 \mathrm{~km} / \mathrm{s}$. (a) If, due to a small distur. bance in its orbit, the asteroid were to hit the earth, how much kinetic energy would it deliver? (b) The Iargest nuclear bomb ever tested by the United States was the "Custie/Bravo" bounb, having " yield of 15 megatons of 'TNT. (A megaton of TNT releases $4.184 \times 10^{15} \mathrm{~J}$ of canggy.) How mary Castle/Bravo bombs would be equivalent to the energy of Apophis?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:34

Problem 57

A luggage handler pulls a $20.0-\mathrm{kg}$ suitease up a ramp inclined at $25.0^{\circ}$ above the horizontal by a foroe $F$ of mapnitude $140 \mathrm{~N}$ that acts parallel to the ramp. The coeficient of lainetic frictipa between the ramp and the incline is $\mu_{2}=0.300$. If the senitcase travels $3.80 \mathrm{~m}$ along the ramp, calculate (a) the work done on the suitease by the force $\vec{F}$; (b) the wark done on the suitease by the gravitational foroe;
(c) the work done on the saitcase by the nommal force; (d) the work done on the suitcase by the friction
forve; (c) the total work dobe on the suitcase. (f) If the speed of the suitcase is ucro at the bottom of the ramp, what is its speed after it has traveled $3.80 \mathrm{~m}$ along the ramp?

Surjit Tewari
Surjit Tewari
Numerade Educator