Student Worksheets

Unit 4 - Work, Energy, and Power

Worksheet - Is it Work?

Work has a very special meaning for scientists. Work is done when a force causes something to move. When an object does not move, even though there is a force exerted on it, no work has been done. Something must be moved for work to be done. The amount of work done depends upon the amount of force used and the distance that an object is moved. 1. A boy holds a heavy package for one hour. He is very tired but has not done any work. Explain why he did not do any work. ____________________________________________________________________________ 2. A girl is coasting on a bicycle. The bicycle is moving very fast but she is not doing any work. Explain why no work is being done. ____________________________________________________________________________ 3. Why is no work being done when a rocket ship moves through space? ____________________________________________________________________________ 4. Would you do more work pushing open an unlocked door or pushing as hard as you can against a locked door? Explain. ____________________________________________________________________________ 5. You push a shopping cart and cause the cart to move. Have you done any work? How do you know? ____________________________________________________________________________ 6. Suppose you stop pushing on the cart, but the cart keeps moving. Are you doing any work now? How do you know? ____________________________________________________________________________ 7. If Mary studied for four hours, did she do any work? Explain. ____________________________________________________________________________ 8. Circle the letter of each sentence below that describes work being done.

a. John is thinking about his math test. b. Joe is rowing a boat across the lake. c. Sue is standing in line holding her groceries. d. A pillar is holding up the ceiling. e. Kathy handed a pencil to Sam.

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9. Look at the following sentences. Each one contains the word “work”. For each sentence, decide if the word “work” is used as a scientist uses it. If not, write the sentence over so the sentence does not include the word “work”.

a. John’s painting is a work of art. __________________________________________________________________________

b. Laura did a lot of work moving tables. __________________________________________________________________________

c. My flashlight won’t work. __________________________________________________________________________

d. Thinking up an answer to this problem is a lot of work. __________________________________________________________________________

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Name:_______________________________________ Period:______ Date:___________

WorkPracticeProblemsWorksheet#1

1) Amyuses20Nofforcetopushalawnmower10meters.Howmuchworkdoesshedo?

2) Howmuchworkdoesanelephantdowhilemovingacircuswagon20meterswithapullingforceof200N?

3) A900Nmountainclimberscalesa100mcliff.Howmuchworkisdonebythemountainclimber?

4) Shawnuses45Nofforcetostopthecart1meterfromrunninghisfootover.Howmuchworkdoeshedo?

5) Howmuchworkisdonewhenaforceof33Npullsawagon13meters?

6) Howmuchworkisrequiredtopullasled5metersifyouuse60Nofforce?

7) Tommydoes15Joulesofworktopushthepencilover1meter.Howmuchforcedidheuse?

8) Angelausesaforceof25Newtonstolifthergrocerybagwhiledoing50Joulesofwork.Howfardidsheliftthegrocerybags?

9) Thebaseballplayerdoes1234Joulesofworkwhenhittingabaseballintoleftfield.Assumingthebaseballlanded100metersawayfromhomeplate,howmuchforcedidtheplayerusetohittheball?

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(Ans. 200 J)

(Ans. 4000 J)

(Ans. 90,000 J)

(Ans. 45 J)

(Ans. 429 J)

(Ans. 300 J)

(Ans. 15 N)

(Ans. 2 m)

(Ans. 12.3 N)

6.A60.0kgstudentrunsataconstantvelocityupaflightofstairs.Iftheheightofthestairsis3.2m,whatistheworkdoneagainstgravity?

7.A90.0Nboxofpapayasispulled10.0malongalevelsurfacebyarope.Iftheropemakesanangleof20owiththesurface,andtheforceintheropeis75.0N,howmuchworkisdoneonthebox?

8.An80.0kgpumpkinispushedupataconstantvelocityalongafrictionlessinclineasshowninthediagram.Howmuchworkisdoneonthepumpkininmovingituptheincline?

9.A25.0kgpickleisacceleratedfromrestthroughadistanceof6.0min4.0sacrossalevelfloor.Ifthefrictionforcebetweenthepickleandtheflooris3.8N,whatistheworkdonetomovetheobject?

10.A1165kgcartravelingat55km/hisbroughttoastopwhileskidding38m.Calculatetheworkdoneonthecarbythefrictionforces.

1)294J2)18.0J3)0J4)605J5)540J6)1882J7)705J8)5488J9)135J10)136,357J

10.0m7.0m

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what is the work done by the applied force in moving the object?

Work, Energy, and Power

© The Physics Classroom, 2009 Page 2

The amount of work (W) done on an object by a given force can be calculated using the formula

W = F d cos Θ where F is the force and d is the distance over which the force acts and Θ is the angle between F and d. It is important to recognize that the angle included in the equation is not just any old angle; it has a distinct definition that must be remembered when solving such work problems.

5. For each situation below, calculate the amount of work done by the applied force. PSYW

A 100 N force is applied to move a 15 kg object a horizontal distance of 5 meters at constant speed.

A 100 N force is applied at an

angle of 30o to the horizontal to move a 15 kg object at a constant speed for a horizontal distance of 5 m.

An upward force is applied to lift a 15 kg object to a height of 5 meters at constant speed.

6. Indicate whether there is positive (+) or negative (-) work being done on the object.

a. An eastward-moving car skids to a stop across dry pavement.

b. A freshman stands on his toes and lifts a World Civilization book to the top shelf of his locker.

c. At Great America, a roller coaster car is lifted to the peak of the first hill on the Shock Wave.

d. A catcher puts out his mitt and catches the baseball.

e. A falling parachutist opens the chute and slows down.

7. Before beginning its initial descent, a roller coaster car is always pulled up the first hill to a high initial height. Work is done on the car (usually by a chain) to achieve this initial height. A coaster designer is considering three different angles at which to drag the 2000-kg car train to the top of the 60-meter high hill. Her big question is: which angle would require the most work? _______________ Show your answers and explain.

Angle Force Distance Work

35° 1.15 * 104 N 105 m

45° 1.41 * 104 N 84.9 m

55° 1.64 * 104 N 73.2 m

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Work, Energy, and Power Name:

© The Physics Classroom, 2009 Page 3

8. The following descriptions and their accompanying free-body diagrams show the forces acting upon an object. For each case, calculate the work done by these forces; use the format of force • displacement • cosine(Θ). Finally, calculate the total work done by all forces.

Free-Body Diagram

Forces Doing Work on the Object Amount of Work Done by Each Force

a. A 10-N force is applied to push a block across a frictionless surface for a displacement of 5.0 m to the right.

Wnorm = • • cos( ) = J Wapp = • • cos( ) = J Wgrav = • • cos( ) = J Wtotal = J

b. A 10-N frictional force slows a moving block to a stop along a horizontal surface after a displacement of 5.0 m to the right.

Wnorm = • • cos( ) = J Wgrav = • • cos( ) = J Wfrict = • • cos( ) = J Wtotal = J

c. A 10-N forces is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m to the right.

Wnorm = • • cos( ) = J Wapp = • • cos( ) = J Wgrav = • • cos( ) = J Wfrict = • • cos( ) = J Wtotal = J

d. A 2-kg object is sliding at constant speed across a frictionless surface for a displacement of 5.0 m to the right.

Wnorm = • • cos( ) = J Wgrav = • • cos( ) = J Wtotal = J

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Work, Energy, and Power

© The Physics Classroom, 2009 Page 4

Free-Body Diagram

Forces Doing Work on the Object Amount of Work Done by Each Force

e. A 2-kg object is pulled upward at constant speed by a 20-N force for a vertical displacement of 5.0 m.

Wtens = • • cos( ) = J Wgrav = • • cos( ) = J Wtotal = J

f. A 2-kg tray of dinner plates is held in the air and carried a distance of 5.0 m to the right.

Wapp = • • cos( ) = J Wgrav = • • cos( ) = J Wtotal = J

9. When a force is applied to do work on an object, does the object always accelerate? __________ Explain why or why not.

10. Determine the work done in the following situations.

a. Jim Neysweeper is applying a 21.6-N force downward at an angle of 57.2° with the horizontal to displace a broom a distance of 6.28 m.

b. Ben Pumpiniron applies an upward force to lift a 129-kg barbell to a height of 1.98 m at a

constant speed. c. An elevator lifts 12 occupants up 21 floors (76.8 meters) at a constant speed. The average mass

of the occupants is 62.8 kg.

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WorkDonebyForcesActingatanAngle1.A35kgboxispulledtotherightbyexertingatensionforceof40Nonaropethatmakesa37oanglewiththehorizontal.Iftheboxispulledadistanceof4m,howmuchworkhasbeendonetoit?(Ans.128J)2.Acarispushedadistanceof10musingaforceof100Nthatisdirecteddownwardatanangleof50otothehorizontal.Howmuchworkhasbeendonetothecar.(Ans.643J)3.Awomandoes54Jofworkonatrunkbyslidingitadistanceof5malongthefloor.Ifshepushesdownwardonthetrunkatanangleof62otothehorizontal,howmuchforceissheusing?(Ans.23N)4.600Jofworkisdoneonawatermelonbyaforceof83Npushingitacrossafrictionlessfloor.Iftheforceisappliedatanangleof25otothehorizontal,howfardidthewatermelonmove?(Ans.8m)5.Howfaralongthefloordoesthe50Nforceshowninthisdiagramhavetodragtheboxinordertodo750Jofworkonit?(Careful!)(Ans.25m)6.Theforceshowninthisdiagrampullstheobjectadistanceof12malongtheflooranddoes637Jofwork.Whatistheangleθ?(Ans.35o)7.Theobjectinthediagramisdraggedadistanceof18malongthefloor.Findthefollowing:a)Theworkdonebytheappliedforce(Ans.1471J)b)Theworkdonebyfriction(Ans.-540J)c)Thenetworkdoneontheobject(Ans.931J)

37o50N

65N

57o

150N

Ffr = 30N

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Physics Name: _________________________ Date: ____________________

KINETIC ENERGY

1. A bumblebee has a mass of 0.002 kg and is flying at 2 m/s. What is the kinetic energy of the bumblebee? Given:

Find:

2. A lion has a mass of 300 kg. If it runs at 6.5 m/s, what is its kinetic Energy?

Given:

Find:

3. A world-class sprinter runs at 9 m/s. If her mass is 63 kg, what is her kinetic energy? Given: Find:

4. A 71 kg skier reached a speed of 50 m/s at the bottom of a hill. Find his kinetic energy.

Given:

Find:

5. The space shuttle, with a mass of 2,029,000 kg, can travel at 7,900 m/s. What is the kinetic energy of the space shuttle at this speed? Given: Find:

6. A male polar bear has an average mass of 500 kg and can typically reach speeds as fast as 15

m/s. What is the kinetic energy of the polar bear? Given:

Find:

7. A US speed skater won an Olympic medal skating at 14 m/s. If his mass is 78 kg, what was his kinetic energy? Given:

Find:

8. A 750 kg car moves at 20 m/s. Find the kinetic energy of the car. Given:

Find:

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(Ans. .004 J )

(Ans. 6,338 J )

(Ans. 2,552 J )

(Ans. 88,750 J )

(Ans. 6.3 x 10¹³ J )

(Ans. 56,250 J )

(Ans. 7,644 J )

(Ans. 150,000 J )

Physics Name: ___________________________ Date: ______________________

POTENTIAL ENERGY

1. During the pole vault, an athlete with a mass of 55 kg is lifted to a height of 6.1 m. What is the athlete’s potential energy at this height? Given:

Find:

2. What is the potential energy of a 100 kg barbell lifted 1.7 m?

Given:

Find:

3. A 1.5 kg ball reaches a height of 7.5 m. What is the potential energy of the ball? Given:

Find:

4. A car with a mass of 905 kg is driven to the top of a hill 55 m high. What is the car’s potential

energy at the top of the hill? Given:

Find:

5. A rock climber has a mass of 62 kg and is 100 m above the ground. What is the rock

climber’s potential energy? Given:

Find:

6. A bird with a mass of 3.5 kg is sitting in a nest 12.2 m above the ground. Find the potential

energy of the bird. Given:

Find:

7. A 10 kg box of books is resting on a 3 m high shelf. Calculate the potential energy of the box

of books. Given:

Find:

8. A 35 kg child reaches a maximum height of 3 m while swinging on a swing. Find his

potential energy at the maximum height. Given:

Find:

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(Ans. 3,288 J )

(Ans. 1,666 J )

(Ans. 110 J )

(Ans. 487,795 J )

(Ans. 60,760 J )

(Ans. 418.5 J )

(Ans. 294 J )

(Ans. 1,029 J )

Work and Energy Practice Sheet

1. What is the potential energy of a 2-kilogram potted plant that is on a 1 meter-high plant stand? 2. What is the kinetic energy of a 3-kilogram ball that is rolling at 2 meters per second? 3.2 3. The potential energy of an apple is 6.00 joules. The apple is 3.00-meters high. What is the mass of the apple? 4. Determine the amount of potential energy of a 5-newton book that is moved to three different shelves on a bookcase. The height of each shelf is 1.0 meter, 1.5 meters, and 2.0 meters. 5. Two objects were lifted by a machine. One object had a mass of 2 kilograms, and was lifted at a speed of 2 m/sec. The other had a mass of 4 kilograms and was lifted at a rate of 3 m/sec. a. Which object had more kinetic energy while it was being lifted? b. Which object had more potential energy when it was lifted to a distance of 10 meters? Show your calculation. (Remember that gravity = 9.8 m/sec2 ) 6. You are on roller blades on top of a small hill. Your potential energy is equal to 1,000.0 joules. The last time you checked your mass was 60.0 kilograms. a. What is your weight in newtons? b. What is the height of the hill? c. If you start skating down this hill, your potential energy will be converted to kinetic energy. At the bottom of the hill, your kinetic energy will be equal to your potential energy at the top. What will be your speed at the bottom of the hill? 7. Answer the following: a. What is the kinetic energy of a 1-kilogram ball is thrown into the air with an initial velocity of 30 m/sec? b. How much potential energy does the ball have when it reaches the top of its ascent? c. How high into the air did the ball travel? 8. What is the potential energy of a 3 kilogram-ball that is on the ground? 9. What is the kinetic energy of a 2,000-kilogram boat moving at 5 m/sec? 10. What is the velocity of a 500-kilogram elevator that has 4,000 joules of energy?

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PE/KE Energy Worksheet

1. A 25.0 N object is held 2.10 m above the ground. What is the potential energy with respect to the ground?

2. A 2.75 kg box is at the top of a frictionless incline as shown in the diagram. What is the potential energy with respect to the bottom of the incline?

3. The bob of a pendulum has a mass of 2.0 kg and hangs 0.50 m above the floor. The bob is pulled sideways so that it is 0.75 m above the floor. What is its potential energy with respect to its equilibrium position?

4. A 2.00 x103 kg object is pushed to the top of an incline as shown. If the force applied along the incline is 6.00 x 102 N, what is the potential energy of the object when it is at the top of the incline with respect to the bottom?

5. A 3.0 kg object is traveling at a constant speed of 7.5 m/s. What is its kinetic energy?

6. The kinetic energy of a 20.0 N goat is 5.00 x 102 J. What is the speed of the goat?

7.00 m 10.0 m

6.0 m 12.0 m

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ANSWERS ON NEXT PAGE

7. A 10.0 N lightsaber is accelerated from rest at a rate of 2.5 m/s2. What is the kinetic energy of the lightsaber after it has accelerated over a distance of 15.0 m.

8. A 1200.0 N Yak falls off a cliff on Earth. What is its kinetic energy after it falls for 4.50 s? 9. An 8.0 kg Chinchilla is dropped from a height of 7.0 m. What is the kinetic energy of the Chinchilla just before it hits the ground? (Note: Chinchillas always land on their feet.)

10. A 9.00 kg object falls off of a 1.2 m high table. If all of the object's potential energy is converted into kinetic energy just before it hits the floor, how fast is it moving?

1) 52.5 J 2) 189 J 3) 4.9 J 4) 120000 J 5) 84 J 6) 22.1 m/s 7) 38 J 8) 1.2x105 J 9) 550 J 10) 4.85 m/s

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Conceptual Physics Name: ________________________ Date: ___________________

Mechanical Energy Examples

1. A 0.75 kg football is moving through the air at 15 m/s and is 3 m above the ground. (A) Find its Kinetic Energy. (B) Find its Potential Energy. (C) Find its Mechanical Energy.

2. A 2 kg bird is 18 m above the ground and flying at 8 m/s. (A) Find its Kinetic Energy. (B) Find its Potential Energy. (C) Find its Mechanical Energy.

3. An 8000 kg car moving at 35 m/s is on a bridge that is 25 m high. (A) Find its Kinetic Energy. (B) Find its Potential Energy. (C) Find its Mechanical Energy.

4. A 1 kg box is being pulled across the ground at a speed of 3 m/s. (A) Find its Kinetic Energy. (B) Find its Potential Energy. (C) Find its Mechanical Energy.

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(Ans. A) 84.4 J B) 22 J C) 106.4 J )

(Ans. A) 64 J B) 352.8 J C) 416.8 J)

(Ans. A) 4,900,000 J B) 196,000 J C) 5,096,000 J )

(Ans. A) 4.5 J B) 0 J C) 4.5 J )

Physics Name: ______________________________ Date: _________________________

MECHANICAL ENERGY

1. A 3 kg bird is flying at 6 m/s at a height of 20 m above the ground. (A) Find its kinetic energy. (B) Find its potential energy. (C) Find its total mechanical energy.

2. A 4,000 kg rollercoaster is moving at 3 m/s at the top of a 33 m high hill. (A) Find the coaster’s kinetic energy. (B) Find the coaster’s potential energy. (C) Find the coaster’s total mechanical energy.

3. A 40 kg child rides a 7 kg bike up and over a 4 m high hill. If the child’s speed is 9 m/s at the top of the hill, find the following. (A) The kinetic energy at the top of the hill. (B) The potential energy at the top of the hill. (C) the total mechanical energy at the top of the hill.

4. A 3.5 kg model airplane 10 m above the ground. When it is moving at 13 m/s, find (A) its kinetic energy, (B) its potential energy, and (C) its total mechanical energy.

5. A 2.5 kg football is moving at 20 m/s and is 4 m above the ground. (A) Find its kinetic energy. (B) Find its potential energy. (C) Find its total mechanical energy.

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(Ans. A) 54 J B) 588 J C) 642 J )

(Ans. A) 1903.5 J B) 1,842.4 J C) 3745.9 J )

(Ans. A) 500 J B) 98 J C) 598 J )

(Ans. A) 295.8 J B) 343 J C) 638.8 J )

(Ans. A) 54 J B) 588 J C) 642 J )

(Ans. A) 18,000 J B) 1,293,600 J C) 1,311,600 J )

Physics Name: ______________________________ Date: _________________________

CONSERVATION OF MECHANICAL ENERGY

1. A child on a sled starts at the top of a hill with 400 J of kinetic energy and 2,000 J of

gravitational potential energy. (A) After a few seconds, the child and sled have 1,200 J of kinetic energy. How much gravitational potential energy does the child and sled have at this time? (B) What will be the kinetic energy at the bottom of the hill? (C) What will be the gravitational potential energy at the bottom of the hill? Sketch:

2. A roller coaster has 4,500 J of kinetic energy and 200,000 J of gravitational potential energy at the top of the hill. (A) When the roller coaster has 100,000 J of gravitational potential energy, how much kinetic energy must it have? (B) How much gravitational potential energy does it have at the bottom (ground level)? (C) How much kinetic energy does it have at the bottom? Sketch:

3. A child has 600 J of gravitational potential energy and 0 J of kinetic energy when sitting at the top of a slide. (A) Half way down he has 300 J of kinetic energy. How much gravitational potential energy does he have at the half-way point? (B) How much kinetic energy does he have at the bottom (ground level)? Sketch:

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4. A ball rolling on a table has 150 J of kinetic energy and 90 J of gravitational potential energy. The ball rolls off of the table. How much kinetic energy does it have just as it hits the floor? Sketch:

5. As a pendulum swings from side to side, the energy is transformed from PE to KE and the back. (A) If a pendulum has 25 J of gravitational potential energy at the top of its swing, how much kinetic energy will it have when it has 15 J of gravitational potential energy? (B) How much kinetic energy will it have at the bottom of the swing when the gravitational potential energy is zero joules? Sketch:

6. A skier approaches a hill with 1150 J of kinetic energy and no gravitational potential energy. (A) When he is almost at the top of the hill he has 700 J of gravitational potential energy. How much kinetic energy does he have at this point? (B) At the top he has 950 J of gravitational potential energy. How much kinetic energy does he have at the top? Sketch:

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Conservation of Energy Worksheet

Name ______________________ 1) State the law of conservation of energy. 2) A 200-kg boulder is 1000-m above the ground. a) What is its potential energy when it is 1000-m above the ground? b) What is its kinetic energy when it is 1000-m above the ground? c) The boulder begins to fall. What is its potential energy when it is 500-m above the ground? Where did the “lost” potential energy go? d) What is the kinetic energy of the boulder when it has fallen 500-m? e) What is the kinetic energy of the boulder just before it hits the ground? 3) A rollercoaster is designed as shown below. If the roller coaster starts at the top of the first hill from rest, describe what will happen to the rollercoaster. How could you fix this problem?

START

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4) When you use a slingshot to fire a rock you stretch the rubber band storing potential energy. If you stretched the rubber band so that it had 100-J of potential energy, a) with how much kinetic energy will the rock leave the slingshot? b) with how much kinetic energy will the rock leave the slingshot if it loses 10-J to heat & sound? 5) A pendulum has 15-J of potential energy at the top of its swing. a) What is its kinetic energy at the bottom of its swing? b) At another time the pendulum has 8-J of potential energy. What is its kinetic energy? c) For the pendulum in “b”, what will its kinetic energy be if it loses 2-J to heat? 6) A 1-kg ball is 10-m above a table when it is dropped. It bounces to a height of 7-m. a) How much energy is transferred to heat & sound during the bounce? b) Explain why this ball cannot bounce to a height of 12-m if it is dropped. c) What could you do to make the ball bounce to a height of 12-m?

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Name ____________________________________________________________ Date ________________________________ Class _________ CONSERVATION OF ENERGY WORKSHEET [Unless otherwise stated , assume there is no air resistance and that all surfaces are frictionless]

1. Fill in the missing values.

2. Fill in the missing values.

3. An electric motor is used to hoist building supplies from the ground to the roof of a buidling.

A. How much work can the motor do in 12 seconds if its power output is 1.5 kW (1,500 W)?

B. How high can it lift a 131 kg bundle of shingles in that time?

Eg= 200 J

Ek= 0 J

Etotal=

Eg= 150 J

Ek=

Etotal=

Eg=

Ek= 60 J

Etotal=

Eg=

Ek= 200 J

Etotal=

Eg = 0 J

Ek = ____

Etotal = 15 J

Eg = ____

Ek = 7 J

Etotal =____

Eg = 15 J

Ek = ____

Etotal = ___

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4. A 1.8 kg book has been dropped from the top of the football stadium. Its speed is 4.8 m/s when it is 2.9 meters above the ground. A. What is its total mechanical energy? (mechanical energy includes kinetic, gravitational potential, and

elastic potential but not internal forms of energy such as thermal or chemical) B. What was the total mechanical energy of the book at the instant it was released? C. How high is the stadium?

5. A 28 kg child on a swing is traveling at 4.2 m/s and has 315 J of total mechanical energy. What is his gravitational potential energy? How high is he above the ground?

6. A 3.2 kg ball that is moving straight upward has 17 J of kinetic energy and its total mechanical energy is 25 J. a. Find the gravitational potential energy of the ball.

b. What is its height above the ground?

c. What is the speed of the ball?

d. What will be its gravitational energy when it is at its highest point above the ground?

e. What is its maximum height above the ground?

f. What will be its speed just before it lands on the ground?

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Conservation of Energy Worksheet Name: ___________________ PE before + KE before = PE after + KE after PE = mgh KE = ½ mv2 g = 9.81 m/s2 3. A 100 kg roller coaster comes over the first hill at 2 m/sec (vo). The height of the first hill (h) is 20 meters. See roller diagram below.

1) Find the total energy for the roller coaster at the initial point. 2) Find the potential energy at point A using the PE formula. 3) Use the conservation of energy to find the kinetic energy (KE) at point B. 4) Find the potential energy at point C. 5) Use the conservation of energy to find the Kinetic Energy (KE) of the roller coaster at point C. 6) Use the Kinetic Energy from C, find velocity of the roller coaster at point C.

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Name___________________________________________Date___________________Pd.____________

WorkandEnergyReview

1.Ifa34kgrockisdroppedfromthetopofacliffwithaninitialvelocityofzero,anditistraveling27m/swhenithitsthegroundbelow,howtallisthecliff?(Ans.37.2m)2.Anobjectweighing102Nisrestingonthefloor.Apersonpushesdownontheobjectwithaforceof46Natanangleof68otothehorizontal.Iftheobjectslides12malongthefloor,howmuchworkdidthepersondo?(Ans.207J)3.Asledwithmass8kgisslidingalongaflat,frozenlake.Itsinitialvelocityis2.3m/s.Afterslidingadistanceof20m,thesled'svelocityis1.4m/s.Whatistheforceoffrictionbetweenthesledandtheice?(Ans..67N)4.A35kgshoppingcartismovingataspeedof2m/sacrossalevelparkinglot.Apersonappliesaforceof20Ninthedirectionofthecart'smotionforadistanceof3m.Whatwillbetheshoppingcart'snewspeed?(Ans.2.7m/s)

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5.Howmuchworkdoesittaketolifta60gapplestraightupwardbyadistanceof45cm?(Ans..26J)6.A16kgpaperweightfallsoutawindow60mabovetheground.Howfastwillitbetravelingwhenitis30mabovetheground?Howfastwoulditbetravelingifitwerethrownoutthesamewindowinanupwarddirectionwithaninitialvelocityof4.5m/s?(Ans.24.2m/s;24.7m/s)7.Atoydartguncontainsaspringwhoseconstantis250N/m.Ifa15gdartcompressesthespringby4cmandthedartisfiredstraightintotheair,whatisthemaximumheightitwillriseto?(Ans.1.4m)8.Ifittakesaforceof56Ntostretchaspringwhoserelaxedlengthis24cmtoalengthof37cm,whatisthevalueofthespringconstantforthespring?(Ans.431N/m)

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Unit4End-of-UnitReviewSheet

1.An100kgmountainclimberscalesa130mcliff.Howmuchworkisdonebythemountainclimber?(Ans.

127,400J)

2.Julesdoes19Joulesofworktopushabox.7meter.Howmuchforcedidheuse?(Ans.27.1N)

3.A370.0Nboxofavocadosispulled4.0malongalevelsurfacebyarope.Iftheropemakesanangleof30o

withthesurface,andtheforceintheropeis75.0N,howmuchworkisdoneonthebox?(Ans.259.8J)

4.An12.0kggourdispushedupataconstantvelocityalongafrictionlessinclineasshownin

thediagram.Howmuchworkisdoneinmovingituptheincline? (Ans.470.4J)

5.A5.0kgpickleisacceleratedfromrestthroughadistanceof3min12sacrossalevelfloor.Ifthefriction

forcebetweenthepickleandtheflooris1.1N,whatistheworkdonetomovetheobject?(Ans.3.9J)

6.Betsyisapplyinga33.6Nforcedownwardatanangleof48.6°withthehorizontal

tomoveaboxadistanceof6.28m.Howmuchworkisdonetotheboxbythisforce?(Ans.139.5J)

7.543Jofworkisdoneonahoneydewmelonbyaforceof34Npushingitacrossafrictionlessfloor.

Iftheforceisappliedatanangleof25otothehorizontal,howfardidthehoneydewmove?(Ans.17.6m)

8.Theobjectinthediagramisbegindraggedadistanceof5m.Findtheworkdonebythe

appliedforce,theworkdonebyfriction,andtheNetWorkdonetotheobject.

(Ans.Wapp=689.5J;Wfr=-200J;Wnet=689.5-200=489.5J)

9.Thespaceshuttle,withamassof3,038,000kg,cantravelat7,500m/s.Whatisthekineticenergyofthe

spaceshuttleatthisspeed?(Ans.8.54x1013J)

10.Abirdwithamassof4.2kgissittinginanest8.4mabovetheground.Findthepotentialenergyofthe

bird.(Ans.345.7J)

11.Youareonrollerbladesontopofasmallhill.Yourpotentialenergyisequalto2,500joules.Thelasttime

youcheckedyourmasswas50kilograms.

a.Whatisyourweightinnewtons?(Ans.490N)

b.Whatistheheightofthehill?(Ans.5.1m)

c.Whatwillbeyourspeedatthebottomofthehill?(Ans.10m/s)

12.An11000Napefallsfromrestoffacliff.Whatisitskineticenergyafteritfallsfor3.5s?(Ans.660,275J)

13.A10.00kgobjectfallsfromrestfroma.75mhightable.Howfastisitmovingwhenithitstheground?

(Note:Useanenergyapproach,notPVAT.)(Ans.3.83m/s)

14.An12000kgcarmovingat26m/sisonabridgethatis35mhigh.(A)FinditsKineticEnergy.(B)Findits

PotentialEnergy.(C)FinditsMechanicalEnergy.(Ans.A)413,878JB)420,000JC)833,878J)

15.Arollercoasterofmass700kgstartsatrestfrompointAinthediagrambelow.Findthefollowing:

5m

4m

40o

180N

Ff=40N

25

by the applied force?

N

a)ThevelocityoftherollercoasterwhenitreachespointB.(Ans.26.9m/s)b)ThepotentialenergyoftherollercoasteratpointC.(Ans.240,100J)c)ThekineticenergyoftherollercoasterandpointE.(Ans.274,400J)d)(HonorsOnly):WhatfrictionforceisnecessarytostopthecoasterbythetimeitreachespointFifthebrakesareappliedatpointE?(Ans.21,108N) HonorsOnly16.Astudentwearingfrictionlessrollerskatesonahorizontalsurfaceispushedbyafriendwithaconstantforceof45N.Howfarmustthestudentbepushed,startingfromrest,sothatherfinalkineticenergyis352J?(Ans.7.8m)17.A75kgbobsledispushedalongahorizontalsurfacebytwoathletes.Afterthebobsledispushedadistanceof4.5mstartingfromrest,itsspeedis6.0m/s.Findthemagnitudeofthenetforceonthebobsled.(Ans.300N)18.A755Ndiverdropsfromaboard10.0mabovethewater’ssurface.Findthediver’sspeed5.00mabovethewater’ssurface.Thenfindthediver’sspeedjustbeforestrikingthewater.(Ans.9.9m/s;14m/s)19.A1500kgcaracceleratesuniformlyfromrestto10.0m/sin3.00s.a.Whatistheworkdoneonthecarinthistimeinterval?(Ans.73,508J)b.Whatisthepowerdeliveredbytheengineinthistimeinterval?(Ans.24,503W)20.Howmuchpowerdoesittaketolifta7kgchair1.4moffthefloorin.6seconds?(Ans.160W)

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233

13m

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SUPPLEMENTAL MATERIALS

(ADDITIONAL PRACTICE)

(ADDITIONAL PRACTICE)

(ADDITIONAL PRACTICE)

(ADDITIONAL PRACTICE)

KE/PE and Work- Energy Theorem Worksheet

1. What is the kinetic energy of a 25 kg object moving at a velocity of 5.0 m/s?

2. What is the gravitational potential energy of a 1.50 x 102 kg object suspended 6.0 m above the ground?

3. Justin Thyme is traveling down Lake Avenue at 32.8 m/s in his 1.51 x 103 kg 1992 Camaro. He spots a police car with a radar gun and quickly slows down to a legal speed of 20.1 m/s.

a) Determine the car's change in kinetic energy. b) How much work was done on the car to slow it down to 20.1 m/s?

4. An 85 kg object has 2.16 x 102 J of kinetic energy. What is the object's velocity?

5. How much work is required to stop a car of mass 100.0 kg moving at a velocity of 25.0 m/s?

6. A 43 kg object is hanging from a rope. If the object has 3.16 x 103 J of gravitational potential energy, how high above the ground is it?

7. What is the kinetic energy of a 152 g object moving at a velocity of 34 km/h east?

8. A bicycle has a kinetic energy of 124 J. What kinetic energy would the bicycle have if it had:

a) twice the mass and was moving at the same speed? b) the same mass and was moving with twice the speed? c) one-half the mass and was moving with twice the speed? d) the same mass and was moving with one-half the speed? e) three times the mass and was moving with one-half the speed?

9. A 2.50 x 102 N object has 1.13 x 103 J of kinetic energy. What is its velocity?

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10. A 1.0 kg book is dropped from a height of 3.0 m. What is the book's gravitational potential energy when it reaches the floor?

11. A 1.2 kg javelin is thrown at a velocity of 28 m/s. How much force does the athlete exert on the javelin over a throwing distance of 1.5 m?

12. The graph below shows a ball rolling from A to G.

a) At what position does the ball have its greatest amount of kinetic energy?

b) At which position does the ball have its greatest amount of gravitational potential energy?

c) At which position does the ball have its least amount of gravitational potential energy?

13. You do 2.0 J of positive work when you lift a 182 g apple above the ground. What is the apple's gravitational potential energy at its new height?

14. A 2.0 kg object is dropped from a height of 30.0 m. What is the object's kinetic energy and its gravitational potential energy after it free falls for 2.0 s?

Answers

1. 3.1 x 102 J 6. 7.5 m 10. 0J

2. 8.8 x 103J 7. 6.8 J 11. 6.3 x 102N

3. a) -5.07 x 105J 8. a) 248 J 12. a) D b) 496 J b) A

b) -5.07 x 105J c ) 248 J d ) 31 .0 J

c) D

4. 2.3 m/s e) 93.0 J 13. 2.0 J

5. -3.13 x 104J 9. 9.41 m/s 14. KE: 3.8 x 102 J; GPE: 2.0 x 102J

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Mechanics: Work, Energy and Power Worksheet Name:

Work Questions:

1. A tugboat pulls a ship with a constant net horizontal force of 5.00 x 103 N and causes the ship to move through a harbor. How much work is done on the ship if it moves a distance of 3.00 km?

2. A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25° downward from the horizontal. Find the work done by the shopper on the cart as the shopper moves along a 50.0 m length of aisle.

3. If 2.0 J of work is done in raising a 180 g apple, how far is it lifted?

4. For each of the following cases, indicate whether the work done on the second object in each example will have a positive or negative value.

a. The road exerts a friction force on a speeding car skidding to a stop.

b. A rope exerts a force on a bucket as the bucket is raised up a well.

c. Air exerts a force on a parachute as the parachutist falls to Earth.

Kinetic Energy Questions:

5. What is the speed of a 0.145 kg baseball if its kinetic energy is 109 J?

6. Two 3.0 g bullets are fired with speeds of 40.0 m/s and 80.0 m/s respectively. What are their kinetic energies? Which bullet has more kinetic energy? What is the ratio of their kinetic energies?

7. A car has a kinetic energy of 4.32 x 105 J when traveling at a speed of 23 m/s. What is its mass? Work-Kinetic Energy Theorem Questions:

8. A student wearing frictionless roller skates on a horizontal surface is pushed by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J?

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9. A 2.1 x 103 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0° with the horizontal. An average friction force of 4.0 x 103 N impedes the car’s motion so that the car’s speed at the bottom of the driveway is 3.8 m/s. What was the length of the driveway?

10. A 75 kg bobsled is pushed along a horizontal surface by two athletes. After the bobsled is pushed a distance of 4.5 m starting from rest, its speed is 6.0 m/s. Find the magnitude of the net force on the bobsled.

11. A 755 N diver drops from a board 10.0 m above the water’s surface. Find the diver’s speed 5.00 m above the water’s surface. Then find the diver’s speed just before striking the water.

12. If the diver in problem 11 leaves the board with an initial upward speed of 2.00 m/s, find the diver’s speed when striking the water.

13. A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1.9 m/s. What is the initial height of the bob?

Power Questions:

14. A 1.0 x 103 kg elevator carries a maximum load of 800.0 kg. A constant frictional force of 4.0 x 103 N retards the elevator’s upward motion. What minimum power, in kilowatts, must the motor deliver to lift the fully loaded elevator at a constant speed of 3.00 m/s?

15. A rain cloud contains 2.66 x 107 kg of water vapor. How long would it take for a 2.00 kW pump to raise the same amount of water to the cloud’s altitude of 2.00 km?

16. A 1.50 x 103 kg car accelerates uniformly from rest to 10.0 m/s in 3.00 s.

a. What is the work done on the car in this time interval? b. What is the power delivered by the engine in this time interval?

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