Work, Power, and Energy:

Work (W) is the product of a force on an object (force is constant and non-changing) and the object moves in the direction of the force. The unit for Work is joules (J).

Power (P) is the rate at which work is done. The unit for Power is watts (W).

Energy is the ability to do work, and can many different forms, including heat, mechanical, and chemical. The two main classes of energy are Kinetic energy (KE) and Potential energy (PE).The unit for Energy is joules (J).Conservation of energy is the idea that energy is never lost, it simply changes form. The simplest example of this is Kinetic Energy being transformed into Potential Energy (and vice versa).The Work-Energy Theorem states that the Work done on an object is equal to its change in Kinetic Energy.

Objectives:

• To define and calculate the work done by a force.• To utilize the Work-Energy Theorem and interpret a Force vs. Displacement

graph.• To utilize the Power output of a system.• To calculate the Kinetic and Gravitational Potential Energy.• To solve problems using the law of conservation of Energy.• To analyze systems and solve problems involving springs.

Work, Power, and Energy Formulas:

𝑊𝑊 = 𝐹𝐹𝐹𝐹

𝑊𝑊 = 𝛥𝛥𝛥𝛥𝛥𝛥 = 𝛥𝛥𝛥𝛥 − 𝛥𝛥𝛥𝛥0

𝑃𝑃 =𝑊𝑊𝑡𝑡

=𝐹𝐹𝐹𝐹𝑡𝑡

= 𝐹𝐹𝐹𝐹

𝛥𝛥𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑃𝑃𝛥𝛥 + 𝛥𝛥𝛥𝛥 + 𝑄𝑄

𝑃𝑃𝛥𝛥𝑆𝑆 =12𝑘𝑘𝑥𝑥2

𝛥𝛥𝑃𝑃𝛥𝛥 = 𝑚𝑚𝑚𝑚𝛥𝛥ℎ

𝛥𝛥𝛥𝛥 =12𝑚𝑚𝐹𝐹2

Concepts to Watch Out For:

• Work is only done when an object moves in the same plane as the forceapplied.

• No work is done if a force is applied perpendicular to the displacement.• When force is parallel (0o) to the direction of motion, use W=Fd• When force is applied at an angle, work is found using either the vertical or

horizontal component of the displacement, depending on direction of theobject.

• Power is a scalar quantity.• If work is positive, Kinetic Energy will increase (and vice versa)• All moving objects must have some amount of Kinetic Energy• If an object is at rest, it has no Kinetic Energy• Other potential energies include gravitational potential and spring potential• If friction is present energy is lost to internal energy

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The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

PHYSICAL SETTING

PHYSICSWork / Power / Energy NOTES:

Notice. . .

A scientific or graphing calculator, a centimeter ruler, a protractor, and a copy of the 2002Edition Reference Tables for Physical Setting/Physics, which you may need to answer somequestions in this examination, must be available for your use while taking this examination.

The use of any communications device is strictly prohibited when taking thisexamination. If you use any communications device, no matter how briefly, yourexamination will be invalidated and no score will be calculated for you.

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

PS/PHYSICSPS/PHYSICS

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1 The spring in a scale in the produce department of a supermarket stretches 0.025 meter when a

watermelon weighing 1.0 × 102 newtons is placed on the scale. The spring constant for this spring is (1) 3.2 × 105 N/m (3) 2.5 N/m(2) 4.0 × 103 N/m (4) 3.1 × 10–2 N/m

Part AAnswer all questions in this part.

Directions (1–18): For each statement or question, write on the separate answer sheet the number of the word or expression that, of those given, best completes the statement or answers the question.

2 As shown in the diagram below, a student exertsan average force of 600. newtons on a rope to lifta 50.0-kilogram crate a vertical distance of 3.00 meters.

Compared to the work done by the student, thegravitational potential energy gained by the crate is(1) exactly the same(2) 330 J less

(3) 330 J more(4) 150 J more

m = 50.0 kg

d = 3.00 m

F= 60

F= 6

5 A 1.0-kilogram book resting on the ground ismoved 1.0 meter at various angles relative to thehorizontal. In which direction does the 1.0-meterdisplacement produce the greatest increase in thebook’s gravitational potential energy?

Ground

0°

( 1 )

Ground

45°

( 3 )

Ground

20°

( 2 )

Ground

90°

( 4 )

Book Book

Book Book

3 A 95-kilogram student climbs 4.0 meters up arope in 3.0 seconds. What is the power output ofthe student?(1) 1.3 × 102 W(2) 3.8 × 102 W

(3) 1.2 × 103 W(4) 3.7 × 103 W

6 A person weighing 6.0 × 102 newtons rides anelevator upward at an average speed of 3.0 metersper second for 5.0 seconds. How much does thisperson’s gravitational potential energy increaseas a result of this ride?(1) 3.6 × 102 J(2) 1.8 × 103 J

(3) 3.0 × 103 J(4) 9.0 × 103 J

7 The potential energy stored in a compressedspring is to the change in the spring’s length as thekinetic energy of a moving body is to the body’s(1) speed(2) mass

(3) radius(4) acceleration

4 A 2.0-kilogram block sliding down a ramp froma height of 3.0 meters above the ground reachesthe ground with a kinetic energy of 50. joules.The total work done by friction on the block as itslides down the ramp is approximately(1) 6 J(2) 9 J

(3) 18 J(4) 44 J

8 During an emergency stop, a 1.5 × 103-kilogramcar lost a total of 3.0 × 105 joules of kineticenergy. What was the speed of the car at themoment the brakes were applied?(1) 10. m/s(2) 14 m/s

(3) 20. m/s(4) 25 m/s

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Note that question 9 has only three choices.

9 The diagram below shows an ideal simplependulum.

As the pendulum swings from position A to posi-tion B, what happens to its total mechanicalenergy? [Neglect friction.](1) It decreases.(2) It increases.(3) It remains the same.

AB

10 What is the power output of an electric motorthat lifts a 2.0-kilogram block 15 metersvertically in 6.0 seconds?(1) 5.0 J(2) 5.0 W

(3) 49 J(4) 49 W

11 Which statement describes the kinetic energy and total mechanical energy of a block as it is pulled at

constant speed up an incline?

(1) Kinetic energy decreases and total mechanicalenergy increases.

(2) Kinetic energy decreases and total mechanicalenergy remains the same.

(3) Kinetic energy remains the same and totalmechanical energy increases.

(4) Kinetic energy remains the same and totalmechanical energy remains the same.

13 A car uses its brakes to stop on a level road.During this process, there must be a conversionof kinetic energy into(1) light energy(2) nuclear energy(3) gravitational potential energy(4) internal energy

14 How much work is done by the force lifting a 0.1-kilogram hamburger vertically upward atconstant velocity 0.3 meter from a table?(1) 0.03 J(2) 0.1 J

(3) 0.3 J(4) 0.4 J

(85)

12 How much work is required to move 3.0 coulombs of electric charge a distance of0.010 meter through a potential difference of 9.0 volts?(1) 2.7 × 103 J(2) 27 J

(3) 3.0 J(4) 3.0 × 10−2 J

15 Two pieces of flint rock produce a visible sparkwhen they are struck together. During thisprocess, mechanical energy is converted into(1) nuclear energy and electromagnetic energy(2) internal energy and nuclear energy(3) electromagnetic energy and internal energy(4) elastic potential energy and nuclear energy

16 When a mass is placed on a spring with a springconstant of 60.0 newtons per meter, the spring iscompressed 0.500 meter. How much energy isstored in the spring?(1) 60.0 J(2) 30.0 J

(3) 15.0 J(4) 7.50 J

17 A vertical spring has a spring constant of 100. newtons per meter. When an object isattached to the bottom of the spring, the springchanges from its unstretched length of 0.50 meterto a length of 0.65 meter. The magnitude of theweight of the attached object is(1) 1.1 N(2) 15 N

(3) 50. N(4) 65 N

18 A spring gains 2.34 joules of elastic potentialenergy as it is compressed 0.250 meter from itsequilibrium position. What is the spring constantof this spring?(1) 9.36 N/m(2) 18.7 N/m

(3) 37.4 N/m(4) 74.9 N/m

with a spring constant of 30.0 newtons per meter,the spring is compressed 0.500 meter. Howmuch energy is stored in the spring?(1) 3.75 J(2) 7.50 J

(3) 15.0 J(4) 30.0 J

Part B–1

Answer all questions in this part.

Directions (19-35): For each statement or question, write on the separate answer sheet the number of the word or expression that, of those given, best completes the statement or answers the question.

19 When a 1.53-kilogram mass is placed on a spring

20 Two elevators, A and B, move at constant speed. Elevator B moves with twice the speed of elevator A. Elevator B weighs twice as much as elevator A. Compared to the power needed to lift elevator A, the power needed to lift elevator B is(1) the same(2) twice as great

(3) half as great(4) four times as great

22 What is the maximum height to which a motorhaving a power rating of 20.4 watts can lift a 5.00-kilogram stone vertically in 10.0 seconds?(1) 0.0416 m(2) 0.408 m

(3) 4.16 m(4) 40.8 m

42 Which graph represents the relationship between the gravitational potential energy (GPE) of an object nearthe surface of Earth and its height above the surface of Earth?

( 1 )

GPE

Height

( 2 )

GPE

Height

( 4 )

GPE

Height

( 3 )

GPE

Height

42 Which graph represents the relationship between the gravitational potential energy (GPE) of an object nearthe surface of Earth and its height above the surface of Earth?

( 1 )

GPE

Height

( 2 )

GPE

Height

( 4 )

GPE

Height

( 3 )

GPE

Height

21 The graph below represents the relationshipbetween the force applied to a spring and springelongation for four different springs.

Elongation

Which spring has the greatest spring constant?(1) A(2) B

(3) C(4) D

Force vs. Elongation

Forc

e

A

B

C

D

23 A pendulum is made from a 7.50-kilogram mass

(1) 11 J(2) 94 J

(3) 110 J(4) 920 J

attached to a rope connected to the ceiling of a gymnasium. The mass is pushed to the side until it is at position A, 1.5 meters higher than its equilibrium position. After it is released from rest at position A, the pendulum moves freely back and forth between positions A and B, as shown in the diagram below.

What is the total amount of kinetic energy that the mass has as it swings freely through its equilibrium position? [Neglect friction.]

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42 A 25-gram paper cup falls from rest off the edgeof a tabletop 0.90 meter above the floor. If thecup has 0.20 joule of kinetic energy when it hitsthe floor, what is the total amount of energyconverted into internal (thermal) energy duringthe cup’s fall?(1) 0.02 J(2) 0.22 J

(3) 2.2 J(4) 220 J

24 Which graph represents the relationship between the gravitational potential energy (GPE) of an object nearthe surface of Earth and its height above the surface of Earth?

25 A box is pushed to the right with a varying horizontal force. The graph below represents the relationshipbetween the applied force and the distance the box moves.

(1) 9.0 J(2) 18 J

(3) 27 J(4) 36 J

9.0

6.0

3.0

03.0 6.0

Forc

e (N

)

Force vs. Distance

( 1 )

GPE

Height

(87)

26 A shopping cart slows as it moves along a level floor. Which statement describes the energies of the cart?(1) The kinetic energy increases and the gravitational potential energy remains the same.(2) The kinetic energy increases and the gravitational potential energy decreases.(3) The kinetic energy decreases and the gravitational potential energy remains the same.(4) The kinetic energy decreases and the gravitational potential energy increases.

27 In the diagram below, an ideal pendulum released from position A swings freely to position B.

A B

As the pendulum swings from A to B, its total mechanical energy(1) decreases, then increases(2) increases, only

(3) increases, then decreases(4) remains the same

Distance (m)

What is the total work done in moving the box 6.0 meters?

28 If a motor lifts a 400.-kilogram mass a verticaldistance of 10. meters in 8.0 seconds, theminimum power generated by the motor is(1) 3.2 × 102 W(2) 5.0 × 102 W

(3) ×4.9 103 W(4) ×3.2 104 W

32 Which graph represents the relationship between the kinetic energy and the speed of a freely falling object?

Speed

Kin

etic

En

erg

y

( 1 )

Speed

Kin

etic

En

erg

y

( 2 )

Speed

Kin

etic

En

erg

y

( 3 )

Speed

( 4 )

Kin

etic

En

erg

y

29 Which graph best represents an object inequilibrium moving in a straight line?

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!�

#��������

��

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30 Which combination of fundamental units can beused to express the amount of work done on anobject?(1) kg•m/s(2) kg•m/s2

(3) kg•m2/s2

(4) kg•m2/s3

31 Which graph best represents the relationshipbetween the potential energy stored in a springand the change in the spring’s length from itsequilibrium position?

( 1 )

Po

ten

tial

En

erg

y

Changein Length

Po

ten

tial

En

erg

y

( 2 )

Changein Length

Po

ten

tial

En

erg

y

( 3 )

Changein Length

Po

ten

tial

En

erg

y( 4 )

Changein Length

(88)

35 The graph below represents the work done against gravity by a student as she walks up a flight of stairs atconstant speed.

Compared to the power generated by the student after 2.0 seconds, the power generated by the studentafter 4.0 seconds is (1) the same(2) twice as great

(3) half as great(4) four times as great

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34 The graph below represents the relationshipbetween the force exerted on an elevator and thedistance the elevator is lifted.

Distance Lifted (m)

How much total work is done by the force inlifting the elevator from 0.0 m to 9.0 m?(1) 9.0 × 104 J(2) 1.2 × 105 J

(3) 1.5 × 105 J(4) 1.8 × 105 J

2.0 × 104

1.0 × 104

3.0 6.0 9.0

Fo

rce

Exe

rted

(N

)

0.0

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�

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33 Which graph best represents the greatest amount of work?

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(89)

[9]

Part B–2

Answer all questions in this part.

Directions (21–27): Record your answers in the spaces provided in your answer booklet.

Base your answers to questions 36 through 38 on the information and diagram below.

A 10.-kilogram block is pushed across a floor by a horizontal force of 50. newtons. Theblock moves from point A to point B in 3.0 seconds.

36 Using a scale of 1.0 centimeter = 1.0 meter, determine the magnitude of the displacement of the block asit moves from point A to point B. [1]

37-38 Calculate the power required to move the block from point A to point B in 3.0 seconds. [Show all work,including the equation and substitution with units.] [2]

10.-kgblock

F = 50. N

A B

Base your answers to questions 39 through 41 on the information below.

39 Determine the spring constant of the spring. [1]

40-41 Calculate the energy stored in the spring when the elongation is 0.30 meter. [Show all work, includingthe equation and substitution with units.] [2]

8.00

4.00

0.000.00 0.40

A student produced various elongations of a spring by applying a series of forces to the spring.The graph below represents the relationship between the applied force and the elongation of thespring.

Force vs. Elongation

0.20Elongation (m)

Forc

e (N

)

(90)

42-43 Calculate the kinetic energy of a particle with amass of 3.34 × 10–27 kilogram and a speed of 2.89 × 105 meters per second. [Show all work,including the equation and substitution withunits.] [2]

(91)

44-45 A 3.00-newton force causes a spring to stretch 60.0 centimeters. Calculate the spring constant of thisspring. [Show all work, including the equation and substitution with units.] [2]

46 Regardless of the method used to generate electrical energy, the amount of energy provided by thesource is always greater than the amount of electrical energy produced. Explain why there is adifference between the amount of energy provided by the source and the amount of electrical energyproduced. [1]

47-48 Calculate the minimum power output of an electric motor that lifts a 1.30 × 104-newton elevator carvertically upward at a constant speed of 1.50 meters per second. [Show all work, including the equation and substitution with units.] [2]

Part C

Answer all questions in this part. Directions (49–72): Record your answers in the spaces provided in your answer booklet.

Base your answers to questions 49 through 53 on the information and diagram below.

A 250.-kilogram car is initially at rest at point A on a roller coaster track. The car carriesa 75-kilogram passenger and is 20. meters above the ground at point A. [Neglect friction.]

49-50 Calculate the total gravitational potential energy, relative to the ground, of the car and the passenger atpoint A. [Show all work, including the equation and substitution with units.] [2]

51-52 Calculate the speed of the car and passenger at point B. [Show all work, including the equation and sub-stitution with units.] [2]

53 Compare the total mechanical energy of the car and passenger at points A, B, and C. [1]

Ground

20.m

A

B

75 kg250. kg

C

A runner accelerates uniformly from rest to a speed of 8.00 meters per second. The kineticenergy of the runner was determined at 2.00-meter-per-second intervals and recorded in the datatable below.

Data Table

Directions (54–55): Using the information in the data table, construct a graph on the grid in your answer booklet following the directions below.

54 Plot the data points for kinetic energy of the runner versus his speed. [1]

55 Draw the line or curve of best fit. [1]

56-57 Calculate the mass of the runner. [Show all work, including the equation and substitution with units.] [2]

58 A soccer player having less mass than the runner also accelerates uniformly from rest to a speed of8.00 meters per second. Compare the kinetic energy of the less massive soccer player to the kineticenergy of the more massive runner when both are traveling at the same speed. [1]

Speed (m/s) Kinetic Energy (J)

0.00 0.00

2.00 140.

4.00 560.

6.00 1260

8.00 2240

Base your answers to questions 54 through 58 on the information below.

(92)

Base your answers to questions 59 through 62 on the information below.

A vertically hung spring has a spring constant of 150. newtons per meter. A 2.00-kilogram mass is suspended from the spring and allowed to come to rest.

59-60 Calculate the elongation of the spring produced by the suspended 2.00-kilogram mass. [Show allwork, including the equation and substitution with units.] [2]

61-62 Calculate the total elastic potential energy stored in the spring due to the suspended2.00-kilogram mass. [Show all work, including the equation and substitution with units.] [2]

Directions (63-67): Record your answers in the spaces provided in your answer booklet.

Base your answers to questions 63 through 67 on the information and diagram below.

A 3.0-kilogram object is placed on a frictionless track at point A and released fromrest. (Assume the gravitational potential energy of the system to be zero at point C.)

63-64 Calculate the gravitational potential energy of the object at point A. [Show all work, including the equationand substitution with units.] [2]

65-66 Calculate the kinetic energy of the object at point B. [Show all work, including the equation and substitu-tion with units.] [2]

67 Which letter represents the farthest point on the track that the object will reach? [1]

A

B

C

D

E

F

G

H Im = 3.0 kg4.0 m

3.0 m

2.0 m

1.0 m

0.0 m

(93)

Base your answers to questions 68 through 72 on the information and diagram below.

A 30.4-newton force is used to slide a 40.0-newton crate a distance of 6.00 meters at constantspeed along an incline to a vertical height of 3.00 meters.

68 Determine the total work done by the 30.4-newton force in sliding the crate along the incline. [1]

69-70 Calculate the total increase in the gravitational potential energy of the crate after it has slid 6.00 meters along the incline. [Show all work, including the equation and substitution with units.] [2]

71 State what happens to the kinetic energy of the crate as it slides along the incline. [1]

72 State what happens to the internal energy of the crate as it slides along the incline. [1]

30.°

F = 30.4 N6.00 m

3.00 m

40.0 N

(94)

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

PHYSICAL SETTING PHYSICS

ANSWER SHEET

Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: ■■ Male ■■ Female Grade . . . . . . . . . . . .

Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Record your answers to Part A and Part B–1 on this answer sheet.

Write your answers to Part B–2 and Part C in your answer booklet.

The declaration below should be signed when you have completed the examination.

I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior tothe examination and that I have neither given nor received assistance in answering any of the questions during the examination.

Signature

Tear

Her

eTe

ar H

ere

Part A

1 . . . . . . . . . . . . 13 . . . . . . . . . . . .

7 . . . . . . . . . . . .

8 . . . . . . . . . . . .

9 . . . . . . . . . . . .

10 . . . . . . . . . . . .

11 . . . . . . . . . . . .

12 . . . . . . . . . . . .

Part B–1

19 . . . . . . . . . . . .

20 . . . . . . . . . . . .

21 . . . . . . . . . . . .

22 . . . . . . . . . . . .

23 . . . . . . . . . . . .

Part A Score Part B–1 Score

24 . . . . . . . . . . . .

25 . . . . . . . . . . . .

(95)

26 . . . . . . . . . . . .

27 . . . . . . . . . . . .

2 . . . . . . . . . . . . 14 . . . . . . . . . . . .

3 . . . . . . . . . . . . 15 . . . . . . . . . . . .

4 . . . . . . . . . . . . 16 . . . . . . . . . . . .

5 . . . . . . . . . . . . 17 . . . . . . . . . . . .

6 . . . . . . . . . . . . 18 . . . . . . . . . . . .

28 . . . . . . . . . . . .

29 . . . . . . . . . . . .

30 . . . . . . . . . . . .

31 . . . . . . . . . . . .

32 . . . . . . . . . . . .

33 . . . . . . . . . . . .

34 . . . . . . . . . . . .

35 . . . . . . . . . . . .

Maximum Student’sPart Score Score

A 13

B–1 17

B–2 8

C 19

Total Written Test Score(Maximum Raw Score: 85)

Final Score(From Conversion Chart)

Raters’ Initials:

Rater 1 . . . . . . . . . . Rater 2 . . . . . . . . . .

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

PHYSICAL SETTINGPHYSICS

ANSWER BOOKLET

Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: ■■ Female

Teacher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grade . . . . . . . . .

Answer all questions in Part B–2 and Part C. Record your answers in thisbooklet.

■■ Male

Part B–2

36 __________________ m

37-38

38

For Raters Only

36

37

39 _______________________ N/m

40-4140

39

41

42-4342

43

(96)

Part B–2For Raters

Only

48

44

45

46

47-48

44-45

46 _____________________________________________________________________________

____________________________________________________________________________

____________________________________________________________________________

47

(97)

Part C

49-50

51-52

53 ____________________________________________

____________________________________________

____________________________________________

____________________________________________

51

49

50

52

53

(98)

54-55

56-57

58

2500.

2000.

1500.

1000.

500.

0

Kin

etic

En

erg

y (J

)

Kinetic Energy vs. Speed

Speed (m/s)0.00 2.00 4.00 6.00 8.00 10.00

56

54

55

57

58

(99)

For Raters Only

59-60

61-62

61

62

59

60

(100)

63-64

65-66

67 ______________

65

66

63

64

67

(101)

68 _______________________ J

69-70

71

72

68

69

70

71

72