CHAPTER 6: IN AN ISOLATED SYSTEM, ENERGY IS TRANSFERRED FROM ONE OBJECT TO ANOTHER WHENEVER WORK IS DONE

Size: px
Start display at page:

Download "CHAPTER 6: IN AN ISOLATED SYSTEM, ENERGY IS TRANSFERRED FROM ONE OBJECT TO ANOTHER WHENEVER WORK IS DONE"

Transcription

1 CHAPTER 6: IN AN ISOLATED SYSTEM, ENERGY IS TRANSFERRED FROM ONE OBJECT TO ANOTHER WHENEVER WORK IS DONE 6.1 Work and Energy In science, work is done when a force acts over a displacement; energy is transferred. Both the force and displacement are necessary for work to be done, and the force must act in the direction of the displacement. The simplest formula for work is W = F d, with force in newtons (N), displacement in meters (m) and work in joules (J.) Because energy is transferred when work is done, it should seem reasonable that the units for work are the same as the units for energy. If the force doing the work acts at an angle to the resulting displacement, only the force component in the displacement direction does work. This gives the more general formula for work, with θ being the angle between the force and displacement: W = (F cos θ) d EXERCISE A student lifts a box with a weight of 100 N from the floor (a distance of m) and carries it horizontally a distance of 4.50 m across a room. Where is work done, in the lifting of the box, the carrying of the box, or both? How much work is done in total? (85.0 J) 2. Describe a situation where a force acts on an object but no work is done. Describe a second situation where an object undergoes a displacement but no work is done. 3. The sketch shows a wagon being that is pulled across a horizontal driveway by a child. The child pulls the handle of the wagon with a force of 55.0 N to overcome the force of kinetic friction acting against the motion. If the wagon moves a distance of 15.0 m, find the work done. 42Þ 46.0 (573 J) PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 1

2 4. When an object is lifted vertically against the force of gravity, work is done against gravity. If the object is released and allowed to fall, gravity does work on the object to increase its velocity and its kinetic energy (energy of motion.) Clearly, lifting an object against gravity stores energy in some form. Name this type of stored energy; state the equation including units. 5. Find the E p when a box with a mass of 25.0 kg is lifted from ground level to a height of 1.50 m. 6. Consider the sketch to the right. Calculate E p when the box shown is lifted from the ground level (II) to level III. Calculate the E p when the box is lifted from level III to level IV. Finally, calculate the E p when the box is lifted directly from the ground level to level IV. Does the total change in E p from ground level to level IV change if you go from ground level to level III and then to level IV? (368 J) 15.0 kg box IV 5.00 m 7.00 m III (736 J; 1.03 kj; 1.77 kj; 1.77 kj) GROUND II 7. Again consider the sketch to the right. What E p will the box have at level IV, measured with respect to level I? ( Measured with respect to identifies the starting or reference point.) What I E p will the box have at level III, measured with respect to level I? How does the change in E p between levels III and IV compare to the value you found in the previous question? Does it matter what you use as a reference point when calculating changes in E p? 3.00 m (2.21 kj; 1.18 kj; 1.03 kj) PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 2

3 Hooke s Law To stretch or compress a spring, force is required; because this force acts through a distance, work is done. For a linear spring (also called a Hooke s Law spring), proportionally more force is required to stretch a spring a greater distance. For example, as sketched at right, if a particular spring stretches 2.0 cm (from its normal length) when a force of 5.0 N is applied, it should stretch to 4.0 cm if the force is increased to 10 N, and to 6.0 cm for a force of 15 N cm 4.0 cm 6.0 cm 5.0 N Generally, the force needed to stretch a spring depends on how strong the spring is, and how far it 10 N is stretched. The strength of a spring is given by the spring constant (or elastic constant) k the value 15 N of k ranges from around 2 N/m for the spring in a retractable pen, to around 150 N/m for the spring cable at a bungie jump, to 2500 N/m for the suspension springs in a car. The relationship between force F (in newtons), stretch x (in meters) and constant k (in N/m) is given by Hooke s Law: F = kx When work is done to stretch a spring, energy is stored. This stored energy is called elastic potential energy. To calculate the stored energy in the spring above when it is stretched 6.0 cm, note that the average force needed between zero stretch and 6.0 cm is or 7.5 N; this average force moved the end of the 2 spring a distance of 6.0 cm (0.060 m.) So the work done in stretching the spring (and therefore the energy stored) is equal to (7.5)(0.060) or 0.45 J. Generally, for any spring, the elastic potential energy can be found in a similar manner. Work done = energy stored Energy stored = average force times stretch For a spring with constant k and stretch x from zero, the force at this stretch is given by F = kx. At zero stretch, the force is zero. So the work done (elastic potential energy stored) is: This is the average force; zero force at zero stretch added to force kx at stretch x, divided by two E p = 0 + kx x 2 E p = 1 2 kx2 This is x, or how far the force acts (the displacement in the work equation) EXAMPLE A spring with an elastic constant of 12.0 N/m is stretched an amount of 10.0 cm. How much force is needed to do this, and how much elastic potential energy is stored in the stretched spring? Use F = kx to find the force: F = (12.0)(0.100) F = 1.20 N Use E p = 1 2 kx2 to find the stored energy: Ep = 1 2 (12.0)(0.100)2 Ep = J PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 3

4 8. A spring is 25.0 cm long. When a force of 40.0 N is applied to it, the spring stretches by 20.0 cm. What is the elastic constant k of the spring? (200 N/m) 9. A spring-operated ping-pong ball launcher requires a force of 24.0 N to fully compress the spring, which has an elastic constant of 12.0 N/m. How far does the spring compress, and how much elastic potential energy is stored in the compressed spring? (66.7 cm; 2.67 J) 10. State the formula for translational kinetic energy (E k ), with correct units. What other form of kinetic energy is there? 11. Find the kinetic energy of a cyclist riding at 25.0 km/h, if the rider and his bicycle have a total mass of 86.0 kg. (2.07 kj) 12. An arrow in flight has a kinetic energy of 170 J. If the arrow has a mass of 65.0 g, what is its speed? (72.3 m/s) 13. A 1920 kg car brakes from a speed of 100 km/h to 50.0 km/h. How much does its kinetic energy change? Where do you suppose this energy goes? (556 kj) PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 4

5 6.2 Mechanical Energy EXERCISE Name the three forms of energy referred to by mechanical energy. 2. A runner with a mass of 78.0 kg follows a horizontal trail along a cliff overlooking a lake. The trail is 13.0 m above the lake, and the runner is moving at 4.50 m/s. What is the runner s total mechanical energy? (The lake is the reference point.) (10.7 kj) To change the total mechanical energy of an object, it must lose energy by doing work on something, or something must do work on it to increase its energy. The amount the object s energy changes must equal the net work that is done. This is a law of energy conservation called the work-energy theorem, and can be stated as: The net work done on a system is equal to the sum of the changes in the potential energy (including gravitational and elastic) and in the kinetic energy of the system:s W = E k + E p. EXAMPLE A 2400 kg truck traveling at 18.0 m/s (about 65 km/h) reaches the bottom of a steep hill. As it moves up the hill, the truck s speed drops, finally to 11.1 m/s (about 40 km/h) at it reaches the top of the 35.0 m high hill. How much useful work does the truck s engine do from the bottom to the top of the hill? In driving up the hill, the truck gains gravitational potential energy, but loses kinetic energy. The total of these changes will be the useful work done by the engine. E k = 1 2 mv2 E k1 = 1 2 (2400)(18.0)2 E k2 = 1 2 (2400)(11.1)2 E p = (2400)(9.81)(35.0) E p = mgh E k1 = J E k2 = J E p = J E k = E k2 - E k1 = J W = E k + E p W = W = J W = +583 kj 3. A cyclist traveling on a horizontal roadway at 35.0 km/h brakes to a stop. If the cyclist and her bike have a total mass of 73.0 kg, how much work is done by forces of friction? (3.45 kj) PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 5

6 6.3 Mechanical Energy in Isolated and Non-isolated Systems In physics, one or more objects that have and exchange amounts of energy form what is called a system. If a system is defined or designed so that no mechanical energy can be exchanged with any other object outside the system, it is said to be an isolated system. (Recall from Science 10 that in a closed system nothing, no matter nor any form of energy, can be exchanged with the outside.) Isolated systems are frictionless (because friction would generate heat, which could leave the system) and have no net external forces acting on any object in the system. In such a carefully-defined isolated system, total mechanical energy is constant. That is, within the system, mechanical energy can be transferred from one form to another, or traded among the objects in the system, but the total number of joules of kinetic, gravitational potential and elastic potential remains the same. This is the law of conservation of mechanical energy. It s somewhat the same as the work-energy theorem above, but describes energy changes occurring within a system, rather than connecting work done by outside forces to changes in energy. Many common forces (like kinetic friction) cause mechanical energy to be transferred to another form, typically heat. Such forces are called non-conservative forces. Other forces (like the force of gravity) can act without changing the overall mechanical energy of a system; these are conservative forces and they are associated with isolated systems. (Note that a system that includes gravity must include the earth as one of the objects in the system.) In the real word, just about any system has some non-conservative forces that act, and is not completely isolated from its surroundings. To allow us to solve problems using the law of mechanical energy conservation, we often assume a system is isolated and has only conservative forces and we recognize that our answers might be slightly different if we accounted for energy losses due to friction, etc. Such assumptions are often indicated by the phrase friction can be neglected. Real systems involving non-conservative forces can also be analyzed. For example, if a known amount of energy is lost through frictional forces, the total amount of mechanical energy in the system at the start can be reduced by this amount, before equating total energy before to total energy after and solving for an unknown. In some problems, the amount of energy lost to friction may be the actual unknown. In summary, to solve energy conservation problems: Calculate the total amount of mechanical energy (kinetic plus gravitational potential and spring potential) at the start, before anything happens to objects in the system If a known amount of energy is lost through friction, subtract this value from the total at the start; if an unknown amount is lost and this is what you are trying to find, include a variable for this value in the energy equation (i.e., write E f on the before or starting side) Calculate the total amount of mechanical energy after something occurs Equate the two total energy values: energy before equals energy after (remember, mechanical energy is conserved) and solve for the unknown EXAMPLES 1. A car with a mass of 1250 kg is parked at the top of a 25.0 m long driveway. The end of the driveway where the car is parked is m above the level of the street. Due to a mechanical malfunction, the car slips out of park, rolls down the driveway and across the street. Friction can be neglected. How fast is the car rolling as it crosses the street? At the start, the car has only gravitational potential energy. This will be the total before something (in this case, rolling down the driveway) occurs. When the car reaches the level street, only kinetic energy remains. This will be the total energy after. Start: E T = E p E p = mgh E p = (1250)(9.81)(0.850) E p = J Across driveway: E T = E k E k = 1 2 mv2 E k = 1 2 (1250)v2 Make the two totals equal and solve: = 1 2 (1250)v2 v = m/s v = 4.08 m/s PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 6

7 2. An arrow of mass 85.0 g is fired straight upwards with an initial speed of 48.0 m/s. If friction is neglected, find how high it goes. Equate the kinetic energy at the start (before) to the gravitational potential energy at the highest point (after remember that at the highest point, the arrow will have no kinetic energy why?) and solve for h. E k = 1 2 mv2 1 = E p = mgh 2 (0.0850)(48.0)2 = (0.085)(9.81)h h = m h = 117 m 3. The arrow in the previous question actually rises to a measured height of 76.0 m. How much energy is lost through air resistance (a kind of frictional force) as the arrow rises? How fast should the arrow be traveling after it falls back down to ground level? E k E f = E p 1 2 (0.0850)(48.0)2 E f = (0.085)(9.81)(75.0) E f = J E f = 35.4 J To find the speed on the way back down, note that the arrow will lose an additional J as it falls back to the ground. Use the highest point at 76.0 m as the start (before energy will all be gravitational potential energy) and calculate after at ground level (when energy less that lost to friction will all be kinetic energy.) E p E f = E k (0.085)(9.81)(75.0) (35.381) = 1 2 (0.0850)v2 v = m/s v = 25.3 m/s EXERCISE A flowerpot of mass 2.20 kg falls from a second floor window to the ground 7.50 m below. Friction can be neglected. How fast was the flowerpot traveling just before it hit the ground? (12.1 m/s) 2. A pendulum with a mass of 250 g is released from rest from a height of 10.0 cm above its lowest point. How fast will the pendulum be moving as it passes through the lowest point? (1.40 m/s) 3. A 5.00 g pellet is placed in the barrel of a toy gun and is propelled by a spring with a force constant of 50.0 N/m that has been compressed 20.0 cm and then released. Friction can be neglected. a) Calculate the maximum velocity of the pellet when it is fired horizontally. b) If the pellet is fired vertically, how high will it go? (20.0 m/s) PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 7

8 (20.4 m) c) If J of mechanical energy are lost from the system due to air resistance, how high will the pellet go? (13.3 m) 4. A frictionless roller coaster car arrives at point X at right with a speed of 1.60 m/s. The car plus occupants has a mass of 545 kg. Find the speed of the car as it passes point Y and point Z. X 33.5 m 26.0 m Z Y (25.7 m/s; 12.2 m/s) 5. The speed of the roller coaster car in the previous question is actually 9.40 m/s at point Z. How much energy is lost due to frictional forces between points X and Z? 6.4 Work and Power (16.7 kj) The same amount of energy can be transferred over a short or long amount of time. The rate of energy transfer is power; in SI, power is measured in watts (W.) One watt is a rate of energy transfer of one joule every second. Historically in the British system of measurement (still in common use in the United States, and also still found in Canada) the unit for power is the horsepower (HP.) These units can be converted using the equivalence 1.00 HP = 746 W. P(watts) = W(joules) time(seconds) or P(watts) = E(joules) time(seconds) ; P = E t EXERCISE 6.4 PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 8

9 1. The crane shown lifts a load of logs with a mass of 450 kg a vertical distance of 3.50 m in a time of 10.5 s. Find the power developed by the crane s engine in lifting the logs, in watts and horsepower. (1.47 kw; 1.97 HP) 2. A off-road truck with a total mass of 3250 kg travels at a constant speed from the bottom to the top of a hill in a time of 1.40 minutes. If the top of the hill is 22.5 m higher than the bottom, find the power of the truck s engine in watts and horsepower. (Note that non-conservative forces are acting in this problem; the actual work done by the engine and the power produced are definitely larger than the value you found.) (8.54 kw; 11.5 HP) 3. In question #2, suppose the truck started at the bottom of the hill with a speed of 7.00 m/s and reached the top with a speed of 13.6 m/s. Find the power produced by the truck in watts. (11.2 kw) 4. Two students helping a neighbor drag a small refrigerator on a pallet a horizontal distance of 21.5 m from the door of a house to the back of a truck. The total horizontal force the students exert is 855 N. a) If moving the refrigerator takes 3.50 minutes, how much power do the students generate? (87.5 W) b) The refrigerator has a mass of 44.0 kg. If the students lift the refrigerator from the pallet into the truck through a vertical distance of 75.0 cm, how much work do they do? If lifting the refrigerator takes 2.50 s, what power is generated? (324 J; 129 W) PHYSICS 20N NOTES AND OUTLINE QUESTIONS CHAPTER 6 REVISED JANUARY 08 PAGE 9

Chapter 6 Energy and Oscillations

Chapter 6 Energy and Oscillations Chapter 6 Energy and Oscillations Conservation of Energy In this chapter we will discuss one of the most important and fundamental principles in the universe. Energy is conserved. This means that in any

More information

2. What would happen to his acceleration if his speed were half? Energy The ability to do work

2. What would happen to his acceleration if his speed were half? Energy The ability to do work 1. A 40 kilogram boy is traveling around a carousel with radius 0.5 meters at a constant speed of 1.7 meters per second. Calculate his centripetal acceleration. 2. What would happen to his acceleration

More information

Work Done by a Constant Force

Work Done by a Constant Force Work and Energy Work Done by a Constant Force In physics, work is described by what is accomplished when a force acts on an object, and the object moves through a distance. The work done by a constant

More information

Chapter 6 Work, Energy, and Power. Copyright 2010 Pearson Education, Inc.

Chapter 6 Work, Energy, and Power. Copyright 2010 Pearson Education, Inc. Chapter 6 Work, Energy, and Power What Is Physics All About? Matter Energy Force Work Done by a Constant Force The definition of work, when the force is parallel to the displacement: W = Fs SI unit: newton-meter

More information

Review. Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91

Review. Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91 Review Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91 The unit of work is the A. Newton B. Watt C. Joule D. Meter E. Second 2/91 The unit of work is the A. Newton

More information

AP Physics 1 Work Energy and Power Practice Test Name

AP Physics 1 Work Energy and Power Practice Test Name AP Physics 1 Work Energy and Power Practice Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Two objects, one of mass m and the other

More information

Momentum, Impulse, Work, Energy, Power, and Conservation Laws

Momentum, Impulse, Work, Energy, Power, and Conservation Laws Momentum, Impulse, Work, Energy, Power, and Conservation Laws 1. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second.

More information

Period: Date: Review - UCM & Energy. Page 1. Base your answers to questions 1 and 2 on the information and diagram below.

Period: Date: Review - UCM & Energy. Page 1. Base your answers to questions 1 and 2 on the information and diagram below. Base your answers to questions 1 and 2 on the information and diagram below. The diagram shows the top view of a -kilogram student at point A on an amusement park ride. The ride spins the student in a

More information

Energy Storage and Transfer Model: Review Sheet

Energy Storage and Transfer Model: Review Sheet Name Energy Storage and Transfer Model: Review Sheet Date Pd 1. A softball (m = 180 g) traveling at 22.3 m/s moves a fielder's glove backward 25 cm when the ball is caught. a. Construct an energy bar graph

More information

CHAPTER 6 TEST REVIEW -- MARKSCHEME

CHAPTER 6 TEST REVIEW -- MARKSCHEME Force (N) AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM CHAPTER

More information

Physics Worksheet Work and Energy Section: Name:

Physics Worksheet Work and Energy Section: Name: 1. oncept of Energy a) Energy: quantity that is often understood as the on a physical system. b) We observe only the effects of energy when something is happening. When energy is being, or when energy

More information

WEP-Energy. 2. If the speed of a car is doubled, the kinetic energy of the car is 1. quadrupled 2. quartered 3. doubled 4. halved

WEP-Energy. 2. If the speed of a car is doubled, the kinetic energy of the car is 1. quadrupled 2. quartered 3. doubled 4. halved 1. A 1-kilogram rock is dropped from a cliff 90 meters high. After falling 20 meters, the kinetic energy of the rock is approximately 1. 20 J 2. 200 J 3. 700 J 4. 900 J 2. If the speed of a car is doubled,

More information

Name: Date: Period: AP Physics C Work HO11

Name: Date: Period: AP Physics C Work HO11 Name: Date: Period: AP Physics C Work HO11 1.) Rat pushes a 25.0 kg crate a distance of 6.0 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction

More information

D) No, because of the way work is defined D) remains constant at zero. D) 0 J D) zero

D) No, because of the way work is defined D) remains constant at zero. D) 0 J D) zero CHAPTER 6 REVIEW NAME 1) Can work be done on a system if there is no motion? A) Yes, if an outside force is provided. B) Yes, since motion is only relative. C) No, since a system which is not moving has

More information

Physics Test Review: Mechanics Session: Name:

Physics Test Review: Mechanics Session: Name: Directions: For each statement or question, write in the answer box, the number of the word or expression that, of those given, best completes the statement or answers the question. 1. The diagram below

More information

Momentum, Impulse, Work, Energy, Power, and Conservation Laws

Momentum, Impulse, Work, Energy, Power, and Conservation Laws Momentum, Impulse, Work, Energy, Power, and Conservation Laws 1. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second.

More information

Name. Honors Physics AND POTENTIAL KINETIC

Name. Honors Physics AND POTENTIAL KINETIC KINETIC Name Honors Physics AND POTENTIAL Name Period Work and Energy Intro questions Read chapter 9 pages 144 146 (Section 9.1) 1. Define work in terms of physics? 2. In order to do work on an object,

More information

Announcements. Principle of Work and Energy - Sections Engr222 Spring 2004 Chapter Test Wednesday

Announcements. Principle of Work and Energy - Sections Engr222 Spring 2004 Chapter Test Wednesday Announcements Test Wednesday Closed book 3 page sheet sheet (on web) Calculator Chap 12.6-10, 13.1-6 Principle of Work and Energy - Sections 14.1-3 Today s Objectives: Students will be able to: a) Calculate

More information

Momentum, Work and Energy Review

Momentum, Work and Energy Review Momentum, Work and Energy Review 1.5 Momentum Be able to: o solve simple momentum and impulse problems o determine impulse from the area under a force-time graph o solve problems involving the impulse-momentum

More information

Efficiency = power out x 100% power in

Efficiency = power out x 100% power in Work, Energy and Power Review Package 1) Work: change in energy. Measured in Joules, J. W = Fd W = ΔE Work is scalar, but can be negative. To remember this, ask yourself either: Is the object is losing

More information

Name 09-MAR-04. Work Power and Energy

Name 09-MAR-04. Work Power and Energy Page 1 of 16 Work Power and Energy Name 09-MAR-04 1. A spring has a spring constant of 120 newtons/meter. How much potential energy is stored in the spring as it is stretched 0.20 meter? 1. 2.4 J 3. 12

More information

1 1. A spring has a spring constant of 120 newtons/meter. How much potential energy is stored in the spring as it is stretched 0.20 meter?

1 1. A spring has a spring constant of 120 newtons/meter. How much potential energy is stored in the spring as it is stretched 0.20 meter? Page of 3 Work Power And Energy TEACHER ANSWER KEY March 09, 200. A spring has a spring constant of 20 newtons/meter. How much potential energy is stored in the spring as it is stretched 0.20 meter?. 2.

More information

Potential and Kinetic Energy

Potential and Kinetic Energy Potential and Kinetic Energy 1 of 31 Boardworks Ltd 2016 Potential and Kinetic Energy 2 of 31 Boardworks Ltd 2016 What is a system? 3 of 31 Boardworks Ltd 2016 A system is an object or a group of objects.

More information

Preparing for Six Flags Physics Concepts

Preparing for Six Flags Physics Concepts Preparing for Six Flags Physics Concepts uniform means constant, unchanging At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given

More information

2 possibilities. 2.) Work is done and... 1.) Work is done and... *** The function of work is to change energy ***

2 possibilities. 2.) Work is done and... 1.) Work is done and... *** The function of work is to change energy *** Work-Energy Theorem and Energy Conservation *** The function of work is to change energy *** 2 possibilities 1.) Work is done and... or 2.) Work is done and... 1 EX: A 100 N box is 10 m above the ground

More information

This chapter covers all kinds of problems having to do with work in physics terms. Work

This chapter covers all kinds of problems having to do with work in physics terms. Work Chapter 7 Working the Physics Way In This Chapter Understanding work Working with net force Calculating kinetic energy Handling potential energy Relating kinetic energy to work This chapter covers all

More information

Conceptual Questions. Problems. Fig.5.42 EXERCISES. 5.2 Work

Conceptual Questions. Problems. Fig.5.42 EXERCISES. 5.2 Work EXERCISES Conceptual Questions 1. Holding your physics book steady in your outstretched arm seems like a lot of work. Explain why it is not considered work in physics. 2. A golf ball and a football have

More information

Potential Energy and Conservation of Energy Chap. 7 & 8

Potential Energy and Conservation of Energy Chap. 7 & 8 Level : AP Physics Potential Energy and Conservation of Energy Chap. 7 & 8 Potential Energy of a System see p.191 in the textbook - Potential energy is the energy associated with the arrangement of a system

More information

- Conservation of Energy Notes Teacher Key -

- Conservation of Energy Notes Teacher Key - NAME: DATE: PERIOD: PHYSICS - Conservation of Energy Notes Teacher Key - - Is Energy Conserved? - Determine the max height that a 5kg cannonball will reach if fired vertically with an initial velocity

More information

v (m/s) 10 d. displacement from 0-4 s 28 m e. time interval during which the net force is zero 0-2 s f. average velocity from 0-4 s 7 m/s x (m) 20

v (m/s) 10 d. displacement from 0-4 s 28 m e. time interval during which the net force is zero 0-2 s f. average velocity from 0-4 s 7 m/s x (m) 20 Physics Final Exam Mechanics Review Answers 1. Use the velocity-time graph below to find the: a. velocity at 2 s 6 m/s v (m/s) 1 b. acceleration from -2 s 6 c. acceleration from 2-4 s 2 m/s 2 2 4 t (s)

More information

What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics.

What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics. Bell Ringer Define Kinetic Energy, Potential Energy, and Work. What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics.

More information

(35+70) 35 g (m 1+m 2)a=m1g a = 35 a= =3.27 g 105

(35+70) 35 g (m 1+m 2)a=m1g a = 35 a= =3.27 g 105 Coordinator: Dr. W. L-Basheer Monday, March 16, 2015 Page: 1 Q1. 70 N block and a 35 N block are connected by a massless inextendable string which is wrapped over a frictionless pulley as shown in Figure

More information

Essentially, the amount of work accomplished can be determined two ways:

Essentially, the amount of work accomplished can be determined two ways: 1 Work and Energy Work is done on an object that can exert a resisting force and is only accomplished if that object will move. In particular, we can describe work done by a specific object (where a force

More information

9.2 Work & Energy Homework - KINETIC, GRAVITATIONAL & SPRING ENERGY

9.2 Work & Energy Homework - KINETIC, GRAVITATIONAL & SPRING ENERGY 9. Work & Energy Homework - KINETIC, GRAVITATIONAL & SPRING ENERGY KINETIC ENERGY QUESTIONS 9.H Energy.doc 1. A 500 kilogram car is driving at 15 meters/second. Calculate its kinetic energy? How much does

More information

Mechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time.

Mechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time. Mechanics Symbols: Equations: Kinematics The Study of Motion s = distance or displacement v = final speed or velocity u = initial speed or velocity a = average acceleration s u+ v v v u v= also v= a =

More information

Student Exploration: Roller Coaster Physics

Student Exploration: Roller Coaster Physics Name: Date: Student Exploration: Roller Coaster Physics Vocabulary: friction, gravitational potential energy, kinetic energy, momentum, velocity Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

More information

Physics 11 Comprehensive Exam Preparation

Physics 11 Comprehensive Exam Preparation Physics 11 Comprehensive Exam Preparation Kinematics 1. A bike first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, then continues at this constant speed for another 4.5 s. What is the total distance traveled

More information

Chapter 7. The Conservation of Energy

Chapter 7. The Conservation of Energy Chapter 7 The Conservation of Energy Consider an object dropped near the surface of the earth. If the distance is small then the gravitational force between the earth and the object will be nearly constant.

More information

MECHANICAL (TOTAL) ENERGY

MECHANICAL (TOTAL) ENERGY DO NOW: 1/19 If you haven t already, please take the short google form survey posted on Edmodo Please turn in your Work done by friction Lab in the top tray POTENTIAL ENERGY Stored energy An object that

More information

Mechanics and Heat. Chapter 5: Work and Energy. Dr. Rashid Hamdan

Mechanics and Heat. Chapter 5: Work and Energy. Dr. Rashid Hamdan Mechanics and Heat Chapter 5: Work and Energy Dr. Rashid Hamdan 5.1 Work Done by a Constant Force Work Done by a Constant Force A force is said to do work if, when acting on a body, there is a displacement

More information

WEP-Energy. 2. If the speed of a car is doubled, the kinetic energy of the car is 1. quadrupled 2. quartered 3. doubled 4. halved

WEP-Energy. 2. If the speed of a car is doubled, the kinetic energy of the car is 1. quadrupled 2. quartered 3. doubled 4. halved 1. A 1-kilogram rock is dropped from a cliff 90 meters high. After falling 20 meters, the kinetic energy of the rock is approximately 1. 20 J 2. 200 J 3. 700 J 4. 900 J 2. If the speed of a car is doubled,

More information

Question 8.1 Sign of the Energy II

Question 8.1 Sign of the Energy II Question 8. Sign of the Energy II Is it possible for the gravitational potential energy of an object to be negative? a) yes b) no Question 8. Sign of the Energy II Is it possible for the gravitational

More information

Chapter 10-Work, Energy & Power

Chapter 10-Work, Energy & Power DULLES HIGH SCHOOL Chapter 10-Work, Energy & Power Energy Transformations Judy Matney 1/12/2016 In this chapter, we will study the concepts of force and work; we will understand the transformations of

More information

Energy Whiteboard Problems

Energy Whiteboard Problems Energy Whiteboard Problems 1. (a) Consider an object that is thrown vertically up into the air. Draw a graph of gravitational force vs. height for that object. (b) Based on your experience with the formula

More information

Work and Energy Chapter Questions. 2. Contrast the effects of external forces and internal forces on the total energy of a system.

Work and Energy Chapter Questions. 2. Contrast the effects of external forces and internal forces on the total energy of a system. PSI AP Physics I Work and Energy Chapter Questions 1. Define a system, the environment and the system boundary. 2. Contrast the effects of external forces and internal forces on the total energy of a system.

More information

Physics Unit 4:Work & Energy Name:

Physics Unit 4:Work & Energy Name: Name: Review and Preview We have come a long way in our study of mechanics. We started with the concepts of displacement and time, and built up to the more complex quantities of velocity and acceleration.

More information

Chapter Work, Energy and Power. Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Ans: (a)

Chapter Work, Energy and Power. Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Ans: (a) Chapter Work, Energy and Power Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Q2. A bullet of mass 10g leaves a rifle at an initial velocity of

More information

Physics Midterm Review KEY

Physics Midterm Review KEY Name: Date: 1. Which quantities are scalar? A. speed and work B. velocity and force C. distance and acceleration D. momentum and power 2. A 160.-kilogram space vehicle is traveling along a straight line

More information

Conservation of Energy and Momentum

Conservation of Energy and Momentum Conservation of Energy and Momentum Three criteria for Work There must be a force. There must be a displacement, d. The force must have a component parallel to the displacement. Work, W = F x d, W = Fd

More information

Physics. Chapter 7 Energy

Physics. Chapter 7 Energy Physics Chapter 7 Energy Work How long does a force act? Last week, we meant time as in impulse (Ft) This week, we will take how long to mean distance Force x distance (Fd) is what we call WORK W = Fd

More information

Chapter 8 Conservation of Energy. Copyright 2009 Pearson Education, Inc.

Chapter 8 Conservation of Energy. Copyright 2009 Pearson Education, Inc. Chapter 8 Conservation of Energy Units of Chapter 8 Conservative and Nonconservative Forces Potential Energy Mechanical Energy and Its Conservation Problem Solving Using Conservation of Mechanical Energy

More information

Ch 11 ENERGY and its CONSERVATION. work causes a change in the energy of a system KE (an increase or decrease in KE) ket.

Ch 11 ENERGY and its CONSERVATION. work causes a change in the energy of a system KE (an increase or decrease in KE) ket. Ch 11 ENERGY and its CONSERVATION 11.1 The Many Forms of Energy work causes a change in the energy of a system W = KE (an increase or decrease in KE) work energy theorem object + work object work increase

More information

Phys101 Lectures 9 and 10 Conservation of Mechanical Energy

Phys101 Lectures 9 and 10 Conservation of Mechanical Energy Phys101 Lectures 9 and 10 Conservation of Mechanical Energy Key points: Conservative and Nonconservative Forces Potential Energy Generalized work-energy principle Mechanical Energy and Its Conservation

More information

PH7_UnitPacketCompleteKey

PH7_UnitPacketCompleteKey Page 1 of 45 Page 2 of 45 Unit Packet Contents 1. Unit Objectives 2. Notes: Potential / Kinetic Energy 3. Guided Practice: Potential and Kinetic Energy 4. Independent Practice Potential and Kinetic Energy

More information

4.) A baseball that weighs 1.6 N leaves a bat with a speed of 40.0 m/s. Calculate the kinetic energy of the ball. 130 J

4.) A baseball that weighs 1.6 N leaves a bat with a speed of 40.0 m/s. Calculate the kinetic energy of the ball. 130 J AP Physics-B Energy And Its Conservation Introduction: Energy is a term that most of us take for granted and use quite freely. We assume we know what we are talking about when speaking of energy. In truth,

More information

Physics Year 11 Term 1 Week 7

Physics Year 11 Term 1 Week 7 Physics Year 11 Term 1 Week 7 Energy According to Einstein, a counterpart to mass An enormously important but abstract concept Energy can be stored (coal, oil, a watch spring) Energy is something moving

More information

Phys101 Lectures 9 and 10 Conservation of Mechanical Energy

Phys101 Lectures 9 and 10 Conservation of Mechanical Energy Phys101 Lectures 9 and 10 Conservation of Mechanical Energy Key points: Conservative and Nonconservative Forces Potential Energy Generalized work-energy principle Mechanical Energy and Its Conservation

More information

PSI AP Physics I Work and Energy

PSI AP Physics I Work and Energy PSI AP Physics I Work and Energy Multiple-Choice questions 1. A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to accelerate

More information

1. Which one of the following situations is an example of an object with a non-zero kinetic energy?

1. Which one of the following situations is an example of an object with a non-zero kinetic energy? Name: Date: 1. Which one of the following situations is an example of an object with a non-zero kinetic energy? A) a drum of diesel fuel on a parked truck B) a stationary pendulum C) a satellite in geosynchronous

More information

Work Work has a variety of meanings (taking out the trash is hard work; the toaster doesn t work; Mom goes to work)

Work Work has a variety of meanings (taking out the trash is hard work; the toaster doesn t work; Mom goes to work) Physics Work, Power, and Energy Notes (Chapter 8 in Textbook) Key Terms Work Power Energy Potential Kinetic Mechanical Energy Law of Conservation of Energy Work-Energy Theorem Joule Watt Work Work has

More information

Regents Physics. Physics Midterm Review - Multiple Choice Problems

Regents Physics. Physics Midterm Review - Multiple Choice Problems Name Physics Midterm Review - Multiple Choice Problems Regents Physics 1. A car traveling on a straight road at 15.0 meters per second accelerates uniformly to a speed of 21.0 meters per second in 12.0

More information

Chapter 2 Physics in Action Sample Problem 1 A weightlifter uses a force of 325 N to lift a set of weights 2.00 m off the ground. How much work did th

Chapter 2 Physics in Action Sample Problem 1 A weightlifter uses a force of 325 N to lift a set of weights 2.00 m off the ground. How much work did th Chapter Physics in Action Sample Problem 1 A weightlifter uses a force of 35 N to lift a set of weights.00 m off the ground. How much work did the weightlifter do? Strategy: You can use the following equation

More information

Chapter 5: Energy. Energy is one of the most important concepts in the world of science. Common forms of Energy

Chapter 5: Energy. Energy is one of the most important concepts in the world of science. Common forms of Energy Chapter 5: Energy Energy is one of the most important concepts in the world of science. Common forms of Energy Mechanical Chemical Thermal Electromagnetic Nuclear One form of energy can be converted to

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 Work and Energy Midterm exams will be available next Thursday. Assignment 6 Textbook (Giancoli, 6 th edition), Chapter 6: Due on Thursday, November 5 1. On page 162 of Giancoli, problem 4. 2.

More information

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m Work/nergy 1. student throws a ball upward where the initial potential energy is 0. t a height of 15 meters the ball has a potential energy of 60 joules and is moving upward with a kinetic energy of 40

More information

AP PHYSICS 1. Energy 2016 EDITION

AP PHYSICS 1. Energy 2016 EDITION AP PHYSICS 1 Energy 2016 EDITION Copyright 2016 National Math + Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. 1 Pre-Assessment Questions Consider a system which could

More information

Unit V: Mechanical Energy

Unit V: Mechanical Energy Unit V: Mechanical Energy Work In physics, we have two definitions of work. 1) Work is a transfer of energy. This means that energy changes forms or energy is transferred from one object to another object.

More information

General Physics I Work & Energy

General Physics I Work & Energy General Physics I Work & Energy Forms of Energy Kinetic: Energy of motion. A car on the highway has kinetic energy. We have to remove this energy to stop it. The brakes of a car get HOT! This is an example

More information

Class IX Chapter 11 Work and Energy Science

Class IX Chapter 11 Work and Energy Science Class IX Chapter 11 Work and Energy Science Question 1: A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 11.3). Let us take it that the force acts on

More information

Honor Physics Final Exam Review. What is the difference between series, parallel, and combination circuits?

Honor Physics Final Exam Review. What is the difference between series, parallel, and combination circuits? Name Period Date Honor Physics Final Exam Review Circuits You should be able to: Calculate the total (net) resistance of a circuit. Calculate current in individual resistors and the total circuit current.

More information

Page 1. Name:

Page 1. Name: Name: 3834-1 - Page 1 1) If a woman runs 100 meters north and then 70 meters south, her total displacement is A) 170 m south B) 170 m north C) 30 m south D) 30 m north 2) The graph below represents the

More information

WEP-Work and Power. What is the amount of work done against gravity as an identical mass is moved from A to C? J J J 4.

WEP-Work and Power. What is the amount of work done against gravity as an identical mass is moved from A to C? J J J 4. 1. The work done in accelerating an object along a frictionless horizontal surface is equal to the change in the object s 1. momentum 2. velocity 3. potential energy 4. kinetic energy 2. The graph below

More information

Work changes Energy. Do Work Son!

Work changes Energy. Do Work Son! 1 Work changes Energy Do Work Son! 2 Do Work Son! 3 Work Energy Relationship 2 types of energy kinetic : energy of an object in motion potential: stored energy due to position or stored in a spring Work

More information

Elastic Potential Energy

Elastic Potential Energy Elastic Potential Energy If you pull on a spring and stretch it, then you do work. That is because you are applying a force over a displacement. Your pull is the force and the amount that you stretch the

More information

Beginning of a paper by Gottfried Wilhelm von Leibnitz and his followers denouncing the Law of Conservation of Momentum.

Beginning of a paper by Gottfried Wilhelm von Leibnitz and his followers denouncing the Law of Conservation of Momentum. AP Physics Energy and its Conservation Part I Introduction: Energy is a term that most of us take for granted and use quite freely. We assume we know what we are talking about when speaking of energy.

More information

Potential Energy & Conservation of Energy Physics

Potential Energy & Conservation of Energy Physics Potential Energy & Conservation of Energy Physics Work and Change in Energy If we rearrange the Work-Kinetic Energy theorem as follows Ki +Fcosφ d = Kf => Fcosφ d = Kf - Ki => Fcosφ d = K => Ki + ΣΣW =

More information

3. What name is given to the force of gravity? In what direction (on earth) does this force always act?

3. What name is given to the force of gravity? In what direction (on earth) does this force always act? CHAPTER 3: FORCES CAN CHANGE VELOCITY 3.1 The Nature of Force EXERCISE 3.1 1. Explain the difference between kinematics and dynamics. 2. Define force. What is the SI unit for force? 3. What name is given

More information

NCERT solution for Work and energy

NCERT solution for Work and energy 1 NCERT solution for Work and energy Question 1 A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (See below figure). Let us take it that the force acts on the

More information

ENERGY. Conservative Forces Non-Conservative Forces Conservation of Mechanical Energy Power

ENERGY. Conservative Forces Non-Conservative Forces Conservation of Mechanical Energy Power ENERGY Conservative Forces Non-Conservative Forces Conservation of Mechanical Energy Power Conservative Forces A force is conservative if the work it does on an object moving between two points is independent

More information

1. A train moves at a constant velocity of 90 km/h. How far will it move in 0.25 h? A. 10 km B km C. 25 km D. 45 km E. 50 km

1. A train moves at a constant velocity of 90 km/h. How far will it move in 0.25 h? A. 10 km B km C. 25 km D. 45 km E. 50 km Name: Physics I Mid Term Exam Review Multiple Choice Questions Date: Mr. Tiesler 1. A train moves at a constant velocity of 90 km/h. How far will it move in 0.25 h? A. 10 km B. 22.5 km C. 25 km D. 45 km

More information

How does the total energy of the cart change as it goes down the inclined plane?

How does the total energy of the cart change as it goes down the inclined plane? Experiment 6 Conservation of Energy and the Work-Energy Theorem In this experiment you will explore the principle of conservation of mechanical energy. You will see that gravitational energy can be converted

More information

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m PSI AP Physics C Work and Energy (Algebra Based) Multiple Choice Questions (use g = 10 m/s 2 ) 1. A student throws a ball upwards from the ground level where gravitational potential energy is zero. At

More information

Lesson 3A Energy, Work and Power

Lesson 3A Energy, Work and Power Physics 30 Lesson 3A Energy, Work and Power I. Energy and its forms The idea of Energy is the most fundamental principle in all of science. Everything in the universe is a manifestation or form of Energy.

More information

Physics 111. Lecture 15 (Walker: 7.1-2) Work & Energy March 2, Wednesday - Midterm 1

Physics 111. Lecture 15 (Walker: 7.1-2) Work & Energy March 2, Wednesday - Midterm 1 Physics 111 Lecture 15 (Walker: 7.1-2) Work & Energy March 2, 2009 Wednesday - Midterm 1 Lecture 15 1/25 Work Done by a Constant Force The definition of work, when the force is parallel to the displacement:

More information

Ch 8 Conservation of Energy

Ch 8 Conservation of Energy Ch 8 Conservation of Energy Cons. of Energy It has been determined, through experimentation, that the total mechanical energy of a system remains constant in any isolated system of objects that interact

More information

Chapter 6: Work and Kinetic Energy

Chapter 6: Work and Kinetic Energy Chapter 6: Work and Kinetic Energy Suppose you want to find the final velocity of an object being acted on by a variable force. Newton s 2 nd law gives the differential equation (for 1D motion) dv dt =

More information

Slide 1 / 76. Work & Energy Multiple Choice Problems

Slide 1 / 76. Work & Energy Multiple Choice Problems Slide 1 / 76 Work & Energy Multiple Choice Problems Slide 2 / 76 1 A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to

More information

1) To Work or Not to Work

1) To Work or Not to Work 1) To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no 1) To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no Work

More information

Work, Power and Energy Worksheet. 2. Calculate the work done by a 47 N force pushing a kg pencil 0.25 m against a force of 23 N.

Work, Power and Energy Worksheet. 2. Calculate the work done by a 47 N force pushing a kg pencil 0.25 m against a force of 23 N. Work, Power and Energy Worksheet Work and Power 1. Calculate the work done by a 47 N force pushing a pencil 0.26 m. 2. Calculate the work done by a 47 N force pushing a 0.025 kg pencil 0.25 m against a

More information

Potential Energy & Conservation of Energy

Potential Energy & Conservation of Energy Potential Energy & Conservation of Energy Level : Physics I Teacher : Kim Work and Change in Energy If we rearrange the Work-Kinetic Energy theorem as follows K i +Fcosφ d = K f => Fcosφ d = K f - K i

More information

Physics Pre-comp diagnostic Answers

Physics Pre-comp diagnostic Answers Name Element Physics Pre-comp diagnostic Answers Grade 8 2017-2018 Instructions: THIS TEST IS NOT FOR A GRADE. It is to help you determine what you need to study for the precomps. Just do your best. Put

More information

s_3x03 Page 1 Physics Samples

s_3x03 Page 1 Physics Samples Physics Samples KE, PE, Springs 1. A 1.0-kilogram rubber ball traveling east at 4.0 meters per second hits a wall and bounces back toward the west at 2.0 meters per second. Compared to the kinetic energy

More information

Work done on an object = energy gained by the object Work done by an object = energy lost by the object

Work done on an object = energy gained by the object Work done by an object = energy lost by the object Energy Energy can be defined as the capacity for doing work, or the property of a system that diminishes when the system does work on any other system by an amount equal to the work done. 1) When work

More information

Name: Class: 903 Active Physics Winter Break Regents Prep December 2014

Name: Class: 903 Active Physics Winter Break Regents Prep December 2014 In this section use the following equations for velocity and displacement to solve: 1. In a drill during basketball practice, a player runs the length of the 30.meter court and back. The player does this

More information

GPE = m g h. GPE = w h. k = f d. PE elastic = ½ k d 2. Work = Force x distance. KE = ½ m v 2

GPE = m g h. GPE = w h. k = f d. PE elastic = ½ k d 2. Work = Force x distance. KE = ½ m v 2 1 NAME PERIOD PHYSICS GUIDESHEET ENERGY CONVERSIONS POTENTIAL AND KINETIC ENERGY ACTIVITY LESSON DESCRIPTION SCORE/POINTS 1. NT CLASS OVERHEAD NOTES (5 pts/page) (Plus 5 pts/page for sample questions)

More information

ConcepTest PowerPoints

ConcepTest PowerPoints ConcepTest PowerPoints Chapter 6 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

More information

Work and Energy. Work

Work and Energy. Work Work and Energy Objectives: Students will define work. Students will define and give examples of different forms of energy. Students will describe and give examples of kinetic energy and potential energy.

More information

An Introduction. Work

An Introduction. Work Work and Energy An Introduction Work Work tells us how much a force or combination of forces changes the energy of a system. Work is the bridge between force (a vector) and energy (a scalar). W = F Dr

More information

Momentum & Energy Review Checklist

Momentum & Energy Review Checklist Momentum & Energy Review Checklist Impulse and Momentum 3.1.1 Use equations to calculate impulse; momentum; initial speed; final speed; force; or time. An object with a mass of 5 kilograms is moving at

More information

Unit 4 Work, Power & Conservation of Energy Workbook

Unit 4 Work, Power & Conservation of Energy Workbook Name: Per: AP Physics C Semester 1 - Mechanics Unit 4 Work, Power & Conservation of Energy Workbook Unit 4 - Work, Power, & Conservation of Energy Supplements to Text Readings from Fundamentals of Physics

More information