Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Work and Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check - Work Is it possible to do work on an object that remains at rest? 1. yes 2. no

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check - Work Is it possible to do work on an object that remains at rest? 1. yes 2. no force acts over a distance no displacementno work done Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Work

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Play Ball!! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1. catcher has done positive work 2. catcher has done negative work 3. catcher has done zero work

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Play Ball!! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1. catcher has done positive work 2. catcher has done negative work 3. catcher has done zero work opposite in direction to the displacement of the ball, so the work is negative W = F d cos  = 180 o W < 0 The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos  ), since  = 180 o, then W < 0. Note that because the work done on the ball is negative, its speed decreases.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Tension A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? 1. tension does no work at all 2. tension does negative work 3. tension does positive work v T

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Tension A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? 1. tension does no work at all 2. tension does negative work 3. tension does positive work perpendicular W = F d cos   = 90°W = 0 No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F d cos  ), since  = 90°, then W = 0. v T Follow-up: Follow-up: Is there a force in the direction of the velocity?

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Friction A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1. friction does no work at all 2. friction does negative work 3. friction does positive work FkFk FnFn FgFg displacement FaFa

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Friction A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1. friction does no work at all 2. friction does negative work 3. friction does positive work opposite negativeW = F d cos  = 180 o W < 0 Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work (W = F d cos  ), since  = 180 o, then W < 0. FkFk FnFn FgFg displacement FaFa

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Friction (2) Can friction ever do positive work? 1. yes 2. no

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Friction (2) Can friction ever do positive work? 1. yes 2. no moves along with the truckforce of static friction that is making the box move Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of static friction that is making the box move. FnFn FgFg FsFs

Copyright © by Holt, Rinehart and Winston. All rights reserved. Definition of Work

Copyright © by Holt, Rinehart and Winston. All rights reserved. F g = 1.50 x 10 3 N F a = 345 N d = 24.0 m  k = W a = ? W k = ? W n = ? W g = ?  W = ? Which ends up in the form of KE Sample

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Force and Work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are on the box? 1. one force 2. two forces 3. three forces 4. four forces 5. five forces

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Force and Work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are on the box? 1. one force 2. two forces 3. three forces 4. four forces 5. five forces FnFn FkFk FTFT FgFg displacement

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Force and Work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? 1. one force 2. two forces 3. three forces 4. four forces 5. no forces are doing work

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Force and Work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? 1. one force 2. two forces 3. three forces 4. four forces 5. no forces are doing work Any force not perpendicular to the motion will do work: no work F n does no work positive F T does positive work negative F k does negative work negative F g does negative work FnFn FkFk FTFT FgFg displacement

Copyright © by Holt, Rinehart and Winston. All rights reserved. Kinetic Energy Kinetic energy depends on speed and mass.

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Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Kinetic Energy By what factor does the kinetic energy of a car change when its speed is tripled? 1. no change at all 2. factor of 3 3. factor of 6 4. factor of 9 5. factor of 12

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Kinetic Energy By what factor does the kinetic energy of a car change when its speed is tripled? 1. no change at all 2. factor of 3 3. factor of 6 4. factor of 9 5. factor of 12 1/2 mv 2 speed increases by a factor of 3KE will increase by a factor of 9 Since the kinetic energy is 1/2 mv 2, if the speed increases by a factor of 3, then the KE will increase by a factor of 9.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Kinetic Energy (3)

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Kinetic Energy (3)

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Kinetic Energy Is it possible for the kinetic energy of an object to be negative? 1.Yes 2.No

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Kinetic Energy Is it possible for the kinetic energy of an object to be negative? 1.Yes 2.No kinetic energy is 1/2 mv 2 massvelocity squared positiveKE must always be positive The kinetic energy is 1/2 mv 2. The mass and the velocity squared will always be positive, so KE must always be positive.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Gravitational Potential Energy Is it possible for the gravitational potential energy of an object to be negative? 1.Yes 2.No

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Gravitational Potential Energy Is it possible for the gravitational potential energy of an object to be negative? 1.Yes 2.No Gravitational PE is mghheight h is measured relative to some arbitrary reference level where PE = 0 ceiling is the zero levelbook has negative PE on the tabledifferences Gravitational PE is mgh, where height h is measured relative to some arbitrary reference level where PE = 0. For example, a book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level, then the book has negative PE on the table. It is only differences (or changes) in PE that have any physical meaning.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Gravitational Potential Energy You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for h = 0 in this problem. Which of the following quantities will you and your friend agree on? A) skier’s PE B) skier’s change in PE C) skier’s final KE 1.only B 2.only C 3.A, B and C 4.only A and C 5.only B and C

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Gravitational Potential Energy You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y = 0 in this problem. Which of the following quantities will you and your friend agree on? A) skier’s PE B) skier’s change in PE C) skier’s final KE 1.only B 2.only C 3.A, B and C 4.only A and C 5.only B and C gravitational PE depends upon the reference level  PE does not  PE and  KE should be the same The gravitational PE depends upon the reference level, but  PE does not! The work done by gravity must be the same in the two solutions, so  PE and  KE should be the same.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Potential Energy Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? 1. the same 2. twice as much 3. four times as much 4. half as much 5. you gain no PE in either case

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Potential Energy Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? 1. the same 2. twice as much 3. four times as much 4. half as much 5. you gain no PE in either case Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. Follow-up: How much more work do you do in taking the steeper path? Follow-up: Which path would you rather take? Why? h

Copyright © by Holt, Rinehart and Winston. All rights reserved. Gravitational Potential Energy PE g = mgh gravitational PE = mass  free-fall acceleration  height

Copyright © by Holt, Rinehart and Winston. All rights reserved. Elastic Potential Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. Springs in a car

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1. same amount of work 2. twice the work 3. 4 times the work 4. 8 times the work

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1. same amount of work 2. twice the work 3. 4 times the work 4. 8 times the work ½kx 2 elastic PE is 4 times greaterwork required to stretch the spring is also 4 times greater The elastic potential energy is ½kx 2. So in the second case, the elastic PE is 4 times greater than in the first case. Thus, the work required to stretch the spring is also 4 times greater.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Potential Energy A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PE e ) and the gravitational potential energy (PE g ) of the mass? 1.Both PE e and PE g decrease 2.PE e increases and PE g decreases 3.Both PE e and PE g increase 4.PE e decreases and PE g increases 5.PE e increases and PE g is constant

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Potential Energy A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PE e ) and the gravitational potential energy (PE g ) of the mass? 1.Both PE e and PE g decrease 2.PE e increases and PE g decreases 3.Both PE e and PE g increase 4.PE e decreases and PE g increases 5.PE e increases and PE g is constant stretchedelastic PE increasesPE e = 1/2 kx 2 lower positiongravitational PE decreasesPE g = mgh The spring is stretched, so its elastic PE increases, since PE e = 1/2 kx 2. The mass moves down to a lower position, so its gravitational PE decreases, since PE g = mgh.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Hooke’s Law F elastic F (N) x (m)

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Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Conservation of Energy Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 1 4) same speed for all balls 2 3

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Conservation of Energy Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? same initial gravitational PE same height same final KEsame speed All of the balls have the same initial gravitational PE, since they are all at the same height (PE = mgh). Thus, when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mv 2 ). 1 4) same speed for all balls 2 3

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Conservation of Energy Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. At the bottom, whose speed is greater? 1. Paul 2. Kathleen 3. both the same

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Conservation of Energy Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. At the bottom, whose speed is greater? 1. Paul 2. Kathleen 3. both the same Conservation of Energy: ME i = mgh = ME f = 1/2 mv 2 ME i = mgh = ME f = 1/2 mv 2 gh = 1/2 v 2 therefore: gh = 1/2 v 2 same height same velocity Since they both start from the same height, they have the same velocity at the bottom, even though they may not have the same mass.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Conservation of Energy Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? 1. Paul 2. Kathleen 3. both the same

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Conservation of Energy Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? 1. Paul 2. Kathleen 3. both the same Kathleen is at a lower height than Paul for most of her ride larger velocity Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. Thus she always has a larger velocity during her ride and therefore arrives earlier!

Copyright © by Holt, Rinehart and Winston. All rights reserved. Conserved Quantities

Copyright © by Holt, Rinehart and Winston. All rights reserved. Conservation of Mechanical Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. Mechanical Energy Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects. ME = KE + PE g + PE e Mechanical energy is conserved (remains constant) in the absence of friction even though the individual forms may change. ME i = ME f (KE + PE g + PE e ) i = (KE + PE g + PE e ) f

Copyright © by Holt, Rinehart and Winston. All rights reserved. While individual forms of energy may change, the total mechanical energy remains constant if there is… …little or no friction (including air resistance) Procedure: …no collision in which significant heat is released 1. Determine the forms of energy present (KE, PE g, PE e ). 3. Use the Law of Conservation of Energy (the total mechanical energy, ME, remains constant) to produce an equation that can be solved for the unknown. Law of Conservation of Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample h = h i = 3.00 m m = 25.0 kg v i = 0.0 m/s h f = 0 m v f = ? (Top)(Bottom)

Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample m k x v i = 0 v f = ? (Initial)(Final)

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Finding h for a pendulum

Copyright © by Holt, Rinehart and Winston. All rights reserved. Work and Kinetic Energy A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? 1. positive work was done 2. negative work was done 3. zero work was done

Copyright © by Holt, Rinehart and Winston. All rights reserved. Work and Kinetic Energy A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? 1. positive work was done 2. negative work was done 3. zero work was done The kinetic energy of the child increased because her speed increasedincrease in KEpositive work being done KE f > KE i work W must be positive The kinetic energy of the child increased because her speed increased. This increase in KE was the result of positive work being done. Or, from the Work-Kinetic Energy Theorem, W =  KE = KE f – KE i. Since we know that KE f > KE i in this case, then the work W must be positive. Follow-up: What does it mean for negative work to be done on the child?

Copyright © by Holt, Rinehart and Winston. All rights reserved. Work and Kinetic Energy ΣW = ∆KE net work = change in kinetic energy ΣW = W F + W k + W n + W g ∆KE = KE f – KE i ΣW = ∆KE

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Kinetic Energy (2) If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases m m m m m

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Work and Kinetic Energy (2) If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases m m m m m |F| d = 1/2 mv 2 Fd = W net =  KE = 0 – ½mv 2 thus: |F| d = 1/2 mv 2 doublesfour times larger Therefore, if the speed doubles, the stopping distance gets four times larger.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample F a  KE d = ?

Copyright © by Holt, Rinehart and Winston. All rights reserved. m = 10.0 kg  k = 0.10 g = 9.81 m/s 2 v i = 2.2 m/s v f = 0 m/s d = ? Sample Which is the only force that will contribute to the net work?

Copyright © by Holt, Rinehart and Winston. All rights reserved. Power = Rate of Energy Transfer

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check - Power Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? 1. Mike 2. Joe 3. both did the same work

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check - Power Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? 1. Mike 2. Joe 3. both did the same work same forcesame displacement same amount of workTime does not matter for determining the work done Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (2) Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who produced the greater power? 1. Mike 2. Joe 3. both produced the same power

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (2) Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who produced the greater power? 1. Mike 2. Joe 3. both produced the same power Mike produced 3 WJoe produced 0.5 W Both do the same amount of work. Since P = W / t, we see that Mike produced 3 W of power and Joe produced 0.5 W of power. Thus, both did the same work, but Mike did his in less time so he produced more power.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (3) Mike performed 5 J of work in 10 seconds. Joe did 3 J of work in 5 seconds. Who produced the greater power? 1. Mike produced more power 2. Joe produced more power 3. both produced the same amount of power

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (3) Mike performed 5 J of work in 10 seconds. Joe did 3 J of work in 5 seconds. Who produced the greater power? 1. Mike produced more power 2. Joe produced more power 3. both produced the same amount of power Mike produced 0.5 WJoe produced 0.6 W Since P = W / t, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (3) Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? 1. yes 2. no

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (3) Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? 1. yes 2. no No!! We cannot conclude anything about how much work each engine does.work will depend upon how much time is used No!! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used. For example, engine #1 may do the same amount of work as engine #2, but in half the time.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (4) When you pay the electric company by the kilowatt-hour, what are you actually paying for? 1. energy 2. power 3. current 4. voltage 5. none of the above

Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Power (4) When you pay the electric company by the kilowatt-hour, what are you actually paying for? 1. energy 2. power 3. current 4. voltage 5. none of the above Powerenergy We know that Power = energy / time Energypower Therefore, Energy = power x time power energy This means that the unit of power x time (kilowatt-hour) is a unit of energy !!

Copyright © by Holt, Rinehart and Winston. All rights reserved. m = 193 kg  t = 5.0 s d = 7.5 m P = ? Sample The best motor to use is the 3.5 kW motor. The 1.0 kW motor will not lift the curtain fast enough, and the 5.5 kW motor will lift it too fast.

Copyright © by Holt, Rinehart and Winston. All rights reserved. Simple Machines

Copyright © by Holt, Rinehart and Winston. All rights reserved. Levers

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Copyright © by Holt, Rinehart and Winston. All rights reserved. Wheel and Axle