1. Is it possible to do work on an object that remains at rest? a) yes b) no ConcepTest 3.1To Work or Not to Work ConcepTest 3.1 To Work or Not to Work

2. Is it possible to do work on an object that remains at rest? a) yes b) 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. ConcepTest 3.1To Work or Not to Work ConcepTest 3.1 To Work or Not to Work

3. ConcepTest 3.2aFriction and Work I ConcepTest 3.2a Friction and Work I a) friction does no work at all b) friction does negative work c) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

4. f N mg displacement Pull opposite negative W = 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. ConcepTest 3.2aFriction and Work I ConcepTest 3.2a Friction and Work I a) friction does no work at all b) friction does negative work c) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

5. 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? a) catcher has done positive work b) catcher has done negative work c) catcher has done zero work ConcepTest 3.2cPlay Ball! ConcepTest 3.2c Play Ball!

6. 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? a) catcher has done positive work b) catcher has done negative work c) 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. ConcepTest 3.2cPlay Ball! ConcepTest 3.2c Play Ball!

7. ConcepTest 3.2dTension and Work ConcepTest 3.2d Tension and Work a) tension does no work at all b) tension does negative work c) tension does positive work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?

8. ConcepTest 3.2dTension and Work ConcepTest 3.2d Tension and Work a) tension does no work at all b) tension does negative work c) tension does positive work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? v T perpendicular W = F d cos   = 90 o 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 o, then W = 0.

9. By what factor does the kinetic energy of a car change when its speed is tripled? a) no change at all b) factor of 3 c) factor of 6 d) factor of 9 e) factor of 12 ConcepTest 3.5aKinetic Energy I ConcepTest 3.5a Kinetic Energy I

10. By what factor does the kinetic energy of a car change when its speed is tripled? a) no change at all b) factor of 3 c) factor of 6 d) factor of 9 e) 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. ConcepTest 3.5aKinetic Energy I ConcepTest 3.5a Kinetic Energy I

11. ConcepTest 3.6aFree Fall I ConcepTest 3.6a Free Fall I a) quarter as much b) half as much c) the same d) twice as much e) four times as much Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?

12. Consider the work done by gravity to make the stone fall distance d:  KE = W net = F d cos   KE = mg d greater massgreater KEtwice Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone. ConcepTest 3.6aFree Fall I ConcepTest 3.6a Free Fall I a) quarter as much b) half as much c) the same d) twice as much e) four times as much Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?

13. In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? a) quarter as much b) half as much c) the same d) twice as much e) four times as much ConcepTest 3.6bFree Fall II ConcepTest 3.6b Free Fall II

14. In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? a) quarter as much b) half as much c) the same d) twice as much e) four times as much All freely falling objects fall at the same rate, which is g acceleration is the same for bothdistance is the samefinal speeds will be the same All freely falling objects fall at the same rate, which is g. Since the acceleration is the same for both, and the distance is the same, then the final speeds will be the same for both stones. ConcepTest 3.6bFree Fall II ConcepTest 3.6b Free Fall II

15. 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? a) positive work was done b) negative work was done c) zero work was done ConcepTest 3.7Work and KE ConcepTest 3.7 Work and KE

16. 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? a) positive work was done b) negative work was done c) zero work was done The kinetic energy of the child increased because her speed increasedincrease in KE positive 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 definition of work, since W =  KE = KE f – KE i and we know that KE f > KE i in this case, then the work W must be positive. ConcepTest 3.7Work and KE ConcepTest 3.7 Work and KE

17. ConcepTest 3.8bSpeeding Up I ConcepTest 3.8b Speeding Up I a) 0  30 mph b) 30  60 mph c) both the same A car starts from rest and accelerates to 30 mph. Later, it gets on a highway and accelerates to 60 mph. Which takes more energy, the 0  30 mph, or the 30  60 mph?

18. 1/2 mv 2 velocity squared The change in KE (1/2 mv 2 ) involves the velocity squared. 1/2 m (30 2 - 0 2 )= 1/2 m (900) So in the first case, we have: 1/2 m (30 2 - 0 2 )= 1/2 m (900) 1/2 m (60 2 - 30 2 )= 1/2 m (2700) In the second case, we have: 1/2 m (60 2 - 30 2 )= 1/2 m (2700) bigger energy changesecond case Thus, the bigger energy change occurs in the second case. ConcepTest 3.8bSpeeding Up I ConcepTest 3.8b Speeding Up I a) 0  30 mph b) 30  60 mph c) both the same A car starts from rest and accelerates to 30 mph. Later, it gets on a highway and accelerates to 60 mph. Which takes more energy, the 0  30 mph, or the 30  60 mph?

19. Is it possible for the kinetic energy of an object to be negative? a) yes b) no ConcepTest 3.10Sign of the Energy I ConcepTest 3.10 Sign of the Energy I

20. Is it possible for the kinetic energy of an object to be negative? a) yes b) no kinetic energy is 1/2 mv 2 mass velocity squaredpositive KE 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. ConcepTest 3.10Sign of the Energy I ConcepTest 3.10 Sign of the Energy I

21. ConcepTest 3.13Up the Hill ConcepTest 3.13 Up the Hill a) the same b) twice as much c) four times as much d) half as much e) you gain no PE in either case 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?

22. Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. ConcepTest 3.13Up the Hill ConcepTest 3.13 Up the Hill a) the same b) twice as much c) four times as much d) half as much e) you gain no PE in either case 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?

23. 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 s ) and the gravitational potential energy (PE g ) of the mass? a) both PE s and PE g decrease b) PE s increases and PE g decreases c) both PE s and PE g increase d) PE s decreases and PE g increases e) PE s increases and PE g is constant ConcepTest 3.15Springs and Gravity ConcepTest 3.15 Springs and Gravity

24. 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 s ) and the gravitational potential energy (PE g ) of the mass? a) both PE s and PE g decrease b) PE s increases and PE g decreases c) both PE s and PE g increase d) PE s decreases and PE g increases e) PE s increases and PE g is constant stretchedelastic PE increases PE s = 1/2 kx 2 lower positiongravitational PE decreases PE g = mgh The spring is stretched, so its elastic PE increases, since PE s = 1/2 kx 2. The mass moves down to a lower position, so its gravitational PE decreases, since PE g = mgh. ConcepTest 3.15Springs and Gravity ConcepTest 3.15 Springs and Gravity

25. ConcepTest 3.16Down the Hill ConcepTest 3.16 Down the Hill 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 d) same speed for all balls 2 3

26. ConcepTest 3.16Down the Hill ConcepTest 3.16 Down the Hill 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 ). 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 d) same speed for all balls 2 3

27. ConcepTest 3.21a ConcepTest 3.21a Time for Work I a) Mike b) Joe c) both did the same work 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?

28. same forcesame displacementsame 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. ConcepTest 3.21a ConcepTest 3.21a Time for Work I a) Mike b) Joe c) both did the same work 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?

29. Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? a) Mike produced more power b) Joe produced more power c) both produced the same amount of power ConcepTest 3.21b ConcepTest 3.21b Time for Work II

30. Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? a) Mike produced more power b) Joe produced more power c) both produced the same amount of power Mike produced 0.5 W Joe produced 0.6 W Since power = work / time, 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. ConcepTest 3.21b ConcepTest 3.21b Time for Work II

31. Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? a) yes b) no ConcepTest 3.21c ConcepTest 3.21c Power

32. Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? a) yes b) 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. ConcepTest 3.21c ConcepTest 3.21c Power

33. a) energy b) power c) current d) voltage e) none of the above ConcepTest 3.22a ConcepTest 3.22a Electric Bill When you pay the electric company by the kilowatt-hour, what are you actually paying for?

34. (a) energy (b) power (c) current (d) voltage (e) none of the above Powerenergy We have defined: Power = energy / time Energypower So we see that: Energy = power x time power energy This means that the unit of power x time (watt-hour) is a unit of energy !! ConcepTest 3.22a ConcepTest 3.22a Electric Bill When you pay the electric company by the kilowatt-hour, what are you actually paying for?