Work and Energy

1. Work and Energy

2. A note on usage: The clicker slides in this booklet are meant to be used as stimuli to encourage class discussion. They are intended for use in a class that attempts to help students develop a coherent and sophisticated understanding of scientific thinking. They are NOT intended as items to test whether students are “right or wrong” or “know” the correct answerby one-step recall if enough cues are given. This has a number of instructional implications that are reviewed in general on the next four slides. The individual slides also contain annotations discussing their intended use.

3. Usage: 1 • Feedback One of the most important values of a clicker-response system is to provide instructors with some understanding of what students are thinking. Good clicker questions can be highly revealing (and surprising). But the critical fact is not that the students make mistakes but to use those mistakes to probe their thinking and find out why. This raises the importance of a rich subsequent discussion well above “letting the students know what the right answer is.”

4. Usage 2: • Student-student interactions The critical value for student learning occurs in what happens after a clicker question has obtained a mixed response from the students. The standard next cue is, “Find someone who disagreed with the answer you chose and see if you can convince them.” After a minute or two of discussion, a second click may show students having moved dramatically towards the correct answer. A brief call for who changed their answer and why can lead to a useful exchange. When they have not moved significantly, more discussion is called for.

5. Usage: 3 • Incompletely specified questions Some items have questions that are simple if idealized assumptions are made, subtler if they are not. Part of the discussion of these items are intended to include issues of modeling, idealizations, and hidden assumptions. • Questions where answers are not provided. In these items, the intent is to have students come up with potential answers and have the instructor collect them and write them on the board. Occasionally, especially at the beginning of a class, it may take some time before students are willing to contribute answers. It can help if you have some prepared answers ready, walk around the class, and put up the answers as if they came from the students. This can help students get more comfortable with contributing.

6. Usage: 4 • Cluster questions Some questions are meant to be used as part of a group of questions. In this case, resolving the answers to individual questions is better left until the entire group is completed. The value of the questions are often in the comparison of the different items and in having students think about what changes lead to what differences and why. • Problem solving items In these items (indicated by a pencil cluster logo), the intent is to have students work together to solve some small problem. After a few minutes, ask the groups to share their answers, vote on the different answers obtained, and have a discussion.

7. Both balls are launched at the same speed. Which one gets to the end first? • The one on the straight track. • The one on the dipped track. • They are the same.

8. Each row in the following table pairs a force vector with a corresponding displacement resulting in work Wbeing done. In which of these rows is the work done zero? • . • . • . • . • . • None.

9. Each row in the following table pairs a force vector with a corresponding displacement resulting in work Wbeing done. In which of these rows is the work done positive? • . • . • . • . • . • None.

10. A young girl wants to select one of the (frictionless) playground slides illustrated below to give her the greatest possible speed when she reaches the bottom of the slide. Which should she choose? 5. It doesn’t matter. It would be the same for each.

11. A young girl wants to select one of the (frictionless) playground slides illustrated below to reach the ground in the shortest possible time. Which should she choose? 5. It doesn’t matter. It would be the same for each.

12. Two identical carts A and B roll down a hill and collide as shown in the figures at the right. (i): A starts from rest. It rolls down and collides head-on with B which is initially at rest on the ground. The two carts stick together. (ii):A and B are at rest on opposite. They roll down, collide head-on and stick together. Which statement is true about the two-cart system just beforethe carts collide in the two cases? • The kinetic energy of the system is zero in case (ii). • The kinetic energy of the system is greater in case (i) than in case (ii). • The kinetic energy of the system is greater in case (ii) than in case ii). • The kinetic energy of the system is the same in both cases (but not 0). • More than one statement is true.

13. Two identical carts A and B roll down a hill and collide as shown in the figures at the right. (i): A starts from rest. It rolls down and collides head-on with B which is initially at rest on the ground. The two carts stick together. (ii):A and B are at rest on opposite. They roll down, collide head-on and stick together. Which statement is true about the two-cart system just after the carts collide and stick in the two cases? • The kinetic energy of the system is zero in case (ii). • The kinetic energy of the system is greater in case (i) than in case (ii). • The kinetic energy of the system is greater in case (ii) than in case ii). • The kinetic energy of the system is the same in both cases (but not 0). • More than one statement is true.

14. Two identical carts A and B roll down a hill and collide as shown in the figures at the right. (i): A starts from rest. It rolls down and collides head-on with B which is initially at rest on the ground. The two carts stick together. (ii):A and B are at rest on opposite. They roll down, collide head-on and stick together. Which statement is true about the two-cart system just beforethe carts collide in the two cases? • The momentum of the system is zero in case (ii). • The momentum of the system is greater in case (i) than in case (ii). • The momentum of the system is greater in case (ii) than in case ii). • The momentum of the system is the same in both cases (but not 0). • More than one statement is true.

15. Two identical carts A and B roll down a hill and collide as shown in the figures at the right. (i): A starts from rest. It rolls down and collides head-on with B which is initially at rest on the ground. The two carts stick together. (ii):A and B are at rest on opposite. They roll down, collide head-on and stick together. Which statement is true about the two-cart system just after the carts collide and stick in the two cases? • The momentum of the system is zero in case (ii). • The momentum of the system is greater in case (i) than in case (ii). • The momentum of the system is greater in case (ii) than in case ii). • The momentum of the system is the same in both cases (but not 0). • More than one statement is true.

16. A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and air resistance and assuming an ideal spring? • 96 m • 48 m • 24 m • 12 m • 6 m • 3 m • Something else

17. The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I. Starting from rest, the pucks are pushed across the table by two equal forces. Which puck will have the greater KE upon reaching the finish line? • Puck I • Puck II • Both will have the same. • There is not enough information to decide.

18. The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I. Starting from rest, the pucks are pushed across the table by two equal forces. Which puck reach the finish line first? • Puck I • Puck II • Both will have the same. • There is not enough information to decide.

19. The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I. Starting from rest, the pucks are pushed across the table by two equal forces. Which puck will have the greater momentum upon reaching the finish line? • Puck I • Puck II • Both will have the same. • There is not enough information to decide.

20. A bulldog on a skateboard is moving very slowly when he encounters a 2 m dip. How fast will he be going when he is at the bottom of the dip? The bulldog and skateboard combined have a mass of 20 kg. Friction and air drag can be ignored. • Very slowly • About 2 m/s About 6 m/s You can’t tell from the information given.

21. A bulldog on a skateboard is moving very slowly when he encounters a 2 m dip. The bulldog and skateboard combined have a mass of 20 kg. What is their total mechanical energy? • Almost zero • About 200 Joules About 600 Joules You can’t tell from the information given.

22. A bulldog on a skateboard is moving very slowly when he encounters a 2 m dip. How fast will be be going when he is at the bottom of the dip? The bulldog and skateboard combined have a mass of 20 kg. Friction and air drag can be ignored. • Very slowly • About 2 m/s About 6 m/s You can’t tell from the information given.

23. A bulldog on a skateboard is moving very slowly when he encounters a 2 m dip. The bulldog and skateboard combined have a mass of 20 kg. What is their total mechanical energy? • Almost zero • About 200 Joules About 600 Joules You can’t tell from the information given.

24. A bulldog on a skateboard is sitting at the bottom of a 2 m dip. How much KE do you have to give them so they will roll out of the dip? The bulldog and skateboard combined have a mass of 20 kg. Friction and air drag can be ignored. • None • About 400 Joules About 600 Joules You can’t tell from the information given.

25. A bulldog on a skateboard is sitting at the bottom of a 2 m dip. How much KE do you have to give them so they will roll out of the dip? The bulldog and skateboard combined have a mass of 20 kg. Friction and air drag can be ignored. • None • About 400 Joules About 600 Joules You can’t tell from the information given.

26. Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the +x direction and cart 2 moves in the -x direction. They bounce off each other elastically. Identify which graph is a possible display of the momentum of cart 1as a function of time.

27. Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the +x direction and cart 2 moves in the -x direction. They bounce off each other elastically. Identify which graph is a possible display of the force on cart 2as a function of time.

28. Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the +x direction and cart 2 moves in the -x direction. They bounce off each other elastically. Identify which graph is a possible display of the position of cart 1as a function of time.

29. Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the +x direction and cart 2 moves in the -x direction. They bounce off each other elastically. Identify which graph is a possible display of the position of cart 2as a function of time.

30. Is it possible for a system of interacting objects to conserve momentum but not mechanical energy (kinetic + potential)? Yes No

31. Is either momentum, mechanical energy, or both conserved for the following system?–- A ball thrown straight upward. • Momentum only • Mechanical energy only • Both momentum & ME • Neither

32. Is either momentum, mechanical energy, or both conserved for the following system?–- a block sliding on a smooth table after being pushed but before it comes to a stop. (Smooth ≠ frictionless!). • Momentum only • Mechanical energy only • Both momentum & ME • Neither

33. Is either momentum, mechanical energy, or both conserved for the following system?–- a heavy cylinder (A) with frictionless wheels rolling along on a horizontal table top and a lighter cylinder (B) that is lightly dropped onto the moving cylinder • Momentum only • Mechanical energy only • Both momentum & ME • Neither

34. Is either momentum, mechanical energy, or both conserved for the following system?–- an cart on an inclined air track with a spring on the bottom. The cart slides up and down the incline, bouncing off the spring when it hits the bottom. • Momentum only • Mechanical energy only • Both momentum & ME • Neither

35. What does the electric potential energy between two identical charges look like?

36. What does the electric potential energy between two opposite charges look like?

37. Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to point A a distance r from +Q. Next, +q is removed and a test charge +2q is brought to point B a distance 2r from +Q. Compared with the electrostatic potential energy of pair of charges in case A, the PE in case B is 1. greater 2. smaller 3. the same 4. you can’t tell from the information given

38. When a positive (test) charge is released from rest near a fixed positive (source) charge what happens to the electric potential energyof the test charge? • It will increase because the test charge will move towards the source charge. • It will decrease because the test charge will move away from the source charge. • It will increase because the test charge will move away from the source charge. • It will decrease because the test charge will move towards the source charge. • It will remain constant because the test charge remains at rest. • There is not enough information to tell.

39. When a negative (test) charge is released from rest near a fixed positive (source) charge what happens to the electric potential energyof the test charge? • It will increase because the test charge will move towards the source charge. • It will decrease because the test charge will move away from the source charge. • It will increase because the test charge will move away from the source charge. • It will decrease because the test charge will move towards the source charge. • It will remain constant because the test charge remains at rest. • There is not enough information to tell.

40. Which of these configurations has the largest electric PE? A B C D A and C B and D other

41. Topo map = grav PE graph (2D) At which point is the force downhill the strongest? • A • B • C

42. Topo map = grav PE graph (2D) At which point is the force downhill pointing east? (North is up) • A • B • C • None

43. Topo map = grav PE graph (2D) At which point is the force downhill pointing north? (North is up) • A • B • C • None

44. Model of PE for 2 line charges(3D)

45. Model of PE for 2 line charges Where would a test charge feel the strongest electric force? • A • B • C • A and C

46. Model of PE for 2 line charges Where would a test charge feel the strongest electric force? • A • B • C • A and C • It would feel no force at any of the three points

47. Map of electric PE for 3 charges (water molecule) (3D) Where would a test charge feel the strongest electric force? • A • B • C • D • E • More than one