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  1. Two small spheres of putty, A and B, of equal mass m, hang from theceiling on massless strings of equal length.Sphere A is raised to a height h0 as shown below and released. Itcollides with sphere B (which is initially at rest). The two spheres stick and swing together to a maximum height hf. (assume a perfectly inelastic collision, where there is no internal energy lost to deformation, heating, etc.) Find the height hf in terms of h0. y B A A h0 hf B x Lowest point in path is the point of zero gravitational potential

  2. Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7

  3. 1. Which of the following physics principles should we use to solve this problem. A) Conservation of Total Mechanical Energy B) Conservation of Momentum C) Newton’s 2nd Law

  4. Choice ACorrect, but this is not the only principle that we need to apply. We will need to apply this principle to this problem twice in order to find relations between the initial height and the speed of ball A, and between the speed of the merged balls and the maximum height that the two balls reach together. We will also need to think about the conservation of momentum.

  5. Choice BCorrect, but this is not the only principle that we need to apply. We will need to apply this principle to this problem in order to find a relation between the speed of ball A right before collision and the speed of the two balls together. We will also need to think about the conservation of energy.

  6. Choice CIncorrect Newton’s 2nd Law will be of no use to us here. Remember, we are concerned with the speeds of the putty balls, and their initial and final heights. Newton’s 2nd Law will not lead us to useful relations.

  7. 2. We want to find the speed at which putty ball A strikes putty ball B. We can find this using the law of conservation of energy.What types of mechanical energy does ball A have initially and just before colliding with ball B (final)? A) Kinetic Gravitational potential B) Gravitational potential Kinetic C) Kinetic & Gravitational potential Gravitational potential Initial Energy Final Energy

  8. Choice AIncorrect Putty ball A starts from rest, so it will not have kinetic energy initially. Also, the lowest point of the ball’s motion is considered to be the point of zero gravitational potential (h=0).

  9. Choice BCorrect This is true because ball A starts from rest and reaches a point of zero gravitational potential with a speed vA.

  10. Choice CIncorrect Putty ball A starts from rest, so it will not have kinetic energy initially. Also, the lowest point of the balls’ motion is considered to be the point of zero gravitational potential (h=0).

  11. 3. Applying the law of conservation of energy to ball A gives which of the following expressions for the speed of ball A at the moment right before it collides with ball B? A) B) C) Initial Final

  12. Choice ACorrect Reasoning:

  13. Choice BIncorrect kinetic energy gravitational potential energy

  14. Choice CIncorrect kinetic energy gravitational potential energy

  15. 4. In order to find an expression for the speed of the merged balls (vAB), in terms of the speed of ball A immediately before the collision (vA), we need to use which conservation principle? A) Conservation of Momentum B) Conservation of Total Energy C) Conservation of Angular Momentum

  16. Choice ACorrect When we set the momentum before the collision equal to the momentum of the system after the collision, there will not be other variables in our relation between the speeds, because we know that mA=mB=m. Note: In general, this problem can be solved for spheres with different masses. This problem is a more specific case of colliding pendulums.

  17. Choice BIncorrect We can relate the two speeds this way, but this expression will involve other variables.

  18. Choice CIncorrect This does not help us with the problem at hand.

  19. 5. Which of the following expressions correctly relates the speed of ball A immediately before the collision and the speed of both balls moving together? A) B) C)

  20. Choice ACorrect Reasoning: mA=mB=m

  21. Choice BIncorrect P=total linear momentum 0,f subscripts represent before and after collision Since mA=mB=m

  22. Choice CIncorrect P=total linear momentum 0,f subscripts represent before and after collision Since mA=mB=m

  23. 6. Once again, use the law of conservation of energy for the initial moment right before the collision to the final moment where balls A & B reach their maximum height.Which one of the following expressions is correct for hf? A) B) C)

  24. Choice AIncorrect mA=mB=m

  25. Choice BIncorrect mA=mB=m

  26. Choice CCorrect Reasoning:

  27. 7. Use the relations that we found in previous questions to find an expression for the maximum height of the two balls together (hf) in terms of the initial height of ball A (h0).Which of the following expressions is correct? A) B) C)

  28. Choice AIncorrect From our previous expressions: We see that:

  29. Choice BCorrect Reasoning: The two putty balls will reach a maximum height that is 1/4th of ball A’s initial height.

  30. Choice CIncorrect From our previous expressions: We see that:

  31. Reflection Questions: • Answer this question twice more for balls of differing mass:

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