exam02_sol_f08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 TEAL Fall Term 2008 Exam 2 Solutions Problem 1 (25 points). Circle your answer. There are five questions and each question is worth 5 points. Question A (5 points): The figure below shows the experimental setup to study the collision between two carts. In the experiment cart A rolls to the right on the level track, away from the motion sensor at the left end of the track. Cart B is initially at rest. The mass of cart A is equal to the mass of cart B. Suppose the two carts stick together after the collision. Assume the carts move frictionlessly. The kinetic energy of the two carts after the collision 1) is equal to one half the kinetic energy of cart A before the collision 2) is equal to one quarter the kinetic energy of cart A before the collision. 3) is equal to the kinetic energy of cart A before the collision. 4) is equal to twice the kinetic energy of cart A before the collision. 5) is equal to four times the kinetic energy of cart A before the collision. 6) None of the above. Solution (1): Since the carts stick together after the collision and they have equal mass, the final speed of the carts is half the initial speed of cart A. The final kinetic energy of the carts after the collision is therefore K f = 1 2 (2 m ) v 0 2 2 = 1 2 1 2 mv A ,0 2 = 1 2 K A (1.1)
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2 Question B: (5 points) A block attached to a spring is undergoing one dimensional simple harmonic motion along the x axis with some maximum displacement. Your job is to increase the maximum displacement by firing a bullet into the block. When is the best time to fire the bullet? You may assume that the time required for the bullet to reach the block is negligible 1) When the block is at its equilibrium position and moving toward the gun. 2) When the block is at its equilibrium position and moving away from the gun. 3) When the block is closest to the gun. 4) When the block is farthest away from the gun. 5) The answer depends on the ratio of the two masses . Solution (2): Choose the positive x-direction to point in the same direction as the incoming bullet. The bullet-block system will have maximum displacement if the least amount of kinetic energy is lost in the collision. The final kinetic energy is equal to K f = 1 2 m total v f 2 = 1 2 m total m total v f () 2 = p f , x 2 2 m total (1.2) The final x-component of the momentum is constant and given by p f , x = m bullet v bullet , x ,0 + m block v block , x (1.3) This will be maximum is v block , x has maximum value. This occurs when the block is at its equilibrium position and moving away from the gun.
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3 Question C: (5 points) U ( x ) = ax ; x 0 bx 2 ; x > 0 A particle is released from rest at the position x = x 0 in the potential described above.
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This note was uploaded on 10/15/2011 for the course PHYSICS 0207239 taught by Professor Mamar during the Spring '09 term at Jordan University of Science & Tech.

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exam02_sol_f08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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