px132_2008_assignment_4_solutions

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Unformatted text preview: Assignment Display Mode: Warwick2008 PX132 Assignment 4 Due at 11:00am on Monday, December 1, 2008 View Grading Details A Superball Collides Inelastically with a Table Description: A ball is dropped onto a table froma givenheight and rebounds to another (smaller) height. Find the average force and impulse exerted by the table onthe ball, momentum before and after the collision, and change in kinetic energy. All numerical. As showninthe figure , a superball with mass equal to 50 grams is dropped froma height of . It collides witha table, then bounces up to a height of . The duration of the collision(the time duringwhichthe superball is incontact withthetable) is . Inthis problem, take the positive y directionto be upward, and use for the magnitude of the accelerationdue to gravity. Neglect air resistance. Part A Find the y component of the momentum, , of the ball immediately before the collision. Hint A.1 How to approachthe problem To find the superball's speed immediately before the collision, use the fact that energy is conserved as the ball descends. Applyconservationof energybysettingthe initial (potential) energyof the ball equal to its final (kinetic) energyat the moment it hits the table. Determine the velocityof the ball when it hits the table and use that velocityto compute the ball's momentum. Part A.2 Findthe speedof the ball Find the speed of the ball just before it hits the table. Hint A.2.a The speed of the ball Usingconservationof energy, youcan show that the speed of the ball just before it hits the the table is , where is the height it falls through, and is the magnitude of the accelerationdue to gravity. Express your answer numerically inmeters per second. ANSWER: = Now find the momentum(mass times velocity). Remember to use the correct direction. Express youranswer numerically, to two significant figures. ANSWER: = Part B Find the y component of the momentumof the ball immediatelyafter the collision, that is, justas it is leavingthe table. Hint B.1 How to approachthe problem Recall that the ball reaches a height of only on the rebound. To find the ball's velocityimmediatelyafter the collision (that is, just as it is leaving the table), use the fact that energyis conserved as the ball ascends. (Note: Energyis not conserved during the collision!) Apply conservation of energybysetting the initial (kinetic) energy of the ball whenit leaves the table equal to its final (potential) energywhenit reaches the maximumheight of its bounce. Determine the velocityof the ball when it leaves the table and use that to compute the ball's momentum. Part B.2 Findthe speedof the ball Find the speed of the ball just as it is leaving the table. Hint B.2.a The speed of the ball Usingconservationof energy, youcan show that the speed of the ball just before it leaves the table is , where is the maximumheight it rises to, and is the magnitude of the accelerationdue to gravity....
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This note was uploaded on 10/31/2010 for the course PHYSICS 69054 taught by Professor Huang during the Fall '09 term at Berkeley.

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px132_2008_assignment_4_solutions - Assignment Display...

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