QZ_03_S

# QZ_03_S - Ph1a: Solution to Quiz 3 Alejandro Jenkins, Fall...

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Ph1a: Solution to Quiz 3 Alejandro Jenkins, Fall 2004 Problem (6 points) - Double Drop Two balls, the lower one of radius 2 a and the upper one of radius a , are dropped from a height h (measured from the center of the lower ball to the ﬂoor), as shown in the ﬁgure. The mass of the upper ball is m and the mass of the lower ball is M = 3 m . Assume that the centers of the spheres always lie along the vertical line and that all collisions are perfectly elastic. You may neglect air resistance. a 2a h (a) (1 point) Calculate the velocity v 0 of the balls immediately before they hit the ﬂoor. Assume there is a short interval between the lower ball bouncing on the ﬂoor and it hitting the upper ball. What is the velocity of the lower ball immediately after hitting the ﬂoor but before hitting the upper ball? Solution : On their way down, the balls travel a vertical distance h - 2 a . There- fore, by energy conservation, their velocity immediately before hitting the ﬂoor is - p 2 g ( h - 2 a ). If the collision with the ﬂoor is elastic, then the lower ball will bounce up with velocity p 2 g ( h - 2 a ). (b) (3 points) Immediately after the lower ball hits the upper ball, what will the velocity v 1 be for the upper ball? Hint:

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## This note was uploaded on 03/30/2010 for the course PH 1a taught by Professor Goodstein during the Fall '07 term at Caltech.

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QZ_03_S - Ph1a: Solution to Quiz 3 Alejandro Jenkins, Fall...

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