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Unformatted text preview: Ph1a Final Exam Solution Chefung Chan, Fall 2007 Problem 1: Stay and Sway (10 points) (a) (3 points) Notice the diagram uses capital M while the question uses m . Here uses m for the whole question. By conservation of momentum: m 1 (0) m 2 v ˆ x = ( m 1 + m 2 ) ~v ~v = m 1 m 1 + m 2 v ( ˆ x ) (b) (3 points) By Hooke’s law, F = kx m ¨ x = kx ¨ x = k m 1 + m 2 x Above equation is simple harmonic oscillation in x with ω 2 = k m 1 + m 2 . Therefore, m 2 = k ω 2 m 1 (c) (4 points) We know x = A sin ( ω t ) + B cos ( ω t ). We are going to match with the initial conditions to find A and B . x ( t = 0) = 0 ⇒ B = 0 ˙ x ( t = 0) = v = m 1 m 1 + m 2 v ω A = m 1 m 1 + m 2 v A = m 1 m 1 + m 2 v ω Problem 2: Misdirected Meteor (8 points) (a) (2 points) First, we want to find the initial speed of the meteor. Since the meteor is in a circular orbit that the gravitational force on the meteor from the planet is equal to the centripetal force. mv 2 i r = GMm r 2 v 2 i = GM r = GM R + 3 R v i = r GM 4 R 1 After the 50% kinetic energy loss, K f = 1 2 K i ⇒ 1 2 mv 2 f = 1 4 mv 2 i v 2 f = 1 2 v 2 i = GM 8 R v f = r GM 8 R K f = 1 2 mv 2 f = GMm 16 R U f = U i = GMm 4 R L...
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This note was uploaded on 04/28/2010 for the course PH 1b Anal taught by Professor Mckewn during the Winter '08 term at Caltech.
 Winter '08
 McKewn
 Momentum

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