ph1a_07_finals

ph1a_07_finals - Ph1a Final Exam Solution Chefung Chan,...

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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 x = ( m 1 + m 2 ) ~v ~v = m 1 m 1 + m 2 v (- x ) (b) (3 points) By Hookes law, F =- kx m x =- kx x =- k m 1 + m 2 x Above equation is simple harmonic oscillation in x with 2 = k m 1 + m 2 . Therefore, m 2 = k 2- m 1 (c) (4 points) We know x = A sin ( t ) + B cos ( 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 A =- m 1 m 1 + m 2 v A =- m 1 m 1 + m 2 v 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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ph1a_07_finals - Ph1a Final Exam Solution Chefung Chan,...

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