HW_Ch13_Sol - PHY126 HW Set 4 (Chap.13) Problem 13.45...

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Unformatted text preview: PHY126 HW Set 4 (Chap.13) Problem 13.45 Description: A pendulum of length is mounted in a rocket. Part A What is its period if the rocket is at rest on its launch pad? Part B What is its period if the rocket is accelerating upward with acceleration ? Part C What is its period if the rocket is accelerating downward with acceleration ? Part D What is its period if the rocket is in free fall? Solutions Let a be the acceleration of the pendulum relative to the rocket, and let a 0 be the acceleration of the rocket relative to the ground (assumed to be an inertial system.) The Newtons 2 nd law is . ) ( a m a m F a a m F r r r r r r = + = Because of the acceleration the gravity constant g will be modified to g eff, , depending on the magnitude and the direction of the acceleration. For small oscillations about the equilibrium position, which depends on , a r the period is 2 a g L T r r = where L is the length of the pendulum. (a) If then , = a r g L T / 2 = as before. (b) j g a ) 2 / 1 ( = r and j g g = r . This gives . ) 3 /( 2 2 ) ) 2 / 1 ( /( 2 g L g g L T = + = (c) If j g a ) 2...
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HW_Ch13_Sol - PHY126 HW Set 4 (Chap.13) Problem 13.45...

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