PHY2048_Fall09_Homework_Set7

PHY2048_Fall09_Homework_Set7 - PHY2048 Fall 2009 Homework...

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Unformatted text preview: PHY2048 Fall 2009 Homework Set 7 Solutions University of Florida Page 1 of 5 Department of Physics PHY 2048 Homework Set 7 Solutions (Chapters 8 & 9) Problem 8-21**: We use energy conservation as follows: mgL E i + = 2 2 1 f f mv E = Setting E i = E f and solving for E f yields (a) s m m s m gL v f / 85 . 4 ) 2 . 1 )( / 8 . 9 ( 2 2 2 = = = Now if ) ( 2 ) 2 ( 2 2 1 2 2 1 d L mg mv r mg mv E f f f − + = + = then (b) s m m m s m L d g v f / 425 . 2 ) 2 . 1 ) 75 . ( 2 )( / 8 . 9 ( 2 ) 2 ( 2 2 = − = − = , where I used r = L – d. Problem 8-27**: Summing all the forces in the y-direction on the mass when it is at rest ( in equilibrium ) gives = − = − mg kd F F g spring where I used a y = 0. Hence, (a) m N m s m kg d mg k / 784 ) 1 . ( ) / 8 . 9 )( 8 ( 2 = = = (b) J J m m m N d d k U spring 7 . 62 72 . 62 ) 3 . 1 . )( / 784 ( ) ( 2 2 1 2 2 1 ≈ = + = + = (c) mgH U U U i f g = − = Δ (d) We use energy conservation as follows: 2 2 1 ) ( d d k E i + = and mgH E f = Setting E i = E f and solving for H gives cm m m m m d d d mg d d k H 80 8 . ) 1 . ( 2 ) 3 . 1 . ( 2 ) ( ) ( 2 2 2 2 1 = = + = + = + = Problem 8-34***: The kinematic equations of motion tell us that t v t x x ) ( ) ( = and 2 2 1 ) ( gt H t y − = . Let t H be the time the marble hits the ground. Hence, 2 2 1 H gt H − = and g H t H 2 = . Also, g H v t v D x H x 2 ) ( ) ( = = . Energy conservation yields 2 2 1 2 2 1 ) ( kd v m x = , where d is the spring compression and hence mg kH d g H m kd g H v D x 2 2 2 ) ( 2 = = = (eq. 1) We are told that H v x0 y-axis d m m H d initial, y=0 final, y=H PHY2048 Fall 2009 Homework Set 7 Solutions University of Florida...
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This note was uploaded on 02/12/2010 for the course PHY PHY taught by Professor Mueller during the Fall '09 term at University of Florida.

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PHY2048_Fall09_Homework_Set7 - PHY2048 Fall 2009 Homework...

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