PHY2048_Fall09_Homework_Set10

# PHY2048_Fall09_Homework_Set10 - PHY2048 Fall 2009 Homework...

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Unformatted text preview: PHY2048 Fall 2009 Homework Set 10 Solutions University of Florida Page 1 of 4 Department of Physics PHY 2048 Homework Set 10 Solutions (Chapter 12) Problem 12-5*: Summing the y-components of the forces on the ball gives cos = = − y ma mg T θ (eq. 1) , and summing the x-components of the forces on the ball gives sin = = − x wall ma T F θ . (eq. 2) From (eq. 1) we see that (a) N m m m s m kg L r L mg mg T 408 . 9 ) 08 . ( ) 042 . ( 08 . ) / 8 . 9 )( 85 . ( cos 2 2 2 2 2 = + = + = = θ , where I used 2 2 / cos L r L + = θ . From (eq. 2) and (a) we see that (b) N m m s m kg L mgr mg mg T F wall 373 . 4 08 . ) 042 . )( / 8 . 9 )( 85 . ( tan sin cos sin 2 = = = = = = θ θ θ θ , where I used L r / tan = θ . Problem 12-8*: Summing the y-components of the forces on the scaffold gives 2 1 = − − + mg Mg T T and hence g m M T T ) ( 2 1 + = + (eq. 1) , and summing the torques about the origin (left end of scaffold) gives 2 2 = + − − LT Mg xmg L . (eq. 2) and hence ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 2 2 M L xm g T . From (eq. 1) we see that (a) . 8 . 842 2 ) 60 ( . 5 ) 80 )( 5 . 3 ( ) / 8 . 9 ( 2 ) ( 2 ) ( ) ( 2 2 1 N kg m kg m s m M L m x L g M L xm g g m M T g m M T = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − + = − + = (b) N kg m kg m s m M L xm g T 2 . 529 2 ) 60 ( . 5 ) 80 )( 5 . 1 ( ) / 8 . 9 ( 2 2 2 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = Problem 12-10*: First we sum all the forces acting on the center of the rope and set it equal to the mass times the acceleration (which is...
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PHY2048_Fall09_Homework_Set10 - PHY2048 Fall 2009 Homework...

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