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qz9sp08sol

# qz9sp08sol - April4,2008 PHY2053Discussion...

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April 4, 2008 PHY2053 Discussion Quiz 9 (Chapter 8.6 -9.5) Name:                                   UFID: **1. (5 pts) A spherical shell with a mass of 2.00 kg and radius of 0.100 m starts from  rest at the top of a 45.0˚ incline and rolls 2.00 m down the incline without slipping.  Find the final velocity of the shell. (The moment of inertia of a spherical shell is  (2/3)MR ² .) Since   the   sphere   rolls   without   slipping   the   translational   velocity   is   related   to   the   angular velocity as ω  = v/R. The mechanical energy of the sphere is conserved, thus we have Mgh = (1/2)Mv ² +(1/2)I ω ²   Substitute the expression for moment of inertia and angular velocity and solve for linear   velocity: MgLsin  = (1/2)Mv ² +(1/2)(2/3)MR ² (v/R) ² θ  gLsin  = (5/6)v ²   θ  v =  ((6/5) gLsin ) = 4.08 m/s θ **2. (5 pts) A merry-go-round modeled as a disk with a mass of 80.0 kg and radius of

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qz9sp08sol - April4,2008 PHY2053Discussion...

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