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problem05_p102

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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5.102: (a) The retarding force of the surface is the only horizontal force acting. Thus m kt v dt m k v dv dt m k v dv dt dv m kv m F m F a v v v v t R - = = - = = - = = = 0 0 2 1 0 2 1 2 1 2 1 net 2 which gives 2 2 2 2 1 0 0 4 m t k m kt v v v + - = For the rock’s position : 2 2 2 2 1 0 0 2 2 2 2 1 0 0 4 4 m dt t k m ktdt v dt v dx m t k m kt v v dt dx + - = + - = and integrating gives 2 3 2 2 2 1 0 0 12 2 m t k m kt v t v x + - = (b) 2 2 2 2 1 0 0 2 0 m t k m kt v v v + - = = This is a quadratic equation in t ; from the quadratic formula we can find the single
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Unformatted text preview: solution : k mv t 2 1 2 = (c) Substituting the expression for t into the equation for x : k mv k v m m k k v m m k v k mv v x 3 2 8 12 4 2 2 2 3 3 2 3 3 2 2 2 2 2 1 2 1 = ⋅ + ⋅-⋅ =...
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