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Problem 4.6

# Problem 4.6 - Problem 4.6[Difficulty 2 Given Block sliding...

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Problem 4.6 [Difficulty: 2] Given: Block sliding to a stop Find: Distance and time traveled; new coeeficient of friction Solution: Governing equations: Σ F x M a x = F f μ W = Assumptions: Dry friction; neglect air resistance Given data μ 0.6 = V 0 5 m s = M 2 kg = L 2 m = Σ F x F f = μ W = M a x = W g a x = W g 2 t x d d 2 = or 2 t x d d 2 μ g = Integrating, and using I.C. V = V 0 at t = 0 Hence dx dt μ g t c 1 + = μ g t V 0 + = (1) Integrating again x 1 2 g t 2 V 0 t + c 2 + = 1 2 g t 2 V 0 t + = since x = 0 at t = 0 (2) We have the final state, at which x f L = and dx dt 0 = at t t f = From Eq. 1 dx dt 0 = μ g t f V 0 + = so t f V 0 μ g = Using given data
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