Problem 2.51 - Problem 2.51 [Difficulty: 4] Ff = A x, V, a...

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Problem 2.51 [Difficulty: 4] F f τ A = x, V, a Mg Given: Data on the block and incline Find: Initial acceleration; formula for speed of block; plot; find speed after 0.1 s. Find oil viscosity if speed is 0.3 m/s after 0.1 s Solution: Given data M5 k g = A 0.1 m () 2 = d 0.2 mm = θ 30 deg = From Fig. A.2 μ 0.4 Ns m 2 = Applying Newton's 2nd law to initial instant (no friction) Ma sin θ F f = sin θ = so a init g sin θ = 9.81 m s 2 sin 30 deg × = a init 4.9 m s 2 = Applying Newton's 2nd law at any instant sin θ F f = and F f τ A = μ du dy A = μ V d A = so M dV dt = sin θ μ A d V = Separating variables dV g sin θ μ A Md V dt = Integrating and using limits μ A ln 1 μ A d sin θ V t = or Vt d sin θ μ A 1e μ A t = At t = 0.1 s V5 k g 9.81 × m s 2 0.0002 × m sin 30 deg m 2 0.4 N s 0.1 m 2 × 2 kg m × 0.4 0.01
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Problem 2.51 - Problem 2.51 [Difficulty: 4] Ff = A x, V, a...

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