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Problem 4.143

# Problem 4.143 - Problem 4.143[Difficulty 4 Given Data on...

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Problem 4.143 [Difficulty: 4] Given: Data on vane/slider Find: Formula for acceleration and speed; plot Solution: The given data is ρ 999 kg m 3 = M 30 kg = A 0.005 m 2 = V 20 m s = μ k 0.3 = The equation of motion, from Problem 4.141, is dU dt ρ V U ( ) 2 A M g μ k = The acceleration is thus a ρ V U ( ) 2 A M g μ k = Separating variables dU ρ V U ( ) 2 A M g μ k dt = Substitute u V U = dU du = du ρ A u 2 M g μ k dt = But u 1 ρ A u 2 M g μ k d M g μ k ρ A atanh ρ A g μ k M u = and u = V - U so M g μ k ρ A atanh ρ A g μ k M u M g μ k ρ A atanh ρ A g μ k M V U ( ) = Using initial conditions M g μ k ρ A atanh ρ A g μ k M V U ( ) M g μ k

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Problem 4.143 - Problem 4.143[Difficulty 4 Given Data on...

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