Problem 4.1

# Problem 4.1 - Problem 4.1 Given Data on mass and spring...

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Problem 4.1 [Difficulty: 2] Given: Data on mass and spring Find: Maximum spring compression Solution: The given data is M5 l b = h5 f t = k2 5 lbf ft = Apply the First Law of Thermodynamics: for the system consisting of the mass and the spring (the spring has gravitional potential energy and the spring elastic potential energy) Total mechanical energy at initial state E 1 0 = Note: The datum for zero potential is the top of the uncompressed spring Total mechanical energy at instant of maximum compression x E 2 Mg x () 1 2 k x 2 + = But E 1 E 2 = so 0M g x 1 2 k x 2 + = Solving for x x 2M g k = x25 × lb 32.2 × ft s 2 ft 25 lbf × 32.2 lb ft s 2 lbf × = x 0.401 ft = When just resting on the spring x k = x 0.200 ft = When dropped from height h: Total mechanical energy at initial state E 1 h = Total mechanical energy at instant of maximum compression x E 2 x 1 2 k x 2 + =

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Problem 4.1 - Problem 4.1 Given Data on mass and spring...

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