468_Physics ProblemsTechnical Physics

468_Physics - 470*P15.74 Oscillatory Motion(a The block moves with the board in what we take as the positive x direction stretching the spring

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470 Oscillatory Motion *P15.74 (a) The block moves with the board in what we take as the positive x direction, stretching the spring until the spring force kx is equal in magnitude to the maximum force of static friction µµ ss nm g = . This occurs at x mg k s = µ . (b) Since v is small, the block is nearly at the rest at this break point. It starts almost immediately to move back to the left, the forces on it being kx and + k mg . While it is sliding the net force exerted on it can be written as −+ = = − − F H G I K J =− kx mg kx km g k kx mg k kx k kk rel where x rel is the excursion of the block away from the point k mg k . Conclusion: the block goes into simple harmonic motion centered about the equilibrium position where the spring is stretched by k mg k . (d) The amplitude of its motion is its original displacement, A mg k mg k sk . It first comes to rest at spring extension k ks mg k A mg k −= 2 bg . Almost immediately at this point it
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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