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20 June, 01:40

An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 7.0 g when brought to rest. Let M be the total mass of the elevator and passengers. Express your answer in terms of the variables h, M, and appropriate constants.

k = ?

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  1. 20 June, 02:00
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    Acceleration will be in upward direction due to force by spring in upward direction. Let maximum compression be x.

    maximum force = k x - Mg

    k x - Mg = 7Mg

    kx = 8Mg

    After falling by height h, compression in spring is x

    1/2 k x² = Mg (h + x)

    1/2 x 8Mg x = Mgh + Mgx

    4Mgx = Mgh + Mgx

    3 Mgx = Mgh

    x = h / 3

    kx = 8Mg

    k h/3 = 8Mg

    k = 24 Mg / h
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