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15 January, 22:41

A spring has a constant k = 10.32 N/m and is hung vertically. A 0.400kg mass is suspended from the spring. What is the displacement of the end of the spring due to the weight of the. 400kg mass?

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  1. 15 January, 23:06
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    displacement (x) = 0.003798 meters

    Explanation:

    from the fact that the string is hung vertically we can deduce that:

    Total force acting on the mass = Fs (by spring) + Fg (by gravity)

    where

    Fs = k*x, x is the displacement ...

    Fg = m*g

    then:

    Ftot = m*a, but a = 0 m / (s^2) because the mass becames stationary.

    Ftot = 0

    Fs + Fg = 0

    by direction, take down as negative.

    Fs - Fg = 0

    k*x = m*g

    x = m*g/k = [ (0.400) (9.8) ] / (10.32)

    = 0.3798 meters
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