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3 November, 11:23

a spring gun initially compressed 2cm fires a 0.01kg dart straight up into the air. if the dart reaches a height it 5.5m determine the spring constant of the gun

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  1. 3 November, 12:10
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    2697.75N/m

    Explanation:

    Step one

    This problem bothers on energy stored in a spring.

    Step two

    Given data

    Compression x = 2cm

    To meter = 2/100 = 0.02m

    Mass m = 0.01kg

    Height h = 5.5m

    K=?

    Let us assume g = 9.81m/s²

    Step three

    According to the principle of conservation of energy

    We know that the the energy stored in a spring is

    E = 1/2kx²

    1/2kx² = mgh

    Making k subject of formula we have

    kx² = 2mgh

    k = 2mgh/x²

    k = (2*0.01*9.81*5.5) / 0.02²

    k = 1.0791/0.0004

    k = 2697.75N/m

    Hence the spring constant k is 2697.75N/m
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