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21 January, 15:18

If a spring stretches 3 cm when a 2 kg mass is hung from it, how far will it stretch when a 6 kg mass is hung from it? Show work. Use hooke's law.

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  1. 21 January, 15:34
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    displacement (x2) = 0.09 meters

    Explanation:

    let the force by the spring be Fs, force due to gravity be Fg, displacement when 2 kg mass is hung be x1 and the displacement when 6 kg mass is hung be x2.

    take the upward direction as positive.

    then, for both cases:

    Ftot = Fs + Fg = 0, the block gets to a complete stop.

    for when 2 kg mass is hung:

    Fs = Fg

    k*x1 = m1*g

    k = m1*g/x1 = [ (2) * (9.8) ] / (0.03) = 653.3 N/m

    then because k remain constant since we using the same string,

    for when 6 kg mass is hung:

    Fs = Fg

    k*x2 = m2*g

    x2 = [ (6) * (9.8) ] / (653.3) = 0.09 meters

    therefore, the string will stretch for a displacement of 0.09 meters when the 6 kg mass is hung.
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