physics imperfect spring

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The force required to compress an imperfect horizontal spring an amount x is given by F= 150x+12x^3, where x is in meters and F in newtons.

If the spring is compressed 2.1 m, what speed will it give to a 4.0 kg ball held against it and then released?

  • physics imperfect spring -

    Work done = integral F dx
    = 150 x^2/2 + 12 x^4/4
    = 75 x^2 + 3 x^4
    =75 (2.1)^2 + 3 (2.1)^4
    = 389 Joules
    = (1/2) m v^2

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