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Math Help - Rearranging a Difficult Equation

  1. #1
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    Unhappy Rearranging a Difficult Equation

    Hi all,

    I've been trying (unsuccessfully!) to rearrange the following equation so that H is the subject:

    mgH = [k(H - L)^2] / 2

    (Where ^2 means squared.) I also have some test data which shows that if m = 50, g = 9.8, k = 40 and L = 20, H should equal 57.5, or thereabouts.

    I'm going to need the equation in a couple of hours and am stressing out, so any help you can offer would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by mothonthewall86 View Post
    Hi all,

    I've been trying (unsuccessfully!) to rearrange the following equation so that H is the subject:

    mgH = [k(H - L)^2] / 2

    (Where ^2 means squared.) I also have some test data which shows that if m = 50, g = 9.8, k = 40 and L = 20, H should equal 57.5, or thereabouts.

    I'm going to need the equation in a couple of hours and am stressing out, so any help you can offer would be greatly appreciated.
    mgH = \frac{k}{2}(H^2 - 2HL + L^2)

    mgH = \frac{k}{2}H^2 - kHL + \frac{k}{2}L^2

    0 = \frac{k}{2}H^2 - kHL - mgH + \frac{k}{2}L^2

    0 = \frac{k}{2}H^2 - (kL + mg)H + \frac{k}{2}L^2

    use the quadratic formula ... H = \frac{-b \pm \sqrt{b^2-4ac}}{2a} , where ...

    a = \frac{k}{2} , b = -(kL + mg) , c = \frac{k}{2}L^2
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  3. #3
    Super Member craig's Avatar
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    mgH = \frac{k(H - L)^2}{2}

    Multiply both sides by 2

    2mgH = k(H - L)^2

    Multiply out the brackets

    2mgH = k(H^2 - 2LH + L^2) = 2mgH = kH^2 - 2LkH + kL^2.

    You now have a quadratic, rearrange and solve for H.
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  4. #4
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    I must be dense for not seeing that. Internet strangers, you are my knights in shining armor!

    Thanks so much for your help.
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