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Total mechanical work, solving for x

  1. Dec 15, 2012 #1
    1. The problem statement, all variables and given/known data

    I understand the problem conceptually. I just need help solving for x, which is the hardest part of the problem for me.

    1/2mv^2 = 1/2kx^2 + umgx

    3. The attempt at a solution

    Not really sure how to solve this. I tried and tried to separate by x but nothing worked. Here are 1 of the attempts I suppose. I feel pretty stumped here.

    [tex]1/2mv^2 = 1/2kx^2 + umgx[/tex]
    [tex]1/2mv^2 - umgx = 1/2kx^2[/tex]
    [tex]\frac{mv^2}{k} - \frac{2umgx}{k} = x^2[/tex]
    ???
     
  2. jcsd
  3. Dec 15, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Looks like you've got a quadratic equation in x on your hands. Sound familiar?
     
  4. Dec 16, 2012 #3
    I thought a lot about how I couldn't expand x^2 + x.. but when you mentioned quadratic equation it came to me right now.. I'll get back to this once I get home.
     
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