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Force problem with equation! Please see question. Need help with this problem.

  1. Oct 13, 2012 #1
    1. The problem statement, all variables and given/known data

    A one-dimensional force acts on a particle of mass m = 4.48 kg in such a way that its position is given by:

    x = 0.221t^3 - 38.8t

    Find W, the work done by this force during the first 1.41 s.

    2. Relevant equations

    W = F * d
    F = ma

    3. The attempt at a solution

    dx/dt = v = 0.663t² - 38.8
    dv/dt = a = 1.326t

    At t = 1.41, we obtain approximately 1.87.

    Then...

    F = 4.48 * 1.87 ≈ 8.38

    So...

    W = 8.38 * (0.221 * (1.41)³ - 38.8(1.41))
    ≈ -453???

    That answer is wrong.
     
  2. jcsd
  3. Oct 13, 2012 #2

    TSny

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    Hello.

    Are you familiar with the "work-energy theorem" that relates work to kinetic energy?

    If not, you'll have to know how to use calculus to get the work done by a variable force.
     
  4. Oct 13, 2012 #3
    Then, this means I need to use this form? W = ½ * m * v²?

    Nevermind. You said I need to have the force expression .
     
  5. Oct 13, 2012 #4
    Hold up.. I need to use this form!

    W = ∫^(v = v_0,v_f) mv dv
    = mv_f²/2 - mv_0²/2
     
  6. Oct 13, 2012 #5

    TSny

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    Good.
     
  7. Oct 13, 2012 #6
    Then, I need to determine the derivative of the displacement equation. Then, find v(0) and v(1.41) [The velocity at t = 0 AND the velocity at t = 1.41]. Finally, I find the work done, right?

    This is what I have:

    4.48/2 * ((-37.5)² - (-38.8)²) = -222

    Am I on the right track?
     
  8. Oct 13, 2012 #7

    TSny

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    Yes. (You already wrote the answer for the derivative of x in your first post.)
     
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