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Simple work and variable position question

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A one-dimensional force acts on a particle of mass m = 6.26 kg in such a way that its position is given by:

    x = 0.484t^3 - 33.6t

    Find W, the work done by this force during the first 1.49 s.


    2. Relevant equations
    W=F*s
    W=mgs
    Integration


    3. The attempt at a solution
    I just wanted to know whether I'm solving this correctly because I only have one more chance to input an answer in my online homework system (as those of you who have been helping me probably know by now. :frown:

    Anyhow, this is what I've done.

    W=Fs
    F=mg
    W=mgs
    **Because the position is variable but the mass and gravity are constant, we integrate the formula given, and we get:

    W=mg*∫x.dx= (.121t^4) - 16.8(t^2), from 0s to 1.49s

    We come to:

    W=mg*(-36.7)
    W=6.26*9.81*(-36.7)= (-2253.8) J

    Did I do this properly?
     
  2. jcsd
  3. Mar 12, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The problem does not say that the particle is subjected to gravity. F=ma, and the acceleration is second derivative of position. Find the force from the given x(t) function.

    ehild
     
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