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Find Work of a Force Acted on Mass over Frictionless Surface

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data
    A force given by [tex]F(x)=5x^3 (in \frac {N}{m^3})[/tex] acts on a 1-kg mass moving on a frictionless surface. The mass moves from x = 2m to x = 6m.

    a) How much work is done by the force?

    2. Relevant equations

    [tex]W=\int F_x from x_o to x_f [/tex]

    3. The attempt at a solution

    [tex]\int 5x^3 from x=2 to x=6 = 1.6*10^3[/tex]

    Is this correct?
     
  2. jcsd
  3. Sep 25, 2011 #2
    Looks correct to me, mrsteve.
     
  4. Sep 25, 2011 #3
    Also, if the speed of the mass is 2 m/s @ x=2 what is the speed at x=6?

    [tex]KE=\frac{mv^2}{2}[/tex]

    [tex]1600=\frac{(1)(v^2)}{2} => v=5.6*10^1 = 60 m/s[/tex]

    Would that be correct?
     
  5. Sep 25, 2011 #4
    The book has 2,000 J. I suppose that's because there's only 1 significant digit in mass = 1kg?

    [tex]1.6 *10^3 => 2 *10^3[/tex]
     
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