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How to work with non-constant forces?

  1. Dec 16, 2012 #1
    1. The problem statement, all variables and given/known data
    A 1 kg. block at rest is pushed with a force of x^2, where x is the displacement (in meters). What is the speed of the object at 10 meters?


    2. Relevant equations
    F = ma


    3. The attempt at a solution
    I did x^2 = ma and found the acceleration by dividing the mass which is just 1. So a = x^2. I integrated to find the velocity function so I got [(x^3)/3] + C. It's initially at rest so at x = 0, the velocity is 0 which means C = 0 so I can get rid of that. If I plug in 10 meters into the velocity equation: (10^3)/3 I get 333.3 m/s. Solution says this is wrong but I have never worked with integration before so I'm not sure how to do this.
     
  2. jcsd
  3. Dec 16, 2012 #2

    CAF123

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    Gold Member

    I would consider using the Work energy theorem.
     
  4. Dec 16, 2012 #3
    So the total work done is F*d. So that's 10x^2. Initial velocity is 0 at rest so change in KE = Work done: (1/2)mv^2 = 10x^2. Solve for v and it's sqrt(20)*x. At x = 10, I get v = 10sqrt(20). Is this right?
     
  5. Dec 16, 2012 #4

    Doc Al

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    Staff: Mentor

    The force is not constant. You'll have to integrate: W = ∫F(x)dx
     
  6. Dec 16, 2012 #5
    So the total work done is (x^3)/3 ? So can I do:

    (x^3)/3 = (1/2)mv^2
    666.66 = v^2
    v = 25.8 m/s ?
     
  7. Dec 16, 2012 #6

    Doc Al

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    Staff: Mentor

    Looks good to me.
     
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