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Work done given force as a function of position

  1. Nov 20, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the amount of work done between points x1 and x2.
    Force at x1: F=ax1
    Force at x2: F=ax2
    2. Relevant equations
    F=ma
    W=F (dot product) S
    3. The attempt at a solution
    W=ax2*(x2-x1)
     
  2. jcsd
  3. Nov 20, 2016 #2

    Simon Bridge

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    Welcome to PF;
    Is the problem statement exactly as it was written down in front of you?

    Guessing this is a 1D problem... so the equation for work comes out as:
    ##W = \int_{x_1}^{x_2}F(x)\;dx##

    Since the force exists only at two points, that means that ##F(x)=a\big(\delta(x-x_1)+\delta(x-x_2)\big)## ... then the integration comes out to 2a or 0 - not sure about when the delta function is right on the limit of the interval. It would depend if that is ##x\in (x_1,x_2)## or ##x\in (x_1,x_2]## or ##x\in [x_1,x_2)## or ##x\in[x_1,x_2]##...

    Maybe it means that ##F=ax## where a is a constant? Then the integration will work nicely.
    Or maybe it is something else.
     
  4. Nov 20, 2016 #3

    gneill

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    Staff: Mentor

    Mod note: Please note the change of thread title. It was changed in order to conform with the forum rules and posting etiquette for the homework forums.
     
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