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Work done from F vs x graph?

  1. Oct 24, 2017 #1
    1. The problem statement, all variables and given/known data
    x1= -2, x2= 2

    F1= 1, F2= -2

    Graph in uploaded image

    2. Relevant equations
    w= F* del x* cos(theta)

    3. The attempt at a solution
    I am trying to find the area under the points of F and x but it has an irregular shape and i dont know what to do? Should i do w= (f1-f2)(del x)?
     

    Attached Files:

  2. jcsd
  3. Oct 24, 2017 #2
    The general form of work is
    $$W=\int_{x_{1}}^{x_{2}}\mathbf{F}\cdot d\mathbf{x}$$
    Thus if you have a graph of ##F## vs. displacement. The work is the area under the curve from the staring position ##x_{1}## to the final position ##x_{2}##.
     
  4. Oct 24, 2017 #3

    ehild

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    Homework Helper
    Gold Member

    No, the applied force changes with the position. And both the displacement and the force are along the x axis.
    The work is equal to the area between the graph of force and the x axis. You have to calculate the area of both triangles, the blue one and the yellow one. In case of the blue triangle, both the force and the displacement are positive, so cos(theta)=? W1=?
    In case of the yellow triangle, the force is negative, the displacement is positive, so cos(theta)=? W2=?
    The whole work is the sum of the works done from x=-2 to x=0 (W1) and from x=0 to x=2 (W2) .
    upload_2017-10-25_6-13-19.png
     
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