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Derivative of Force in terms of distance?

  1. Sep 29, 2015 #1
    Hi,

    Suppose I have a function on a graph with a vertical axis is Force and the horizontal axis is distance. Then the area under the curve is given by F*d = Work = Energy, correct? If so, then what would the slope of the curve represent? F/d = ?

    Thank you.
     
  2. jcsd
  3. Sep 29, 2015 #2
    It will give you the force per unit distance if your function is linear in x(like in a spring).
    Otherwise it will give you the gradient of the force as a function of x if your function is non-linear(like coulomb's law).
    To know more about gradient https://en.wikipedia.org/wiki/Gradient.
     
  4. Sep 29, 2015 #3

    Ssnow

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    Gold Member

    1. The area under the curve in general is given by ## \int_{x_{i}}^{x_{f}}F(x)d\,x =W ## , if ##F## is constant then ## W=F\Delta x## (I suppose always ## \cos{\theta}=1##)
    2. The slope of the curve is ## \frac{d}{dx}F(x) ## and represent how the force grow or decrease respect the distance, as example if ## F_{Hooke}(x)=-kx ## then ## \frac{d}{dx}F_{Hooke}=-k## is the elastic coefficient ...
     
  5. Sep 29, 2015 #4

    CWatters

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    Essentially the slope gives you the spring constant at that point.
     
  6. Sep 30, 2015 #5
    Thank you all. I will revisit this topic soon. I need to understand a few prerequisite concepts first, for which I need to create a new thread.
     
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