What is the slope of a force vs. distance graph?

  1. JJBladester

    JJBladester 286
    Gold Member

    1. The problem statement, all variables and given/known data
    What is represented by the slope of a Force vs. Distance graph?

    Also, if I had a Force vs. Distance graph and knew my initial velocity was some value, how would I go about finding the velocity at any distance along the way?

    2. Relevant equations
    F=ma

    W=Fd

    v=d/t

    3. The attempt at a solution
    I know that the area under the curve of a Force vs. Distance graph represents work (W=Fd). Is the slope of a Force vs. Distance graph *acceleration*?
     
  2. jcsd
  3. LowlyPion

    LowlyPion 5,328
    Homework Helper

    Consider the units.

    Units of Force = Newtons
    Units of distance = meters

    So the slope of an F/D plot would be N/m wouldn't it?

    What do you know that has N/m as its units? Does anything spring to mind?
     
  4. JJBladester

    JJBladester 286
    Gold Member

    N = m∙kg/s²
    m = m

    N/m = kg/s² = surface tension (slope of Force vs. Distance graph)

    Ok thanks for helping me think. Rise over run... Units of y axis over units of x axis. That makes sense.

    For the other part of my question, I think I've got it under wraps. To find the velocity at a certain distance of a Force vs. Distance graph, I need to:

    Calculate area S below the graph.
    This area is work, because it is equal to
    S = integral of F(x)dx = integral of d(work)

    Using conservation of energy I can now find the velocity:
    S = Work = KE = 1/2 mv²
     
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