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Bridging connection between Newton's second law and Work

  1. Mar 29, 2014 #1
    1. The problem statement, all variables and given/known data

    I'm trying to bridge F =ma to m/2(dv2/dx). It was shown in the course book I have but there's a huge disconnection in the steps.

    3. The attempt at a solution

    F =ma = m.(dv/dt) = m(dv/dx . dx/dt) = mv(dv/dx). Where do I take it from here?
  2. jcsd
  3. Mar 29, 2014 #2

    rude man

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    Formally differentiate d/dx(v^2). What do you get?
  4. Mar 29, 2014 #3
    Multiply both sides of your equation by dx to get

    F dx = mv dv

    Integrate both side, what do you get?
  5. Mar 29, 2014 #4
    Both sides?
    I could arrive at the conclusion if I were to integrate only the left argument.

    ∫F(x).dx = ∫ma.dx = ∫m(dv/dt).dx = ∫m(dv/dx . dx/dt) .dx = ∫m(dv/dx . v).dx = ∫m*dv.v = ∫mv.dv = m∫dv . ∫v.dv = m (0.5v2) = 0.5mv2 + C
  6. Mar 29, 2014 #5
    derivative of v2 = 2v(dv/dx)
    Last edited: Mar 29, 2014
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