1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Homework Helper
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted