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: Simple problem using Work-Energy Theorem

  1. Nov 2, 2006 #1
    Take Two: problem using Work-Energy Theorem

    The only force acting on a 1.5 kg body as it moves along the positive x axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.
    (a) What is the velocity of the body at x = 4.0 m?
    (b) At what positive value of x will the body have a velocity of 5.0 m/s?

    WebAssign says that this problem uses concepts from the sections on Work Done by a Spring Force and Work and Kinetic Energy. I did not see how spring concepts were relevent, so I ignored them, though when I evaluated the integral, it looked a lot like a spring.
    I got part (b) correct, but I'm down to my last response for part (a). Can someone tell me if this looks all right?

    [tex]W=\int{F(x)dx} = \int{-6xdx} = -6\frac{x^2}{2} = -3x^2[/tex]
    I evaluated the integral between x_i=3 and x_f=4 to get [tex]W = -3(4^2)-(-3)(3^2) = -21[/tex]

    [tex]W=\Delta K=\frac{m}{2}(v_f^2-v_i^2)[/tex]
    so [tex]\frac{2W}{m}+v_i^2=v_f^2[/tex]
    so [tex]v_f = \sqrt{36} = 6m/s[/tex]

    Last edited: Nov 2, 2006
  2. jcsd
  3. Nov 2, 2006 #2


    User Avatar

    Your solution is correct. The equation F = -kx, where x is the displacement, is typical of a spring.
  4. Nov 2, 2006 #3
    Thank you very much; getting a fairly simple problem wrong four times in a row does something to a person's self-confidence.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook