Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spring equation proof and work question

  1. Oct 19, 2004 #1
    A particle is attached between two identical springs on a horizontal frictionless table. Both springs have spring constant k and are initially unstressed.

    | \
    | \
    | /
    | /

    a) If the particle is pulled a distance x along a direction perpendicular to the initial configuration of the spring, show that the force exerted by the springs on the particle F=-2kx(1-L/(sqrt(x^2+L^2)))i (where L is the vertical distance of each spring at rest)

    b) Determine the amount of work done by this force in moving the particle from x=A to x=0

    On part a)

    I got that the 2 is there since there are two springs. The L/(sqrt(x^2+L^2) is the sin of the angle between the a spring and the vertical. Where does the (1-) comes from? Also how do I tie the equation together, after figuring out all the parts?

    On part b)

    Do I have to integrate f(x) as x=A goes to x=0?

    Thank you
  2. jcsd
  3. Oct 19, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Calculate the stretch of one spring from its equilibrium length of L. (This is where you'll see the "1-" term.)
    Only the horizontal component of that force survives in the net force.
  4. Oct 19, 2004 #3
    Thank You ! I did not realize that the vertical components cancel out!

  5. Dec 15, 2004 #4
    Need Explanation

    I still don't understand how the problem will work.... could you explain with a few steps how to solve both parts? :redface:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook