1. Not finding help here? Sign up for a free 30min 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!

K in Hookes Law vs. Spring Potential Energy

  1. Mar 7, 2006 #1
    Today in physics class we were discussing the conservation of energy using a ball on a spring as the example. When the instructor completed the problem one of the students stated that the value of K (spring constant) that we found was different (by a factor of 2) than the value of K calculated using Hooke's Law. The instructor could not figure out why the values of K were not the same. Why are they different?

    Potential Energy(before)=Potential Energy (after)
    (1/2)kx^2+mgh = (1/2)kx^2+mgh
    ball on spring at rest = ball on spring extended

    ---------- = k is not equal to k= F/delta h
  2. jcsd
  3. Mar 7, 2006 #2


    User Avatar
    Homework Helper

    You can equate the sum of these Potential Energies only if KE = 0.
    This will occur at the bottom of the bounce and at the top of the bounce.
    [tex]\frac{1}{2} k x_{bottom}^2 + m g h_{bottom} = \frac{1}{2} k x_{top}^2 + m g h_{top}[/tex]
    suppose the spring was unstretched at the top, so x_top = 0 ;
    suppose we measure height from the bottom , so h_bottom = 0 .
    Then : (1/2) k (x_bottom)^2 = m g h_top
    => k = 2 m g h_top / (x_bottom)^2 = 2 m g / x_bottom .

    The adjectives "top" and "bottom" are important here. The ball was moving
    - in particular, the acceleration was NOT = 0 in either location.

    The Force by the spring when the ball was at the bottom was
    F = - k s = - [2 m g / x_bottom] x_bottom = - 2 m g (upward).

    The Force by the spring when the ball was at the top was zero.
    The average Force by spring during this motion was F_average = - m g .

    The form to remember is F = - k s , which will remind you that
    s is the stetch of the spring from its "relaxed" length.
    (not to be confused with horizontal coordinate "x" , nor with height)
  4. Mar 8, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    There are two versions of Hooke's law:
    [tex]T = \frac{kx}{L}[/tex]

    [tex]F = kx[/tex]
    Each equation will yield a different value of k for a given tension or (after integration) potential energy.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: K in Hookes Law vs. Spring Potential Energy