Hooke’s Law

Ref: APlusPhysics: RPE Ch. 7

   Intro to Hooke’s Law
   Hooke’s Law Lab

HW: Video and Questions, APlusPhysics: Springs, due 1/6 at 3 p.m.
        Work and Power WS, due Friday at 3 p.m.


An interesting application of work combined with the Force and Displacement graph is examining the force applied by a spring. The more you stretch a spring, the greater the force of the spring… similarly, the more you compress a spring, the greater the force. This can be modeled as a linear relationship, where the force applied by the spring is equal to some constant time the displacement of the spring. Written mathematically:


F is the force of the spring in newtons, x is the displacement of the spring from its equilibrium (or rest) position, in meters, and k is the spring constant which tells you how stiff or powerful a spring is, in Newtons per meter. The larger the spring constant, k, the more force the spring applies per amount of displacement.

Hookes Law Graph

You can determine the spring constant of a spring by making a graph of the force from a spring on the y-axis, and placing the displacement of the spring from its equilibrium, or rest position, on the x-axis. The slope of the graph will give you the spring constant. For the case of the spring depicted in the graph at right, we can find the spring constant as follows:

Calculate k

You must have done work to compress or stretch the spring, since you applied a force and caused a displacement. How can you find the work done in stretching or compressing the spring? By taking the area under the graph. For the spring shown, to displace the spring 0.1m, we can find the work done as shown:

Hookes Law Work Calculation


See if you can use Hooke’s Law to determine the spring constant in the problem below:


PIA Podcast Episode 23: Star Wars, Newton’s Laws, and Springs!

lady_news_anchor_hg_wht Students have published the first Physics in Action podcast episode of season 3, featuring a look at physics in the Star Wars universe, a retro-styled look at Newton’s Laws of Motion, and an investigation into springs.  You can subscribe for free through iTunes, or download directly from the APlusPhysics.com website.  Great start to a new season, guys!


Subscribe for free through iTunes by clicking here.