AP Physics Lab

Hooke's Law

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To investigate Hooke's Law.


Everybody knows that when you apply a force to a spring or a rubber band, it stretches. A scientist would ask, "How is the force that you apply related to the amount of stretch?" This question was answered by Robert Hooke, a contemporary and rival of Isaac Newton, and the answer has come to be called Hooke's Law.

Hooke's Law says that the stretch of a spring from its rest position is proportional to the applied force (or as the engineers put it: stress is proportional to strain). Symbolically,

F = kx

where F stands for the applied force, x is the amount of stretch, and k is a constant that depends on the "stiffness" of the spring, often called the "spring constant".

Hooke's Law, believe it or not, is a very important and widely-used law in physics and engineering. Its applications go far beyond springs and rubber bands. The chair in which you are sitting supplies the upward support force to keep you from falling by flexing (according to Hooke's Law) until it can supply an upward support force equal to your weight. The floor beneath your feet works the same way.

You can investigate Hooke's Law by measuring how much known forces stretch a spring. A convenient way to apply a precisely-known force is to let the weight of a known mass be the force used to stretch the spring. The force can be calculated from W = mg. The stretch of the spring can be measured by noting the position of the end of the spring before and during the application of the force.

Modern computer software takes just about all of the drudgery out of data analysis. You can add calculated columns to a Graphical AnalysisTM data table much as you would in a spreadsheet. and drawing graphs is a snap - or rather, a click!.


small springs

rubber band

ring stand

ring-stand clamps


spring scale

ruler or meter stick

set of known masses

Graphical AnalysisTM software

apparatus diagram

Safety Notes:


  1. Assemble the apparatus as shown in the diagram at right. Be sure to clamp the ring stand to the lab table, or weight it with several books.
  2. Some springs tend to be "clenched" - their coils are pressing against each other, and it takes a small force to simply get the spring to the point that it will begin to stretch. If this is the case, you may want to hang a small mass (20 g - 50 g) from the spring initially and consider that to be the spring's starting position.
  3. Spend a little mental effort considering how you are going to measure the stretch of the spring precisely. Making a small pointer out of a bent paper clip and fixing it to the end of the spring has worked well for me in the past.
  4. Hooke's Law data table setupThe data that you will need to record are the rest position of the spring (same for each trial), stretched position of the spring, and the total mass hanging from the spring. To set up a data table (a sample is shown at right):
    1. Open the Graphical AnalysisTM program.
    2. Label the first column to hold the rest position of the spring. I used Xo in the example at right.
    3. Label the second column to hold the stretched position.
    4. Add a column to the data table for the hanging mass.
    5. Add a data column to hold the stretch of a spring (X - Xo). In the example, I have converted this value to meters - the actual formula is "=(X-Xo)/100".
    6. Add a data column to hold the force used to stretch the spring, which is the weight of the masses that you used. The formula used in the sample spreadsheet is "=mass*9.81/1000", which gives the force in Newtons.
    7. Graph force (horizontal axis, since this is the quantity you change directly - the independent variable) vs. stretch (vertical axis, since this is the dependent variable)
    8. Change the axes to display a force vs. stretch graph.


  1. For each trial, record the starting position of the spring (before hanging the mass) and the ending position of the spring (while it is being stretched), and the total mass. (For most of our springs, starting with 50 gm and proceding in 50 gm increments will be fine, but use some judgement and keep your eye on the graph.)
  2. Add a new data set (and a new graph) to Graphical AnalysisTM, and repeat the process for another spring, and a rubber band.


  1. You should be able to estimate the uncertainty in measuring the rest and stretched positions of the spring - and justify your estimate. You can then calculate the uncertainty in the stretch calculation. The manufacturer of the hooked masses we use guarantee that they are within 2% of the "real mass", and we will take their word for it. Add error bars to your graph.
  2. If the data points look like a straight line, you can simply add a best fit regression line and regression statistics to the graph - otherwise, you will need to try a curve fit of some type.

Conclusions & Questions:

  1. Do your results confirm or contradict Hooke's Law? Please elaborate.
  2. What measurement contributed the most uncertainty to your results? What could be done to improve it?
  3. What is the value of the spring constant, k, for each of your springs? Show a sample calculation, please.


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BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Measurement-> this page

last update September 13, 2002 by JL Stanbrough