The force exerted by a spring

If you try to stretch a spring, it will pull back against you. The farther you stretch the spring, the harder it pulls back. Can you make this simple description more quantitative?

  1. Acquire one large spring. Measure its mass and its length as it lies horizontally at rest on the table.
  2. Arrange clamps and bars as shown above so that you can hang the spring from a horizontal bar. Your spring is larger in diameter at one end than the other; to start, place the wide end at the top and the narrow end at the bottom. Measure the length of the spring as it hangs by itself; call this Lvert.
  3. Place 7 various weights, ranging from 0 to 200 grams, on the bottom of the spring. Measure the length of the spring for each case. Compute the distance the spring has stretched from Lvert. Include uncertainties in this "distance stretched".
  4. Calculate the force exerted by the spring in each case. Make a neat table of all your measurements and calculations.

  5. Now turn your spring upside down, so that it hangs from the narrow end. Repeat your measurements.

  6. Make graphs, each on its own piece of good graph paper. Each graph should show force exerted by the spring as a function of the distance by which the spring has been stretched beyond Lvert. Each person must make at least one graph. You should have at least one graph for the spring with wide end up, and at least one graph for the spring with wide end down. Yes, this may mean two versions of one graph.
  7. Use your graphs to compute the "spring constant" or "force constant" of your spring. Include uncertainties, and make sure the units of your values make sense.
  8. Is the "spring constant" of your spring the same for both orientations? That is, does the value derived when the wide end is up agree with the value derived when the narrow end is up?
  9. Walk around and talk to at least 3 other groups. Write down their spring constants (with uncertainties) and compare them to yours. Are all the springs in class today "identical"?

Extra

At the center table, I will set up a track tilted at 30 degrees. We will attach your spring to the track so that it lies along the track, and then attach to the lower end a cart of mass m (I'll provide the actual mass during the class period).

How long will your spring be when it comes to rest, supporting the car on this tilted track? Make a prediction. 



  If your prediction is         you gain
    within                    bonus points
  ------------------------------------------
     +/- 2 cm                    +3

     +/- 4 cm                    +2

     +/- 6 cm                    +1 
  ------------------------------------------

Extra extra

  1. Why is the spring longer when it is hanging than when it is lying on the table?
  2. Suppose you were to hang a mass M, equal to the mass of your spring, from your spring. How far would it stretch? Call this the "expected stretch".
  3. Compare this distance to the distance the spring actually did stretch when you hung it by itself. Which is larger? By how much?
  4. Explain in your own words why you think the actual stretch is not equal to the "expected stretch".