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?

Your group will need to make TWO sets of measurements, one with a spring held vertically, one with a spring held horizontally. Your group should use the same spring for both measurements.

However, you can coordinate with the other group at your table: while group A does the horizontal measurements on its spring, group B does the vertical measurements on its spring; then, the two groups switch.

Acquire one small silver spring. Measure its mass and its length as it lies horizontally at rest on the table.
(Horizontal)
Arrange clamps and bars as shown in the first diagram above so that you can hang the spring from a horizontal bar. Measure the length of the spring as it hangs by itself; call this L_vert.
Place 7 various weights, ranging from 0 to 150 grams, on the bottom of the spring. Measure the length of the spring for each case. Compute the distance the spring has stretched from L_vert. Include uncertainties in this "distance stretched".
Calculate the force exerted by the spring in each case. Make a neat table of all your measurements and calculations.
(Vertical)
Now place a track and pulley on your table, as shown in the second diagram above, so that you can measure the force of a spring when it is stretched horizontally. Make a new set of measurements. You may find that you can't go up to 150 grams -- in that case, pick 7 masses which span a smaller range.
(When both sets have been acquired)
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. You should have one graph for the spring hanging vertically, and (on a different piece of paper) a graph for the spring lying on its side.
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.
Is the "spring constant" of your spring the same for both orientations? That is, does the value derived when the spring is vertical agree (within the uncertainties) with the value derived when the spring is horizontal?
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"?

In order to earn full credit for today's activity, your group must turn in, in hardcopy on paper, the following. Neatness counts.

table of horizontal measurements
table of vertical measurements
graph based on horizontal measurements
graph based on vertical measurements
values of the spring constant, derived from both graphs, including uncertainties in each case
a statement about the two values -- do they agree within the uncertainties or not?
a statement about the spring constant of your spring compared to those of other groups -- do they agree within the uncertainties or not?

Extra

At the center table, I will set up a track tilted at θ degrees (I'll write the exact value on the board in class). 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 
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