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 small silver spring. Measure its mass and its length as it lies horizontally at rest on the table.
2. 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 Lvert.
3. 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 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 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.

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. 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.

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 spring is vertical agree (within the uncertainties) with the value derived when the spring is horizontal?
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 15 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.

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

+/- 4 cm                    +2

+/- 6 cm                    +1
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