In an experiment, students are to calculate the spring constant k of a vertical

Question

In an experiment, students are to calculate the spring constant k of a vertical spring in a small jumping toy that initially rests on a table. When the spring in the toy is compressed a distance x from its uncompressed length L and the toy is released, the top of the toy rises to a maximum height h above the point of maximum compression. The students repeat the experiment several times, measuring h with objects of various masses taped to the top of the toy so that the combined mass of the toy and added objects is m. The bottom of the toy and the spring each have negligible mass compared to the top of the toy and the objects taped to it.
(a) Derive an expression for the height h in terms of m, x, k, and fundamental constants.
With the spring compressed a distance of x = 0.020m in each trial, the students obtained the following data for different values of m.

m(kg) h(m)
0.020 0.49
0.030 0.34
0.040 0.28
0.050 0.19
0.060 0.18
(b) What quantitites should be graphed so that the slope of a best-fit straight line through the data points can be used to calculate the spring constant k?

Explanation / Answer

a. PE=Work done by spring mgh=.5kx^2 h=.5kx^2/(mg) b. height and 1/Force(1/mg)

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