A company selling a type of spring makes the following claim: "The elastic potential energy that the spring is capable of storing for a given compression distance does not decrease, even after the spring compresses and/or stretches hundreds of times." The students in a physics class have decided to test the company's claim.

(a)

i. State a basic physics principle or law the students could use in designing an experiment to test the company's claim.

ii. Using the principle or law stated in part (a)i, determine an equation for the elastic potential energy stored in the spring in terms of quantities that can be obtained from measurements made with equipment usually found in a school physics laboratory.

(b) Design an experimental procedure the students could use to collect the data needed to test the company's claim. Assume equipment usually found in a school physics laboratory is available.

In the table below, list the quantities and associated symbols that would be measured in your experiment and the equipment used to measure them. Also list the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need additional rows, you may add them to the space just below the table.

Quantity to Be Measured	Symbol for Quantity	Equipment for Measurement

Describe the overall procedure to be used, referring to the table. Provide enough detail so another student could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the symbols defined in the table and/or include a simple diagram of the setup.

(c) Explain how the students should analyze the data to determine whether the company's claim is true, i.e., whether the energy stored by the spring for a given compression distance does not decrease after the spring has compressed and/or stretched hundreds of times.

(d) The students also investigate two springs, springAand springB, made by another company. The students hang springAvertically, attaching blocks of various known masses from the bottom end of the spring and measuring the total length of the spring for each block. The students graph the spring length as a function of hanging mass and draw the line of best fit, as shown below.

i. The students follow the same procedure using springB, which has the same equilibrium length as springAbut stores more energy than springAfor a given displacement. On the graph above, sketch what the line of best fit could look like for the data obtained using springB.

oscillation. The students then repeat the procedure, but pull the block down by 2cm instead of 1cm. For which initial displacement, if either, is t greater?

t is greater for the 1cm displacement.t is greater for the 2cm displacement.t is the same in both cases.

Briefly explain your reasoning.