This is more of a conceptual problem. How would you determine the spring stiffne

Question

This is more of a conceptual problem. How would you determine the spring stiffness of a "dynamics plunger cart" with a built in spring? I need 2 experiments in which one or both need to utilize the Energy Priciple. Only the following items are available: roller track, dynamics cart, aluminum block, mass sets, meter stick, and motion sensor. Please note the following:
*What measurements need taken?
*Explain the experiment.
*How would I use the measurements in a calculation?
*Can you come up with a single physics problem using 1 of the experiments?
*A sketch of the setup and a full solution strating from a fundamental principle would be nice :)

Physics has turned my brain to mush so any help is appreciated. Thanks

Explanation / Answer

attach the spring to the cart, on the track. Find the equilibrium position, using the meter stick, write this down. Now pull this cart from this equilibrium position and write down how far you displace the cart. Using the motion sensor to find the maximum velocity the cart reach, and the weight of the cart, you can find the KE=(.5)mv^2, this can be set equal to the equation for work done by and spring which I believe is W=(.5)kx^2. Find k which will be the stifness of the spring. Repeat this whole process with an addition mass from the mass set, but don't forget to add the addition mass to the KE eqution. This experiment shows that the potential energy from displacing the cart from the springs equilibrium position is equal to the kinetic energy of the cart after you release the cart. Just to make sure I've got the measurements down for you: you need the carts mass (with and with out the additional mass), its maximum velocity from the motion sensor, the equilibrium "length" of the cart attach to the spring, and the displacement "length" of the cart both times you run the experiment. Example problem let the mass of the cart be 1 kg, its equilibrium position be 1 m. You stretch the cart to 1.25 m, and let it go. It will oscillate back and forth, and you find that the maximum velocity was 2 m/s... m = 1 kg v = 2 m/s x = (1.25 m) - (1 m) = .25 m KE = (.5)mv^2 = W = (.5)kx^2 k = (mv^2)/(x^2) = 64 N/m

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