- #1

evanave

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If you place a mass on a spring, the change in potential energy of the mass should equal the stored potential energy in the spring, correct?

so PE = U

PE = mgh = Fx (F = force = mg, h = change in spring length x)

U = 1/2 k*x^2

Hooke's law: F=-kx, so k=F/x

U= 1/2 (F/x) * x^2 = 1/2 Fx

setting PE = U

Fx = 1/2 Fx

Clearly I'm doing something wrong...

(The original problem is the following...)

5*10^5 Newton force supported by two springs (k_1 = 5.25 E^5, k_2 = 3.6 E^5 N/m)

The second spring is shorter by 0.5 meters (spring 1 compresses 0.5 meters before the weight hits spring 2). Find the spring compression and find the work done by the springs.

So I said F = k_1 x_1 + k_2 (x_1 -0.5) and got x_1 = 0.768 meters, and x_2 = 0.268 meters

So the restoring force F = 5.25*10^5*0.768+3.6*10^5*0.268 = 5*10^5 Newtons (cool, this checks out)

But for the work, change in PE should equal U

But the change in PE of the mass (5*10^5 * 0.768 meters) is not equal to the sum of spring potential energies (1/2 k_1 (x_1)^2 + 1/2 k_2 (x_2)^2 )

Thoughts? Thanks for taking a look!