I with Mechanical Energy, please

[DKPeridot20]

I can't copy the pictures but here's a "reproduction" of one:

Wall----------box
(There's a spring attached to both the wall and the box.)

The box is resting on a frictionless surface. The spring has been stretched to the right by a distance given and it's about to be released. It will proceed to oscillate. We're including only the conservative force of the elastic spring so the mechanical energy is conserved. Rank the figures (there are really 8) from greatest to least on the basis of mechanical energy.

I thought I had the right equation for Mechanical Energy (E) :
Ei = Ui + Uf and that Uf was 0 so Ei = Ui which is 1/2kx^2 but I'm not getting the right answer. The figures have some-value in N/m over the spring, some-value in meters for the stretch, and the mass of the box in kg. I'm under the impression that the mass of the box has no effect on the mechanical energy.
However, I also see this equation E = U + K. Should I be finding U with
1/2kx^2 and K with 1/2mv^2 and adding them? What should I do?

 

[*melinda*]

Actually, your total mechanical energy, denoted by E, is a constant in a conservative system.

E = U + K, where U = potential energy, K = kinetic energy. Your formulas for U and K are correct as well.

The Ei = Ui + Uf comes from conservation of energy, but what you have is not quite complete.

$$E_{initial} = E_{final}$$

substituting with what E is actually composed of, we get:

$$U_{initial} + K_{initial} = U_{final} + K_{final}$$

This set-up is very useful in a before and after situation.

I'm not quite sure what your question is asking. It sounds like you need to compute total mechanical energy, E, eight times.

Also, Newtons/meter (N/m) is the unit for your spring constant.

When you do the computations, make sure your answer is in the correct units. It's a good way to check that you did the problem right.

 

[DKPeridot20]

Does E = U + K give me the total mechanical energy?

If that is so, in order to find K I have to be able to plug in a value for v. With the info I was given (k, x, and m) I should be able to calculate v, right? How do I rearrange 1/2mv^2 to solve for v? (or do I do that at all...)

 

[daniel_i_l]

Since in the beginning the mass had no speed, the total mechanical energy is equal to 1/2kx^2, were x is the distance given. Let's call the total energy Ut. Now at every step of the way you know that Ut = 1/2kx^2 + 1/2mv^2.
If you are given K and x then you know that:
Ut - 1/2kx^2 = 1/2mv^2 and so
sqrt(2*(Ut - 1/2kx^2)/m) = v

 

[DKPeridot20]

Thanks very much.