Calculating Vertical Height from Spring Potential Energy

[shotgunbob]

Homework Statement

A .3 kg mass rest on top of a spring that has been compressed by .04 m. Neglect any frictional effects, and consider the spring to be massless. Then, if the spring has a constant k equal to 2000 n/m, to what height will the mass rise when the system is released.

Homework Equations

PE(spring)= (1/2)kx^2

KE= 1/2mv^2

The Attempt at a Solution

I got the PE in the system to be 1.6 J. I am not sure how this would translate into a vertical height. Thanks in advance!

 

[Doc Al]

I got the PE in the system to be .48 J.

How did you arrive at this?

I am not sure how this would translate into a vertical height.

Consider gravitational PE.

 

[shotgunbob]

How did you arrive at this?


Consider gravitational PE.

I messed up, used PE=1/2kmx^2 for some reason. I got 1.6 J.

And in Grav. PE, the H should be the same as the H I am looking for so PE(grav)=PE(Spring).
Or maybe I am missing something.

 

[shotgunbob]

Ok I got .54 m when i put Pe(grave)=Pe(spring). Thats an answer choice! Is this correct?

 

[Doc Al]

It depends on what the height is being measured with respect to. The initial position on top of the spring? Or the compressed position?

 

[shotgunbob]

I suppose its the top of the spring

 

[Doc Al]

I suppose its the top of the spring

That's what I would say.

 

[shotgunbob]

Thank you!