# Mechanics problem involving work, spring and a-jack-in-the-box

Have you tried to draw a sketch of the problem?
It will help to figure out the relationship between the height in the gravitational PE and the displacement in the elastic PE. They are not the same.

Second, the elastic energy on the RHS does not look OK. It doesn't even have units o energy.

lewando
Homework Helper
Gold Member
@nasu-- he's using modulus, not spring constant.
@dumbledore-- did not say replace. I should have said h and x. Nasu is right--start drawing

@nasu-- he's using modulus, not spring constant.
Yes, I've got this.
No matter what λ is, the equation seems to be inconsistent.
I mean this:
λx^2/2l= mgh+ λx/l

If λ is in N, then λx^2/2l is N*m which is energy
However λx/l is in N and this is not energy.

lewando
Homework Helper
Gold Member
I see what you are saying. To be unit consistent the 3rd term should be the form of:

λ(...)2/2l, with (...) being an expression of length.

So Dumbledore211, visualize the spring going from a state of compression, to neutral (0 stored energy), to being stretched. This should help you figure out what to put into (...).