Block moves down incline, hits spring, find spring constant

[jybe]

Homework Statement

[/B]
The block, initially at rest, slides down the ramp and compresses the spring 0.03 m.

Theta = 30 degrees
L = 1.25 m
M of block = 2 kg
Δx = 0.03 m

1) Write the expression for the initial and final energy states

2) Find the spring constant K

Homework Equations

mgh = 0.5kx²

The Attempt at a Solution

Can I say that when the block compresses the spring and comes to rest, h=0, in which case I wouldn't have to include mgh on the right hand side of the energy equation?

mg(L*sin theta) = 0.5*k*(x²) and solve for k...

This seems too easy, am I approaching this wrong?

 

[Doc Al]

Looks good to me!

 

[scottdave]

I would clarify. Is it saying it comes to rest at Δx, or is it saying that Δx is the maximum compression (more likely scenario)? What do you expect is going to happen from your real life experiences?

It appears you are saying, it "just" is at rest there (before it recoils), so kinetic energy is zero right at that point.

 

[Doc Al]

Is it saying it comes to rest at Δx, or is it saying that Δx is the maximum compression (more likely scenario)?

While it never hurts to ask for clarification, the point of max compression is when it comes to rest (momentarily). That's what I assumed was being described.