Why is mgh equal to mgx in this conservation of energy problem?

[Lori]

Homework Statement

Homework Equations

W spring = 1/2kx^2
Ug = mgh

The Attempt at a Solution

I have the work in the above problem, but I'm kinda confused how there is any potential energy here besides the spring potential energy that we get in the final state. Why is mgh here mgx? why can h =x? in this case

 

[gneill]

I have the work in the above problem, but I'm kinda confused how there is any potential energy here besides the spring potential energy that we get in the final state. Why is mgh here mgx? why can h =x? in this case

mgh represents the change in gravitational PE for the hanging mass M. Assuming that the string is of fixed length, the block M's vertical motion must be equal in magnitude to block 2M's horizontal motion, hence Δh = Δx with the appropriate choice of coordinates.