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**1. Question**

Given an idea spring with constant K, a mass of M is dropped onto the spring from a height of H1. The spring compresses D distance.

We take the mass off, and drop the mass again at a height of H2, where H2 is significantly greater than H1. This time, will the spring compress a greater distance or the same distance?

## Homework Equations

F = - k x

and Conservation of energy:

U = mgh, E

_{s}= ½kx

^{2}, where E

_{s}is elastic potential of spring

U = E

_{s}

**3. Attempt at solution**

So if we think about it only in terms of F = -kx, then no matter how high we drop the mass, it should compress the same distance D, because F (gravity) remains the same.

But if we consider it from an energy perspective, then U (gravitational protential) would be greater if the height is greater. And thus the compression must also be greater to match this greater potential energy.

So which one is correct?