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## Homework Statement

A 14 kg box slides 4.0 {\rm m} down the frictionless ramp shown in the figure , then collides with a spring whose spring constant is 210 N/m.

a)What is the maximum compression of the spring?

b)At what compression of the spring does the box have its maximum speed?

## Homework Equations

PEspring = (1/2)k(s)^2

Fsp = -ks

## The Attempt at a Solution

I thought this was a simple conversion of potential energy to a springs potential energy. So I tried mgh = (1/2)ks^2 where h=4sin(30). That gets me s=1.6 which is not correct. Do you have to take into account the force of gravity on the spring because it is not horizontal?

I haven't started the second part but I believe you would use a free body diagram, and the maximum speed is when the force of the spring exactly equals the force of gravity, i.e. when acceleration=0.

Thanks so much for any help!