Sphere rolls down and compresses spring

[scruffles]

Homework Statement

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A solid sphere rolls without slipping down an incline and compresses a spring. The figure above shows the system with the spring compressed to its turning point (at maximum compression, where the sphere’s velocity is zero.) Assume that no energy is lost due to non-conservative forces such as friction as the sphere rolls down the incline and compresses the spring. The distance h is the vertical displacement of the sphere’s center of mass, m is its mass, R is its radius, and k is the spring constant.
In terms of the variables stated, find an expression for the amount the spring is compressed.

Homework Equations

V= 1/2kx^2
V= mgh
K=1/2mv^2 + Iomega^2

The Attempt at a Solution

I honestly am stuck here. Any tips or ideas would be great! Thanks in advance!

 

[ehild]

Apply conservation of energy. What are the values of all kinds of energy on the top of the hill? And what are at the bottom, when the spring is compressed, and the velocity is zero?


ehild