- #1

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## Homework Statement

A mass of .75kg moves at 1.043m/s across a frictionless surface. Then it hits a .5m rough patch which has a coefficient of friction of .25. After moving through the rough patch, it continues on a frictionless surface. The mass then collides with a long spring. The spring coefficient is 12000N/m. Calculate how far the spring is compressed when the block just comes to rest.

## Homework Equations

Spring Potential energy=.5*k*x^2

Kinetic Energy=.5*m*v^2

Friction force=μ(Fn)

## The Attempt at a Solution

I tried finding the frictional force to be -1.837N and the the work due to friction to be -.9187J. Then I found the initial Kinetic Energy to be .408J. I am stuck here because the oeverall energy would be negative which means I can't find the answer involving the spring. How do I solve this correctly.