# Homework Help: Friction and Springs

1. Mar 16, 2014

### Seahawks

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Spring Potential energy=.5*k*x^2
Kinetic Energy=.5*m*v^2
Friction force=μ(Fn)

3. 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.

2. Mar 16, 2014

### Staff: Mentor

Your calculations look correct. Must be a typo or mistake in the problem statement. (If it's from a textbook, give a reference.)

Have you posted the question exactly as given, word for word?

3. Mar 16, 2014

### rude man

You're right. The mass never makes it to the spring.

4. Mar 16, 2014

### Rellek

Yeah, there must have been a typo or something. If you set your initial kinetic energy equal to the frictional force times the distance, you'll find that the object stops after .2218 meters on the rough patch, so there's no way for it to get past it.

In fact, the absolute minimum velocity to get past the rough patch would be about 1.567 m/s.