Solving Friction & Spring Homework: .75kg Mass, 12000N/m Spring

[Seahawks]

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.

 

[Doc Al]

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.

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?

 

[rude man]

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

 

[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.