Finding Velocity After Sliding with Work-Energy Equations

[cheerspens]

Homework Statement

A 15.0 kg block is sliding across the floor. Initially, it is moving at 1.2 m/s. However, after sliding 20.0 meters, =7.5 J of work are done on it by friction. What is the block's velocity after sliding 20.0 meters?

Homework Equations

KE=.5v²
lw-l=F$$\Delta$$Xcos$$\theta$$
w+=F$$\Delta$$Xcos$$\theta$$

The Attempt at a Solution

I found the initial KE to be 10.8 J.
I found the ending IE to be -7.5 J and the KE to be 3.3 J.
With a velocity of 0.66 m/s as the answer, is this correct?
Thanks!

 

[PhanthomJay]

That answer is correct, but technically, the work done by friction is -7.5 J, thus, the change in the internal energy of the system is +7.5 J. Sometimes it's best to use work-energy equations rather than fool with internal energy, since internal energy is usually associated with molecular motion, and can be confusing if you consider internal energy as the heat and sound, etc., generated by friction, but in any case, just watch your plus and minus signs.