Understanding Conservation of Energy in a Block on a Rough Surface System

[Malabeh]

So negatives always get me, no matter what and I'm having a hard time understanding the conservation of energy. Anywho, I'll continue. In a system, oh let's say a block on a rough surface with some intitial v and kinetic energy K at point A. After it gets to B, friction has done W amount of work on the block and now it has velocity ϑ and kinetic energy k. Consequently, K=k+W, so work by friction would be W=K-k, but then that means, algebraically, W is positive if the block is moving to the right. Friction always works against an object's velocity so the work is actually -W. Why doesn't the algebra show this? What am I missing?

 

[Einj]

The energy dissipated by work is defined as $E_f-E_i = W$ and it's clearly negative. You are simply writing it in the other way. It should be k-K=W and so k = K+W. This just means that the final kinetic energy is smaller than the initial one (remember that W<0) because of dissipation.

 

[Malabeh]

The energy dissipated by work is defined as $E_f-E_i = W$ and it's clearly negative. You are simply writing it in the other way. It should be k-K=W and so k = K+W. This just means that the final kinetic energy is smaller than the initial one (remember that W<0) because of dissipation.

Well that makes sense. I was just reading it wrong. Thank you!