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

AI Thread Summary
The discussion focuses on understanding the conservation of energy in a system involving a block on a rough surface. It explains that the work done by friction is negative, as it opposes the block's motion, leading to a decrease in kinetic energy. The relationship between initial and final kinetic energy is clarified with the equation K = k + W, where W is negative due to energy dissipation. The confusion arises from misinterpreting the signs in the algebraic representation of work and energy changes. Ultimately, the final kinetic energy is less than the initial due to the work done against friction.
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?
 
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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.
 
Einj said:
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!
 

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