Ok, I'm driving myself mad, so if someone could settle this for me, that would be helpful. So, I'm imagining something like a hockey puck going across ice and coming to a stop. I'm trying to account for the initial energy, Ei, and the final energy, Ef. So this hockey puck starts with a velocity, v0, a mass, m, and of course under the influence of gravity, g. So, its Ei is.5mv02. Now, to account for the heat released, you use Eth=μk∫ndx, (n is the normal force). Now, since n is constant in this case, it reduces to Eth=μknΔx. Now we find Δx by finding the time it takes for the puck to come to rest, at+v0=0, -μkgt+v0=0, then we put that time in for the formula, .5at2+v0t=Δx. Then, we set Ei equal to Eth, but I get .5mv02=.5v02, so, what happened to the m? Why am I not getting equal things?