I can't seem to understand what the deal is with work and friction. I understand that friction is going to create heat and thus internal energy of the objects so therefore its not perfect. But I don't seem to understand everything that EK is trying to say in their explanation and I can't find an explanation in my Columbia review text books. Could anyone explain the concept to me and the equation that EK gives us?

I saw EK's explanation of work and friction and found it not very useful as well. What I recommend you do is more passages (and more questions from the EK 1001 book related to work and friction). FYI, there are numerous videos on youtube explaining work and friction in a very simple manner with problems.

Try to think of many equations when you are doing a friction problem.

For example,

W = F*d; this is the formula for work where F is the parallel force (not perpendicular!) and d is the distance.

also, W = -f*d; where f is the friction force opposing the parallel force F. It's negative because it is

*opposing* the parallel force.

Well, lets see... what else do we know about Work formulas?

We know from work-kinetic energy theorem that

W = ΔKE = 0.5mvf^2 - 0.5mvi^2

where vf = final velocity and vi = initial velocity

What else do we know? We know that f = µN

Look what we have so far:

W = F*d = ΔKE = µN

What else? we know that on a horizontal surface, the normal force equals the weight (mg)

so the equation becomes:

W = F*d = ΔKE = µmg

Couple examples may be:

1) Let's say you are lifting a weight, holding it still above your head. You're just holding it; not moving it anywhere. What's the "work" done? ZERO. Because you are not

*moving *it anywhere therefore d = 0; notice that even if d = 0, the whole thing (W = F*d = ΔKE = µmg) becomes zero.

2) You apply a force of 20N horizontally on a box and move it 10 meters. What's the work done? Well, simply 20*10 = 200.

3) What's the work done by the normal force on the previous problem? Zero.. because F in the W=F*d formula is the

*parallel* force.

About heat...

Let's say you start at a height and slide down the hill and come to a stop. What happens is, at the top you have some potential energy (mg

*h*, because you are at a

*height*).. As you slide down, that potential energy is turning into kinetic energy. You come to a stop due to friction. Heating occurs because some of the energy is lost as heat as you come to a stop.

So this is mostly how I think of it. You may have already know all these or not.

Hope it helps