# Homework Help: A block on top of another on a horizontal surface.

1. Oct 25, 2007

### Ahwleung

1. The problem statement, all variables and given/known data
Its not a very difficult problem, and I really only need to know 1 thing about friction; anyways, here's the summed up problem:

(my teacher enjoys making us use constants instead of numbers btw)
A horizontal force F is applied to a small block (mass m1), and it slides across a larger block a length L (mass m2) with the coefficient of friction being u. The larger block in turn slides along a frictionless horizontal surface. Everything starts at rest and the small block starts at the end (left side) of the larger block on the bottom.

We're supposed to find the acceleration of each block relative to the horizontal surfaces, find the time t needed for the small block to slide off the end of the larger block, and find the expression for the energ dissipated as heat due to friction.

2. Relevant equations
Umm, I'd say F=ma, the law of friction (F(kf) = uFn), and also the work equations (for the last question). I can handle all those pretty easily, but I just need something about summing the forces.

3. The attempt at a solution
We have to draw a free body diagram - here is where I find the problem.

Both blocks have a normal force and a force of gravity (duh).
The 1st block has a Force Applied and a Force of Friction opposing it.
Where I'm getting messed up is on the 2nd block. I don't think Force Applied transfers to the 2nd block - am I right in saying that the only horizontal force on the 2nd block is the force due to friction from the 1st block?

Is this force of friction equal to the Force of friction from the 1st block? Is it newton's third law?

What doesn't make sense is that friction forces always oppose motion, yet the 2nd block obviously travels in the same direction as the Applied Force.

2. Oct 25, 2007

### Kurdt

Staff Emeritus
Your thinking is quite correct. Your confusion at the end is that the friction force does oppose the motion of the first block but for there to be a reaction force there must be another force in the opposite direction. Just think of the applied force as being split into two parts. The part that opposes friction and the extra bit that makes it move.

3. Oct 25, 2007

### Ahwleung

Another question about this problem. I found the first part, but I'm sorta confused about the 2nd question. I don't think its a trick question, but it seems really, really easy.

Basically, it says given a distance and both accelerations (and the fact that everything starts at rest), find the time it will take for the block on top to fall off.

Isn't it really, really easy? It's basically a block with an acceleration travelling a distance with an initial velocity equal to 0. Is it just an easy UAM problem?

Or do I have to factor in the fact that the block on the bottom also has an acceleration/is moving?

4. Oct 25, 2007

### Kurdt

Staff Emeritus
As you say its a uniform acceleration problem. You don't have to worry about the motion of the second block.