# Two Blocks being pulled until one slips

1. Oct 3, 2009

### indietro

1. The problem statement, all variables and given/known data
The coefficient of static friction is 0.621 between the two blocks shown. The coefficient of kinetic friction between the lower block and the floor is 0.129. Force F causes both blocks to cross a distance of 5.10 m, starting from rest. What is the least amount of time in which the motion can be completed without the top block sliding on the lower block, if the mass of the lower block is 1.05 kg and the mass of the upper block is 2.91 kg?

__
|__|-->F
|_____|

2. Relevant equations

3. The attempt at a solution
i really have no idea how to start this problem. so i know that both the static friction between the upper and lower block will act to the left and the kinetic friction between the lower block and the floor will act to the left. I think what i ultimately need to find the the maximum acceleration the system can have right before the block slips. This acceleration can be used to find the time, using kinematic equations. So for the whole system:
Fnet = (ml +mu)a = Fext - Ffs - Ffk

I also know that the upper block will slip when the force of static friction is at its max so:
Ffs.max = uFn
= (0.621)(2.91)(9.8)
= 17.7 N
Im just not sure where to go from here...
THANKS!!

2. Oct 4, 2009

### kuruman

1. Find an expression for the common acceleration of the two blocks.
2. Draw a free body diagram of the bottom block only, find an expression for the net force on it when the top block is just about ready to slip. Solve to get a numerical value for the acceleration.
3. Use the appropriate kinematic equation to find the time.

In problems where two masses accelerate as one it is usually a good idea to find the common acceleration first, even if the problem is not directly asking for it.

3. Oct 4, 2009

### indietro

Im not sure why i need to find the common acceleration of the two blocks if im finding the acceleration for just the lower block?

4. Oct 4, 2009

### kuruman

Because you don't know the pulling force and you don't know the acceleration. You have two unknowns, so you need two equations. Also, I didn't say find the acceleration, I said find an expression for the acceleration. This expression will involve F.

5. Oct 4, 2009

### indietro

ok i see, F being the biggest it can be before block 1 slips...?

6. Oct 4, 2009

Correct.