00:01
We've got two stacked blocks, block a and block b is stacked in top of a on a flat, smooth horizontal surface, so there's no friction down here.
00:12
They're given the coefficient of friction between blocks a and b is given as mu.
00:18
And they're asked for what is the value of f, or the minimum value of f, where a begins to slide and slip out from underneath b.
00:27
So let's start this one by drawing some free body diagrams for a and b.
00:31
B, we'll do b first.
00:34
B has mbg, the force of gravity.
00:38
It's got a normal force from a.
00:42
And if a is getting pulled to the right, the only reason b would follow is because there's a force of friction.
00:50
That would be giving it a net force to the right.
00:54
Okay.
00:56
And then let's do one for block a.
00:59
So block a has a m -a -g it's also got a force downwards from b which is the normal force from b and it's got a normal force from the ground it's got a force f to the right and it's got that force of friction to the left just to name our third law pairs those two are a third law pair and these two are a third law pair meaning they represent the same force.
01:34
They're just acting in opposite directions on the individual blocks.
01:39
So with these free body diagrams, we can begin to solve this.
01:43
We want to find out the maximum f where a begins to slide out from under b.
01:48
So let's figure out what is the maximum acceleration that b can have.
01:55
So let's see, what's the acceleration of b? so the acceleration of b is the net force of b, which is the force of friction, as the net force on b, divided by the mass of b.
02:07
Let's do the acceleration of a, which is the big f minus the force of friction, between a and b, divided by the mass of a.
02:20
I'm going to sub in for these forces of friction because they are the same value as mu times the, the force of friction between block a and b is the mu times the normal force between block a and block b.
02:41
So i'm going to put a little a, b, just to differentiate it from the normal force from the ground, divided by mb.
02:48
The acceleration of a, of block a, is this big f, which we'd like to solve for, minus what i just solve for f and a b, divided by the mass of a.
03:00
And block a will begin to slip out when the acceleration of a is greater than the acceleration of b.
03:10
So when they begin to slip as soon as a, acceleration of a begins to get larger than the acceleration of b...