00:01
All right, so we have an incline plane that looks like are partially inclined plane with two blocks on it, and they're connected by a massless pulley that has a cable running over it.
00:13
The mass of block a, which is this one right here, is i think, four and a half kilograms.
00:20
The mass of block b is 2 .4 kilograms.
00:29
And the incline that block a is on, we're told, is 31 degrees.
00:36
And the coefficient of kinetic friction between block b is 0 .54.
00:45
And let's see, the incline plane is frictionless.
00:49
So the coefficient of friction here is 0 .54.
00:52
Okay.
00:52
And so from this information, we want to find what's the tension in the cord and the magnitude of the acceleration of the block.
00:58
So let's draw a free body diagram really quickly.
01:01
For block a, we're going to have the weight of the block going down.
01:06
So the m -a times g.
01:08
We're going to have the two components of the weight along the plan or in the direction of the plane, either m -a -g -sign theta or m -a -g -cosign theta.
01:21
And we'll have the tension going upwards.
01:24
And so basically what we have is our newton -second law for this block.
01:29
M .a.
01:30
Block a is m .a times the acceleration is equal to m .a .g.
01:37
Sine theta minus the tension.
01:41
And then for block b, what does our free body diagram look like? i'll do this over here.
01:46
So here we have the frictional force going to the right, and we have the tension going to the left.
01:52
We also have gravity going down, but this block isn't going to move up or down.
01:56
So this part doesn't really matter.
01:58
But newton's second law for this block is mb times a, they have the same acceleration...