00:01
Okay, so we have this situation.
00:03
We have a mass on the table connected by a string to a pulley and a mass that's hanging.
00:11
The string does not slip on the pulley.
00:14
We're told it has a mass, capital m, and a moment of inertia, i.
00:19
They do not tell us the radius, but it turns out we don't really need it either.
00:27
We wanna find this tension, which i'm gonna call t2.
00:42
So let's see what we need to do.
00:43
So we're gonna draw all three free body diagrams.
00:49
There's one for each mass and one for the pulley.
00:52
So for m1, we've got a tension t1 pointing up, gravity pulling down, m1g, and let's say it's accelerating in the downward direction.
01:07
Okay, there's no x components of force or acceleration on that, so we get t1 minus m1g equals minus t2.
01:18
So we get t1 minus m1 times a.
01:25
Now for the block on the table.
01:27
So we got this.
01:29
This is our block m2.
01:32
So it has a tension t2 pointing to the right.
01:37
The tensions are not equal.
01:41
We got an m2g pointing down for gravity.
01:45
We've got a normal force pointing upward, and we have a frictional force.
01:51
We're actually told the coefficient of friction, mu is 0 .17.
02:02
The thing's in motion, so we don't have to worry ourselves about static friction.
02:07
It's just kinetic friction, okay? so this equation, so in the x direction, we got y direction.
02:18
So in the x direction, we've got t2 minus f.
02:23
The acceleration, because the strings don't stretch, oh, the acceleration is the same for both blocks.
02:31
T2 minus f is m2 times a, and then we have n minus m2g is equal to zero.
02:43
We also know that f, the frictional force is mu times n.
02:52
And then for the pulley, it looks like this.
03:00
We got t1 here, t2 there.
03:06
Thing is accelerating with alpha...