00:01
Okay, so we've got this little mass that's being given a velocity to the right, and it's resting on this large slab, and we need to figure out the minimum speed it will require to make it to the end of the slab.
00:17
So for that, we need to figure out its relative acceleration to the slab.
00:22
And we're also told that the coefficient of friction between the little mass and slab is quite a bit larger than.
00:30
And the coefficient of friction between this lab.
00:35
So first, the net force acting on the block is simply the force of friction, so mu2 times m times g.
00:43
And so the acceleration that it will feel is going to be equal to, so the net force is just the friction force, and it's going to feel a deceleration, acceleration in the negative direction, of negative mu2 times g.
01:01
For the slab, it's going to have two forces acting on it.
01:07
So it's got a mass of 10m, so its net force is 10m.
01:12
And it's going to have the friction force from the block, from the block minus the friction force with the floor.
01:21
And if we plug in our values for those, we can then calculate the acceleration of the slab in terms of the coefficient of friction.
01:32
For those.
01:32
So we have the friction force here.
01:34
This is going to be pulling it to the right, so mu2mg, and then the friction force here, which is going to be trying to slow it down.
01:41
So that's mu 1 times 11m, so the total mass, the slab plus the mass, times g.
01:49
We can factor out the g divide both sides by m and 10.
01:54
We get g over 10 is equal to mu 2 minus 11 mu 1.
02:02
And now to find the acceleration of the block with respect to the slab, we take the difference between those two.
02:11
So this minus this.
02:14
We plug those in.
02:15
We're going to get our deceleration.
02:24
So we have our acceleration in the negative direction.
02:27
We got the acceleration for the block with respect to the ground and the minus the acceleration of the slab with respect to the ground.
02:37
We can take and distribute this g over 10 and factor that out.
02:47
So if we factor out a g over 10 for the whole thing, we'll get a mu2 times 10.
02:56
And a 11 mu 1 minus, since this is minus the minus, this becomes positive, minus mu 2, minus 10 mu2 right there.
03:08
So these two will combine, so there'll be 11, which we can then factor out.
03:15
And so we have 11 over 10g, mu2 minus mu 1.
03:21
Now i put this negative sign in here, so that's why this goes from mute 1 minus me 2 to me 2 minus 1 because this is a deceleration.
03:32
So this will be the acceleration to the left in the negative direction.
03:40
All right, once we have this, we can then look at how we find the minimum speed.
03:47
So the minimum speed means we will be stopping when we get to the edge.
03:51
So this v is going to be zero.
03:53
This speed will be our minimum speed.
03:55
This a will be this acceleration here.
03:58
And this l is the length of the slab...
