00:01
All right, to follow on this question, we're going to look at the immutant park ride, where you spin around a cylinder, and the centripetal force holds you against the wall so you don't fall down when they drop the floor out.
00:10
We're told that we're going to be inside a cylinder with a radius of r.
00:13
It's going to be spinning at some speed omega.
00:17
That's an angular speed.
00:18
And then we have a person of mass m inside the ride.
00:21
So this is kind of a side view, if we were looking at the side.
00:24
So we're asked, in part a, to draw a free body diagram.
00:26
We're going to have our weight going down, because we always have our weight going down.
00:29
And then opposing that, we're going to have the force of friction.
00:32
That's what's holding this person in.
00:34
And the reason that there's a force of friction is because there is going to be some normal force.
00:39
And that normal force points towards the center of the circle.
00:42
So that's going to be a centripetal force there.
00:45
These are our three forces, so that would be a.
00:47
Part b says, what is the maximum period of revolution necessary to keep a person from falling? so we're looking for some period t here.
00:57
In order to do this, we're going to have to go ahead and do a sum of the forces.
01:00
In the x direction, we have our normal force.
01:02
And that is going to be our centripetal force.
01:04
So that's going to be m times our centripetal acceleration.
01:07
We need to figure out what that normal force is.
01:09
And in order to do that, we can do a sum of the forces in the y direction.
01:12
We know that we have the force of friction opposing the force of gravity.
01:15
And in the y direction, hopefully, we're not accelerating.
01:18
Because if we do, that's going to be a bad time.
01:21
Force of friction is mu times our normal force.
01:23
And our weight is equal to mg.
01:26
That equals 0.
01:26
So we can solve this for our normal force.
01:28
It's going to be our weight divided by mu...