00:01
On this problem, we have a kid who is on a merryground.
00:05
And so the mass of the child is 50 kilograms.
00:10
And they are at the edge of the merryground, which has a radius of 1 .70 meters, which means that's how far they are from the center of the merryground.
00:19
The angular speed of the child and the merry ground, they're both going 2 .95 radiance per second because the child is on the merry ground.
00:28
So for part a, we are asked to find centripetal acceleration.
00:33
So centripetal acceleration is equal to tangential speed squared divided by radius.
00:39
I'm going to come over here to the side.
00:41
So we know that tangential speed is equal to angular speed times radius, so we can plug this in where we have v squared.
00:48
And so that gives us centripetal acceleration is equal to angular speed squared times radius squared all over radius.
00:55
Now one of these will cancel out, and that leaves us with.
00:58
Angular speed squared times radius.
01:00
So we can go ahead and plug in what we know.
01:02
We have centripetal acceleration is equal to angular speed squared, which is 2 .95 squared times the radius, which is 1 .70.
01:14
And that leads us with the centripetal acceleration of 14 .79 meters per second squared.
01:22
And i'm going to round this here, but when i'm plugging into part b, i'm using the full number, which is 14 .7 .7 .7.
01:28
And i'm going to round this squared.
01:28
And i'm going to round this here.
01:28
But when i'm plugging into part b, i'm using 7 -9 -425.
01:31
Let's go ahead and go down and switch colors for b.
01:35
So b is now asking us to find which force is needed to keep this child on the merry ground.
01:40
And that force that's doing this is going to be the force of friction.
01:43
So a force that keeps something moving in a circle is our centripetal force.
01:47
And that is simply mass times centripetal acceleration, which we know centripetal acceleration...