00:01
All right, so we have a physics professor spring swinging, excuse me, a bucket of water in a circle.
00:07
And let's say the length of the rope that he swings it at is 1 .2 meters.
00:13
Say we can pick a direction here.
00:16
But we're told he swings it in a direction so that it has a constant speed of four meters a second.
00:22
And the mass of the bucket and the water included is two kilograms.
00:26
So the first part asks, what is the tension in the rope? here.
00:30
So let's look at a free body diagram out of the bucket at the top and the bottom point.
00:37
So let's look at the top first.
00:39
So the tension is going this way and the centripetal force is going this way and also the gravitational force is going this way.
00:47
When the buckets at the top, they're all pointed in the same direction.
00:50
So what that means is our centripetal force, which is mb squared over r, i guess we'll call it l, it's the length of our rope, is equal to t plus m g so we can see t is equal to m times v squared over l minus g um and so if we plug in our numbers we got two kilograms times the speed we so is four meters a second squared so 16 meters squared per second squared over 1 .2 meters minus 9 .8 meters per second squared um so this gives us a tension at the top of about 7 .07 newtons.
01:35
And then at the bottom, what changes at the bottom? well, basically, now the tension and gravity are in the opposite direction.
01:42
So we'll have like mv squared over l is equal to t minus mg...