00:01
All right, so let's say we have a ball whirled around in a circle, around a string, and the string has a length of 2 .2 meters, and the mass of the ball is 5 kilograms.
00:12
So part a asks, what is the minimum speed the ball can be moving at and still maintain a circular path? so basically, at the top of the path, what we need is we're going to have our weight of our ball going down, and our centripetal force needs to go down as well.
00:26
So the tension needs to be approximately, or at this point, to maintain a circular path we need the tension to be like greater than or equal to zero.
00:34
And so what that means is mv squared over l needs to equal m g.
00:40
So v at the top needs to be the square root of g times l.
00:47
So 2 .2 times 9 .8 and we take the square root.
00:51
This is 4 .64 meters per second.
00:56
And then for part b, what is the maximum tension in the string? so this occurs at the bottom where we'll have our centripetal force going up, our weight going down, and the tension going up.
01:09
Now, at that speed, the centripetal force is equal to the weight.
01:13
And so the tension at this point is actually just going to be equal to twice the weight if you look at the free body diagram.
01:19
All right, let's take a step back.
01:21
So we'll have mv squared over l is equal to t minus mg...