00:01
For this problem, we're looking at pendulum motion, and specifically what we want to know is what is the tension in the rope of a pendulum at the bottom of its swing? so we're given the length of the pendulum, the velocity at the bottom of its swing, and the mass of the pendulum.
00:23
So what we should first do is draw out a free body diagram for pendulum.
00:34
So we know that it has a mass.
00:39
So we have an mg that's pointing directly down.
00:46
We have force of tension pointing directly up and nothing else.
00:57
So we know that these two forces should not cancel each other out.
01:05
Because since it's swinging in circular motion here, not uniform because it is slowing down and speeding up as it swings back and forth, but it's definitely accelerating towards the center.
01:20
So we can see that ft should be greater than mg.
01:31
So if we write out newton's second for this particular moment in time in this in the vertical direction here, we'll call it.
01:41
At y.
01:42
So forces in the y direction, or really we'll say it's the radial directions to be proper, is the force of tension minus force of gravity, and this is equal to mv squared over on, specifically v at the bottom of this swing, and r in our case is l...