00:01
In this question, we have a pendulum of length l attached to a bob of mass m.
00:06
It's given a horizontal velocity of the square root of 3gl.
00:10
We want to find out the angle theta at which the string becomes slack.
00:14
So our first step is to use the conservation of energy principle to say that the initial kinetic energy has to be equal to the final kinetic energy plus the change in gravitational potential energy.
00:27
As you can see, it has increased in height.
00:30
So what we can do is we can say that one half, mu squared, as this is the initial kinetic energy, where u is the initial velocity, is equal to one -half mv squared, which is the final kinetic energy, plus mgh, which is the gain in gravitational potential energy.
00:53
So what we can do now is we can see that the height difference is equal to l minus this height here, which is l cos theta.
01:05
So l minus l cos theta is equal to h.
01:12
So we can plug that into here.
01:14
We also know that u is equal to the square root of 3gl, therefore u squared is equal to 3gl.
01:24
So plugging all these values into this expression up here, we can get another expression that says, that v squared is equal to 3gl minus 2gl 1 plus cosine theta...