00:01
Now let's look at in this question a kind of loop loop track, right? so it's something like this.
00:08
And then it's going up to loop right, like this.
00:11
So there's a radius of the loop and this is the top of the loop and radius of the loop.
00:15
Let's say it has a radius artery.
00:18
And then you have you start with a height, move some.
00:22
It's in this question, it's a sphere, right? now imagine you neglect the friction, then the sphere will just slide down, right? there's no rotation waiver.
00:30
At the top point, you must have a velocity v.
00:34
I mean, the translation velocity, the velocity of the center of mass of the sphere, right? and it must have a velocity in this direction.
00:43
So the velocity has to begin up so that it does not leave the track, right? so and actually it's very clear that v squared over our must be just the gravity, right? so that would be equal to g, right? so from this actually, you will see that, you will see that the v actually is squalots of gr, right? and then, of course, you can find the kinetic energy at this point, right? it was the total energy at this point.
01:18
The total energy of this point, of course, is given by the total energy at this point, of course, if we set the potential energy at this point to be a potential point in zero, and then very clearly, the total energy at the highest point there is given by mv squared over two plus two mr right so that is given by a two m r two m gr g's acceleration rati and this you will find mv squared um v squared and v squared is of course mjr so you will find that half m gr so it's actually five m gr over two and this has to be equal to the initial energy, which is just gravitational tension, is equal to mghh...