00:01
All right, so let's say we have a vertical loop in a roller coaster with the radius r, and we have a coaster at the bottom.
00:07
We want to know what velocity does it need to make it over the top without the assistance of the track.
00:13
So at the top, what we'll have is the centripetal force and the gravitational force are going to point down, and without assistance from the track, that means the normal force is zero.
00:23
So that means at the top, we'll write this m v t squared over r is equal to m g, where v t is the speed at the top.
00:32
So we can see v t is the square root of g over r.
00:35
That's the velocity it needs at the top, and the change in potential energy from the bottom to the top is 2 m g r.
00:43
So the change in kinetic energy needs to be, you know, one half m v t squared minus v squared.
00:51
We're solving for v, and this needs to equal negative 2 m g r...