How the Classic Loop the loop works

[PhysicsInNJ]

Through some of the conservation of energy problems we've been working recently with the loop the loop (ball rolls down ramp and around a circular track.) there is one concept that is irritating me. This is not a homework problem but a mash up of the driving concepts from a few different problems.

At the top, what makes the ball stay up there. The normal force and gravity both point downward. There is no force keeping it up. Or is it that the combination of tangential velocity caused by centripetal acceleration along with the downward forces acts to make the motion follow the loop.

Also, to clarify, the centripetal force in this case would be Fn and Fg right?

 

[andrewkirk]

At the top, what makes the ball stay up there. The normal force and gravity both point downward. There is no force keeping it up.

It's not being kept up. It's being accelerated downwards by both gravity and the normal force. But it moves down in a curve that follows the track rather than straight down, because it has horizontal velocity.

A useful comparison is with a projectile like a flung pebble that has the same velocity as the ball. It too is being accelerated downwards, but doesn't fall straight down because of its horizontal velocity component. The ball on the track will accelerate downwards faster than a flung pebble right next to it (but slightly away from the track), with the same velocity, because the ball has the additional downwards acceleration from the track's normal force.

As I'm sure you know, if the ball is going too slowly, it will fall away from the track when it nears the top.

The basic rule is that the ball will stay on the track as long as the angle of the tangent to the track is more downwards-pointing than the ball's velocity vector.

 

[PhysicsInNJ]

So basically its like a projectile that happens to be following the path of the loop