Forces Acting on a Car or Roller Coaster in a Loop

[kamranonline]

I have two questions.

when a car or roller coaster travels in a loop. At the top of the loop the forces that acts on the car are all downwards i.e. W and normal , so the net force is acting downward. I can't figure our any other force acting upward, so what actually will keep the car sticked to surface of the loop?

Secondly, I am confuse as when does the normal force diminish at the top of the loop. I have seen some animations which showed that normal force becomes smaller and smaller until it reaches at the top. But don't really know what is counter-force for the normal force. Something to do with cos component of W i guess, but not clear how cos they are in the same direction.

English is not my first language so sorry for any mistakes.

 

[CompuChip]

You are right, (ignoring friction) all the forces are downwards at the top of the loop. So the cart has an instantaneous acceleration which points downwards. Remember, though, that acceleration changes the velocity, not the position. Usually, when the car is at the top of the loop, it will have a large velocity horizontally. The instantaneous acceleration gives it a small component in the vertical direction, but this will only be for a very brief moment, so the direction of the velocity will stay more or less horizontal. However, if the velocity is too small (or zero) then the vertical component will be relevant and the cart will fall down (which is what you don't want in a rollercoaster ride, but you can try it if you have a toy car track at home and send it in a loop too slowly: it will fall out at the top).

In general, in a circular motion, the acceleration is directed inward. Even if the angular velocity is constant, you need an acceleration to change the direction of the motion, otherwise the object will not stay on the circle but fly off tangentially to it (like what happens when you are swinging a ball on a rope and suddenly cut the rope).