Question

http://tinypic.com/r/2co0f11/7

If the cart is barely able to complete the loop, what is its speed at point P, the top of the loop?

The answer explanation states that the total force is normal force + mg = centripetal force. Why is there normal force? Is it the normal force that is acting on the cart from the track? Also, it says that because the cart barely makes it around the loop, normal force is 0. Why is that?

Answer 1

the speed is sqrt(rg). The track has to hold the cart in to keep it going in a circle... that force is the normal force, and at the top it points downward.... so does the weight of the cart mg. The sum of the radially directed forces must be mv^2/r, since that force is required for circular motion. As the cart goes slower, the track has to do apply less and less force to hold the cart in, until - at just the right speed - it doesn't need to supply any force - the cart would go in a circle even if no tract were there

Answer 2

Perfect balance at the top :
\[V =\sqrt{r*g}\]
It's an intresting result, because it doesn't seem natural that the speed desn't depend of the mass, but just distance and gravity.