Apply centripetal force to a roller coaster. Find the normal force between the cart and the track as the cart travels through a low point on the track. Calculate the maximum speed the cart can travel over a crest in the track without flying off of the track.
Normal force between the cart and track is NOT equal to the centripetal force by the track on the cart. The net force on the cart is the vector sum of gravity and the normal force. In recognizing how those forces add or subtract at the top and bottom of a hill we can find the net force. The net force on the cart is the centripetal force on the cart.
This problem is extremely common in introductory physics and mechanics. It appears in courses such as AP Physics 1 and AP Physics C Mechanics.
