A small car of mass M travels along a straight, horizontal track. As suggested in the figure, the track then bends into a vertical circle of radius R.
-What is the minimum acceleration that the car must have at the top of the track if it is to remain in contact with the track?

Question

A small car of mass M travels along a straight, horizontal track. As suggested in the figure, the track then bends into a vertical circle of radius R.

-What is the minimum acceleration that the car must have at the top of the track if it is to remain in contact with the track?

Quizplus · Accepted Answer

For the car to remain in contact with the track, the normal force on the car must be non-zero at the top of the track. This means that the gravitational force must be balanced by a centrifugal force. At the top of the track, the car is moving in a circular path of radius R with a velocity of v=√(2gR), where g is the acceleration due to gravity. Therefore, the minimum acceleration that the car must have at the top of the track is given by a=v^2/R=2g, which is downward. So, the correct answer is C) 9.8 m/s^2, downward.

A Small Car of Mass M Travels Along a Straight