When you are on a roller coaster at the very bottom of a vertical loop, which of the following best describes the direction of the net force acting on you?

• A. The net force is directed horizontally, tangent to the track.
• B. The net force is directed downward, away from the center of the loop.
• C. The net force is directed upward, toward the center of the loop.
• D. The net force is zero because gravity $g$ and the normal force $N$ cancel each other.

Answer: (C)

Verified step by step guidance

1. Identify the forces acting on you at the bottom of the vertical loop: gravity (weight) acting downward and the normal force from the track acting upward.
2. Understand that at the bottom of the loop, the roller coaster is moving in a circular path, so there must be a net centripetal force directed toward the center of the loop (which is upward at the bottom).
3. Recall that the net force providing centripetal acceleration is the difference between the normal force and the gravitational force, since they act in opposite directions.
4. Express the net force as \(F_{net} = N - mg\), where \(N\) is the normal force (upward) and \(mg\) is the weight (downward). This net force points upward toward the center of the loop.
5. Conclude that the net force cannot be zero or directed downward; it must be upward, providing the centripetal force necessary to keep you moving in the circular path.