Which of the following best explains why passengers feel heavier than normal at the bottom of a roller coaster loop?

• A. The normal force acting on the passengers is less than their weight at the bottom of the loop.
• B. The normal force acting on the passengers is greater than their weight due to the centripetal acceleration required to change direction.$N>W,\text{where}N\text{is the normal force and}W\text{is the weight.}$
• C. The gravitational force increases at the bottom of the loop.
• D. The passengers experience zero net force at the bottom of the loop.

Answer: (B)

Verified step by step guidance

1. Identify the forces acting on the passengers at the bottom of the roller coaster loop: the gravitational force (weight) acting downward and the normal force from the seat acting upward.
2. Recognize that the passengers are undergoing circular motion, which requires a centripetal force directed towards the center of the loop (upward at the bottom of the loop).
3. Apply Newton's second law in the vertical direction, taking upward as positive: the net force towards the center is \(F_{net} = N - W\), where \(N\) is the normal force and \(W\) is the weight.
4. Since the net force provides the centripetal acceleration, set \(F_{net} = m a_c\), where \(a_c = \frac{v^2}{r}\) is the centripetal acceleration, \(m\) is the mass, \(v\) is the speed at the bottom, and \(r\) is the radius of the loop.
5. Conclude that the normal force must be greater than the weight (\(N > W\)) to provide the necessary centripetal force, which makes passengers feel heavier than normal at the bottom of the loop.