A roller coaster has a vertical loop with radius 29.5 m. What is the minimum speed of the roller coaster car at the top of the loop if the passengers do not lose contact with the seats?
A) 10.0 m/s
B) 14.0 m/s
C) 17.0 m/s
D) 19.0 m/s

Question

Quizplus · Accepted Answer

The minimum speed at the top of the loop occurs when the weight force and the normal force just balance each other. This happens when the normal force is equal to zero, which occurs at the top of the loop. At this point, the centripetal force is provided solely by the weight force:
mv^2/r = mg
where m is the mass of the car, v is the speed of the car at the top of the loop, r is the radius of the loop, and g is the acceleration due to gravity. Solving for v, we get:
v = sqrt(gr)
Plugging in the given values, we get:
v = sqrt(9.8 m/s^2 x 29.5 m) ≈ 17.0 m/s
Therefore, the minimum speed of the roller coaster car at the top of the loop is 17.0 m/s, which corresponds to answer choice C.

A Roller Coaster Has a Vertical Loop with Radius 29