A roller coaster has a vertical loop with radius 29.5 m.What is the minimum speed of the roller coaster car can have 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 can be found by setting the gravitational force and the normal force equal to zero. At that point, the centripetal force must be provided by the weight of the car alone.

F_centripetal = F_weight

mv^2 / r = mg

Solving for v, we get:

v = sqrt(gr)

where g is the acceleration due to gravity (9.8 m/s^2), and r is the radius of the loop (29.5 m).

Plugging in the numbers, we get:

v = sqrt(9.8 x 29.5)

v ≈ 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 choice C.

A Roller Coaster Has a Vertical Loop with Radius 29