Question

A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 17.6 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car. (Give answer to the nearest 0.1 m/s)

Answer 1

Centripetal acceleration around a circle is a = v^2/R, where a is the acceleration (positive away from the center of the circle), v is the velocity around the circumference of the circle, and R is the radius of the circle.

In the case of the loop, the acceleration must at least equal the acceleration due to gravity - at the top of the loop the centripetal acceleration is pointing up, gravity is pointing dowm, and the if gravity is greater then the net acceleration is down and away from the seat:

g = v^2/R

v = sqrt(gR) = sqrt(9.81 m/s^2 * 17.6) = 13.1m/s