A Ferris wheel with a radius of 14.0 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the bottom of the wheel?
A) 589 N
B) 562 N
C) 625 N
D) 852 N
E) 432 N

Question

Quizplus · Accepted Answer

The centripetal force required to keep the passenger moving in a circle is provided by the normal force, which is the apparent weight of the passenger. The centripetal force is given by Fc = mv²/r, where m is the mass, v is the speed, and r is the radius of the circle. Since the Ferris wheel completes one revolution in 30.0 s, the angular speed is ω = 2π/30.0 s = 0.2094 rad/s. Therefore, the linear speed is v = ωr = 2.932 m/s. Substituting the values, we get Fc = (60.0 kg)(2.932 m/s)²/(14.0 m) = 625 N. Thus, the apparent weight of the passenger at the bottom of the wheel is 625 N. Therefore, the best choice is C.

A Ferris Wheel with a Radius of 14