Question

A child with a weight of 430 N rides on a Ferris wheel, which has a radius of 17 m, and the linear velocity of the 3.5 m/s at any point on the circle. What is the child’s “apparent weight” at the lowest point of the circular motion? (Hint: The “apparent weight” is the normal force, or the force of the seat on the child at any point.)

Answer 1

At the lowest point on the Ferris wheel, there are two forces acting on the child: their weight of 430 N, and an upward centripetal/normal force with magnitude n; then the net force on the child is

∑ F = ma

n - 430 N = (430 N)/g • a

where m is the child's mass and a is their centripetal acceleration. The child has a linear speed of 3.5 m/s at any point along the path of the wheel whose radius is 17 m, so the centripetal acceleration is

a = (3.5 m/s)² / (17 m) ≈ 0.72 m/s²

and so

n = 430 N + (430 N)/g (0.72 m/s²) ≈ 460 N