Circular Motion: Vertical Loops

Question

A stunt pilot flying an old biplane climbs in a vertical circular loop. While upside down, the force acting upward normally on the seat is 1/3 her usual weight. If the plane is traveling at that moment at 300 km/h, what is the radius of the loop?

Answer 1

At the top of the circle, two forces are acting on the pilot, gravity/weight and contact force from the seat. Weight is simply m g. The contact force has to be equal in magnitude as what the seat gets, so (m g / 3). The total force on the pilot is then (4/3) m g. This is responsible in moving the pilot in the vertical circle i.e. the centripetal force. The centripetal force required to move the pilot of mass m in a radius R with speed v is

m v² / R,

so

m v² / R = (4/3) m g.

After cancelling m on both sides, all quantities in the equation except R are known. So the radius R of the circle can be computed.