Question: A stunt pilot experiences weightlessness momentarily at the top of a ``loop the loop'' maneuver. Given that the speed of the stunt plane is , what is the radius of the loop?
Answer: Let be the mass of the pilot.
Consider the radial acceleration of the pilot at the
top of the loop. The pilot is subject to two radial forces: the gravitational
force , which acts towards the centre of the loop, and the reaction force ,
due to the plane, which acts away from the centre of the loop. Since the pilot
experiences an acceleration towards the centre of the loop, Newton's second
law of motion yields