Explain why a jet fighter pilot experiences "weightlessness" when at the top of a loop-the-loop manoeuvre.

The the pilot will experience two forces acting upon him in opposing directions: gravity and centripetal force. The centripetal force will act outwards from the jet's circular path i.e. towards space; gravity will act downwards towards the Earth. At the top of the loop path, the pilot will experience both forces acting in opposite directions but of equal magnitude. It must be noted that the pilot will experience weightlessness when
centripetal force F_C = m•v²/r = gravitational force = F_G = mg,
where m is the mass of the pilot, v tangental velocity and r the radius of the loop.
The question could be modified so that the student has to find the value of v (jet tangental velocity) where the pilot would be "weightless".