A pilot of weight 70kg loops a loop of radius 100m in an aero plane flying at 180 km/hr. What is the source of the centripetal force acting on the pilot at the highest and lowest points of the loop? On what is the centrifugal force acting at these points? And with what force is the pilot pressed to his seat at the highest and lowest points of the loop?
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Sol. For the pilot to describe the given loop, he must be subject to a centripetal force at all points on the loop of 
= 108.5 kg.
At the lowest point in the loop, this force comes from a part of the seat’s reaction, and at the highest point from the pilot’s weight plus the reaction of the seat. Therefore the centrifugal force at the lowest point of the loop acts entirely on the seat, and at the highest point partly on the seat and partly on the earth. At the lowest point of the loop both the pilot’s weight and centrifugal force are acting on the seat, so the pilot’s pressed to his seat with a force of 178.5 kg; and at the highest point of the loop only part of the centrifugal force is acting on the seat , equal to the centrifugal force minus the weight of the pilot, so the pilot at the highest point of the loop is pressed of his seat with a force of 38.5 kg.
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