Pilots of high-performance fighter planes can be subjected to large centripetal accelerations during high-speed turns. Because of these accelerations, the pilots are subjected to forces that can be much greater than their body weight, leading to an accumulation of blood in the abdomen and legs. As a result, the brain becomes starved for blood, and the pilot can lose consciousness ("black out"). The pilots wear "anti-G suits" to help keep the blood from draining out of the brain. To appreciate the forces that a fighter pilot must endure, consider the magnitude of the normal force that the pilot's seat exerts on him at the bottom of a dive. The plane is traveling at 259 m/s on a vertical circle of radius 721 m. Determine the ratio of the normal force to the magnitude of the pilot's weight.
Explanation / Answer
Applying Newtons second law at the bottom of the dive is N = mg + (mV2 / R ) N is the normal force mg is the weight V is the speed R is the radius of the loop. Dividing the above equationwith ' mg ' on both sides N/ mg = 1 +(V2 / Rg ) = 1 + [ (259m/s)2 / (721m)(9.8m/s^2) ] = 10.5