A stunt pilot in an air show performs a looptheloop in a ver

A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.88 103 m. During this performance the pilot whose weight is 721 N, maintains a constant speed of 2.15 102 m/s.

(a) When the pilot is at the highest point of the loop determine his apparent weight.
N

(b) At what speed will the pilot experience weightlessness?
m/s

(c) When the pilot is at the lowest point of the loop determine his apparent weight.
N

Solution

mg= 721

m = 721/9.81 = 73.496 kg

highest point   apparent weight. = mv^2/ R -mg

= 73.496*( 2.15*10^2) ^2 / ( 2.88*10^3) -721

= 458.64 N

b)

for weightlessness net force = 0

mv^2/ R -mg = 0

v = sqrt( R*g) = sqrt( 2.88*10^3 * 9.81) =168.085 m/s

c)

lowest point   apparent weight. = mv^2/ R +mg

= 73.496*( 2.15*10^2) ^2 / ( 2.88*10^3) +721

= 1900.6364 N