Question

The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle. The speed of the airplane is 305 mi/h, at the top of the loop and 450 mi/h at the bottom, and the radius of the circle is 1 180 ft. Note: His apparent weight is equal to the magnitude of the force exerted by the seat on his body. (a) What is the pilot's apparent weight at the lowest point if his true weight is 160 lb? (b) What is the magnitude of his apparent weight at the highest point?

Answer 1

The pilot exerts a force on the seat. The apparent weight is the weight that the pilot would have to be to put the same force on the seat when the plane is stationary on the ground as he does while the plane is in the loop. When the plane is in level flight, the force provided by the seat will be the pilot's true weight of 160 lb. When the plane goes into a loop, extra force is required from the seat to hold the pilot on a circular course around the loop.

a)
450 mi/h = 450 * 44 / 30
= 660 ft/s

Acceleration due to the loop
= 660^2 / 1180
= 369.152 ft/s^2

Acceleration due to gravity = 32.2 ft/s^2

Total acceleration downward = 369.152 + 32.2
= 401.352 ft/s^2

True weight = 160 lb
Apparent weight = 401.352 * 160 / 32.2
= 1994.29 lb

b)
305 mi/h = 305 * 44 / 30
= 447.33 ft/s

Acceleration due to the loop
= 447.33^2 / 1180
= 169.58 ft/s^2

Total acceleration upwards
= 169.58 - 32.2
= 137.38 ft/s^2

Apparent weight
= 89.624 * 160 / 32.2
= 445.3 lb