The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle. The speed of the airplane is 240 mi/h, at the top of the loop and 450 mi/h at the bottom, and the radius of the circle is 1 340 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?
lb

(b) What is the magnitude of his apparent weight at the highest point?
lb

(c) Describe how the pilot could experience weightlessness if both the radius and the speed can be varied.

Question

The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle. The speed of the airplane is 240 mi/h, at the top of the loop and 450 mi/h at the bottom, and the radius of the circle is 1 340 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?
  lb

(b) What is the magnitude of his apparent weight at the highest point?
  lb 

(c) Describe how the pilot could experience weightlessness if both the radius and the speed can be varied.

turingtest · Answer

add the centripetal force to the gravitational force$$\sum F=F_g+F_c=mg+m\frac{v^2}r$$the force of gravity always acts down, and the centripetal force always acts toward the center of the circle, so you must decide whether the two forces add or subtract at each location.