The apparent weight of the pilot at the lowest point of the loop is 1589.88 N.
a) Apparent weight at the highest point
At the highest point of the loop, the pilot is only acted upon by two forces: gravity and the centripetal force.
The centripetal force is directed towards the center of the loop, and gravity is directed downwards.
The centripetal force is given by:
F_c = mv^2/r
where: m is the mass of the pilot (in kilograms) ,v is the speed of the pilot (in meters per second) ,r is the radius of the loop (in meters)
Plugging in the values, we get:
F_c = (789 N) (205 m/s)^2 / (3840 m) = 799.94 N
Therefore, the apparent weight of the pilot at the highest point of the loop is 799.94 N.
b) Speed for weightlessness
Weightlessness occurs when the centripetal force is equal to the weight of the pilot.
This means that the pilot is not feeling any force pushing them down into the seat of the airplane.
F_c = mg
where: g is the acceleration due to gravity (in meters per second squared)
Plugging in the values, we get:
v^2/r = g
Solving for v, we get:
v = sqrt(rg) = sqrt((3840 m)(9.81 m/s^2)) = 194.08 m/s
Therefore, the pilot will experience weightlessness when the speed of the airplane is 194.08 m/s.
c) Apparent weight at the lowest point
At the lowest point of the loop, the pilot is acted upon by three forces: gravity, the centripetal force, and the normal force from the seat of the airplane.
Since the pilot is moving in a circle, the centripetal force must be equal to the sum of the components of gravity and the normal force acting perpendicular to the pilot's motion.
The normal force is given by:
F_n = mg + F_c
where: F_c is the centripetal force (in Newtons)
Plugging in the values, we get:
F_n = (789 N) + (799.94 N) = 1589.88 N
Therefore, the apparent weight of the pilot at the lowest point of the loop is 1589.88 N.
Question
A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 3.84 x 103 m. During this performance the pilot whose weight is 789 N, maintains a constant speed of 2.05 x 102 m/s. (a) When the pilot is at the highest point of the loop determine his apparent weight in Newtons. (b) At what speed will the pilot experience weightlessness? In m/s (c) When the pilot is at the lowest point of the loop determine his apparent weight in Newtons.