what is the force that a jet pilot feels against his seat as he completes a vertical loop that is 500 m in radius at a speed of 200 m/s? Assume his mass is 70 kg and that he is located at the bottom of the loop.
To determine the force that a jet pilot feels against his seat as he completes a vertical loop, we can start by finding the net force acting on the pilot.
At the bottom of the loop, the net force is the sum of the gravitational force and the normal force from the seat. The gravitational force is given by the equation F_gravity = m * g, where m is the mass of the pilot and g is the acceleration due to gravity. The normal force from the seat will be the force that counters the gravitational force.
In a vertical loop, the normal force also needs to provide the required centripetal force to keep the pilot moving in a circular path. The centripetal force is given by the equation F_centripetal = m * v^2 / r, where v is the velocity of the pilot and r is the radius of the loop.
First, let's calculate the gravitational force:
m = 70 kg (given mass of the pilot)
g = 9.8 m/s^2 (standard acceleration due to gravity)
F_gravity = m * g = 70 kg * 9.8 m/s^2 = 686 N
Next, let's calculate the centripetal force:
v = 200 m/s (given velocity of the pilot)
r = 500 m (given radius of the loop)
F_centripetal = m * v^2 / r = 70 kg * (200 m/s)^2 / 500 m = 11200 N
Since the pilot is at the bottom of the loop, the normal force from the seat must be the sum of the gravitational force and the centripetal force:
F_net = F_gravity + F_centripetal = 686 N + 11200 N = 11886 N
Therefore, the force that a jet pilot feels against his seat at the bottom of the loop is approximately 11886 Newtons.