So I already got the answer for the first part:
An airplane is flying in a horizontal circle at a speed of 102 m/s. The 80.0 kg pilot does not want the centripetal acceleration to exceed 6.18 times free-fall acceleration.
Find the minimum radius of the plane's path. The acceleration due to gravity is 9.81 m/s2.
The answer is 171.79
The second part is what I need help with:
At this radius, what is the magnitude of the net force that maintains circular motion exerted on the pilot by the seat belts, the friction against the seat, and so fourth. Answer in units of N.
Please explain how you got your answer. Thanks so much!
To find the magnitude of the net force that maintains circular motion exerted on the pilot by the seat belts, friction against the seat, and so forth, we can start by using the formula for centripetal force:
F = m * ac
Where F is the net force, m is the mass of the pilot, and ac is the centripetal acceleration. We can find the centripetal acceleration using the formula:
ac = v^2 / r
Where v is the velocity of the airplane and r is the radius of the plane's path. From the first part, we know that the velocity of the airplane is 102 m/s and the radius is 171.79 m. The centripetal acceleration can be calculated as follows:
ac = (102 m/s)^2 / 171.79 m
Now we can substitute the value of the centripetal acceleration back into the formula for the net force:
F = m * ((102 m/s)^2 / 171.79 m)
Using the given mass of the pilot, which is 80.0 kg, we can calculate the net force:
F = 80.0 kg * ((102 m/s)^2 / 171.79 m)
Evaluating this expression will give us the magnitude of the net force in units of Newtons (N).