Question

An airplane is flying in a horizontal circle
at a speed of 104 m/s. The 86.0 kg pilot
does not want the centripetal acceleration to
exceed 6.49 times free-fall acceleration.
Find the minimum radius of the plane’s
path. The acceleration due to gravity is 9.81
m/s2
at this radius, what is the net force that maintain circular motion exerted on the pilot by the seat belts, the friction against the seat and so forth?

Answer 1

we have formula for centripetal acceleration \(\alpha = \dfrac{v^2}{r}\) where \(v= 104m/s\) and \(\alpha = 6.49 g= 6.49*9.8 = 63.602\)
now replace to \(r = \dfrac{v^2}{\alpha}\) we have r = \(\dfrac{104^2}{63.602}= 170.1m\)

Answer 2

at this radius, the net force that maintain circular motion is centripetal force which is calculated by F = \(\dfrac{mv^2}{r} = \dfrac{86.0*104^2}{170.1}=5.4*10^3 N\)