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 6.04...

The centripetal acceleration depends on the speed of the pilot and the radius of the path as

`a = v^2/r`

Since this acceleration cannot exceed 6.04 times free fall acceleration (acceleration due to gravity), the maximum value of the centripetal acceleration is

6.04* 9.81 = 59.25 m/s^2

Then, the minimal radius is determined by

`v^2/r <=59.25`

The given speed of the pilot is 102 m/s, so

`102^2/r <=59.25`

`r >=102^2/59.25 = 175.6 ` m.

The...

The centripetal acceleration depends on the speed of the pilot and the radius of the path as

`a = v^2/r`

Since this acceleration cannot exceed 6.04 times free fall acceleration (acceleration due to gravity), the maximum value of the centripetal acceleration is

6.04* 9.81 = 59.25 m/s^2

Then, the minimal radius is determined by

`v^2/r <=59.25`

The given speed of the pilot is 102 m/s, so

`102^2/r <=59.25`

`r >=102^2/59.25 = 175.6 ` m.

The minimal radius of the plane's path is 175.6 meters.

The net force on the pilot, according to the second Newton's Law, equal mass times acceleration:

`F = ma = mv^2/r` , where m is the mass of the pilot. This net force creates the centripetal acceleration and thus maintains the circular motion.

`F = ma = 80*59.25 = 4,740` N.

The net force on the pilot equals 4,740 N.