# What is the radius of the circular path and the centripetal force in the following case:An airplane is flying in a horizontal circle at a speed of 79.5 m/s. The 41.3 kg pilot does not want his...

What is the radius of the circular path and the centripetal force in the following case:

An airplane is flying in a horizontal circle at a speed of 79.5 m/s. The 41.3 kg pilot does not want his radial acceleration to exceed 10.2*g. The acceleration of gravity is 9.8 m/s^2 .

a)What is the minimum radius of the circular path?

b) At this radius, what is the net centripetal force exerted on the pilot?

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Every object moving in a circular path has an acceleration acting on it towards the center of the circle. This is known as centripetal acceleration.

The velocity at which the airplane is flying is given as 79.5 m/s and it is flying in a path that traces a horizontal circle. If the radius of the path is r, the centripetal acceleration is given by v^2/r

As the pilot does not want the centripetal acceleration to be higher than 10.2*g = 10.2*9.8 = 99.96 m/s^2, the radius of the circle is limited. If the radius is r, (79.5) ^2/r <= 99.96

=> r >= (79.5)^2/99.96

=> r >= 63.22 m

The minimum radius of the circular path is 63.22 m

At this radius, the centripetal force on the pilot is 99.96*41.3 = 4128.35 N