Circular motion problem

Question

An airplane is flying in a horizontal circle at a speed of 103 m/s. The 81.0 kg pilot does not want the centripetal acceleration to exceed 5.29 times free-fall acceleration. Find the minimum radius of the plane’s path. The acceleration due to gravity is 9.8 m/s². Answer in units of m.

Answer 1

Since we have the given information:

v = 103 m/s

m = 81.0 kg

ac_max = 5.29 times free-fall acceleration = 5.29 * 9.8 m/s^2= 51.842 m/s^2

The centripetal acceleration (ac) is given by the formula:

ac = v^2 / r

Where:

v = velocity of the airplane

r = radius of the plane's path

To find r, we can rewrite the equation ac : r = v^2 / ac

r = (103 m/s)^2 / (5.29 * 9.8 m/s^2)

r = 10609 / 51.842

r ≈ 204.64 m

Min radius of the plane's path is approximately 204.64 m.