An airplane is flying in a horizontal circle at a
speed of 106 m/s. The 81.0 kg pilot does not
want the centripetal acceleration to exceed
6.16 times free-fall acceleration.
Find the minimum radius of the plane’s
path. The acceleration due to gravity is 9.81
m/s2.
Answer in units of m
To find the minimum radius of the plane's path, we need to first determine the maximum centripetal acceleration allowed by the pilot.
Given:
Speed of the airplane (v) = 106 m/s
Mass of the pilot (m) = 81.0 kg
Maximum centripetal acceleration allowed (ac_max) = 6.16 times free-fall acceleration = 6.16 * 9.81 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
We need to solve for the minimum radius, so we can rewrite the above equation as:
r = v^2 / ac
Substituting the given values, we have:
r = (106 m/s)^2 / (6.16 * 9.81 m/s^2)
r = 11336 / 60.1696
r ≈ 188.602
Therefore, the minimum radius of the plane's path is approximately 188.602 meters.