An airplane is flying in a horizontal circle at a speed of 117 m/s. The pilot does not
want his centrifugal acceleration to exceed 6.8g (that is, to be more than 6.8 times the
acceleration of gravity). What is the minimum radius (in meters) of the circular path?
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Equate the centripetal force to 6.8g, i.e.
mv²r = 6.8mg
solve for r.
Note that mass of aeroplane cancels out.
To find the minimum radius of the circular path, we need to determine the maximum centrifugal acceleration and then calculate the radius using the formula for centrifugal acceleration.
Centrifugal acceleration (ac) is given by:
ac = (v^2) / r
where v is the velocity and r is the radius.
The given velocity of the airplane is 117 m/s.
To convert the acceleration to units of gravity (g), we need to divide the value by the acceleration due to gravity (g ≈ 9.8 m/s^2).
So, the maximum centrifugal acceleration in terms of g is 6.8g.
Using the formula for centrifugal acceleration, we can rewrite it as:
6.8g = (117^2) / r
To find r, we need to rearrange the equation:
r = (117^2) / (6.8 * 9.8)
Now we can calculate the radius:
r = (117^2) / (6.8 * 9.8) = 234639 / 66.64 ≈ 3520.1 meters
Therefore, the minimum radius of the circular path is approximately 3520.1 meters.