Question

You plan to fly a model airplane of mass 0.550 kg that is attached to a horizontal string. The plane will travel in a horizontal circle of radius 5.10 m. (Assume the weight of the plane is balanced by the upward "lift" force of the air on the wings of the plane.) The plane will make 1.10 revolutions every 3.50 s.
(a) Find the speed at which you must fly the plane.

(b) Find the force exerted on your hand as you hold the string (assume the string is massless).

Answer 1

Since the weight of the plane is balanced by gravity, and the string is horizontal, we need only consider forces applied in the horizontal plane.

(a) The plane travels in a circle with circumference 2*pi*r, which is the distance traveled every revolution. In 1.1 revolutions, the plane travels 1.1 * 2* pi * (5.10m) which takes 3.50 seconds. So the plane's speed is simply d/t.

(b) Once we have the velocity v, we can calculate the centrifugal force using F = mv^2/r. This is equal in magnitude to the force on your hand as you hold the string