An aerobatic airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. The acceleration of gravity is 9.8 m/s 2. If her speed is 450 m/s at this time, find the radius of the loop. Answer in units of km

The radius of the loop is 20.66 km

Explanation:

let the radius of the loop be r

mass of airplane is m

At the top, the pilot experiences two radial forces, which are

1) Gravitational force is mg

2) Centrifugal forces mv²/r out of the center

When the pilot experiences no weight,

then, mg = mv²/r

r = v² / g

= 450² / 9.8

= 20.66 x 10³3

= 20.66 km