An aerobatic airplane pilot experiences weightlessness as she passes over the top of a loop the loop maneuver. The acceleration

Question

3 years ago

11

of gravity is 9.8 m/s^2. If her speed is 430 m/s at this time, find the radius of the loop. Answer in units of km.

1 answer:

Natali5045456 [20] · Answer 1 · 2022-05-20T04:07:13+03:00

The radius of the loop is 18.9 km

Explanation:

When the airplane is at the top of the loop, the pilot experiences two forces:

Since the plane is moving in a circular motion, the net force on the pilot must be equal to the centripetal force, therefore we can write:

$mg+N = m\frac{v^2}{r}$

where

m is the mass of the pilot

$g=9.8 m/s^2$ is the acceleration of gravity

N is the normal reaction

v = 430 m/s is the speed of the plane

r is the radius of the loop

Here we are told that the pilot feel weightless at the top of the loop: this means that the normal reaction is zero,

N = 0

Therefore the equation becomes

$mg=\frac{mv^2}{r}$

And so we can find the radius of the loop:

$r=\frac{v^2}{g}=\frac{430^2}{9.8}=18.9 \cdot 10^3 m = 18.9 km$

Learn more about circular motion:

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