Question

An airplane in a wide “outside” loop can create an apparent zero weight inside the aircraft cabin. What must be the radius of curvature of the flight path for an aircraft moving at 350 km/h to create a condition of weightlessness inside the aircraft? Assume the acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s

Answer 1

Answer:

R = 964.5 m

Explanation:

When plane is moving in vertical loop then at the condition of free fall then force of gravity on the passengers will be balanced by the the pseudo force on them.

In ground frame we can say that normal force on the passengers will become zero

So we have

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

$m(9.8) = \frac{mv^2}{R}$

here we know that

v = 350 km/h = 97.22 m/s

now we have

$9.8 = \frac{97.22^2}{R}$

$R = 964.5 m$