Question

If both the radius of the circular trajectory and the speed of the aircraft were reduced by a factor of two, how would the force exerted on the pilot change from the answer you found above ?

Answer 1

Step-by-step explanation:

Considering aircraft of mass m is moving with constant velocity v in a trajectory of radius r then the force acting on the body is centripetal force.

Centripetal force will acts on a body when a particle moves in a circular trajectory

It is given by

`F_c=(mv^2)/(r)`

if both speed and radius is reduced to half then force become

`F'_c=(m* (0.5v)^2)/(0.5r)`

`F'_c=0.5\cdot (mv^2)/(r)`

Force will reduced to half

Answer 2

halved

Step-by-step explanation:

radius = r

velocity = v

let the mass is m

Force is centripetal force

F = mv²/r ... (1)

Now, r' = r/2 and v' = v/2 So,

F' = m v² x 2 / 4 x r

F' = mv²/2r

F' = F/2 (from equation (1)

Thus, the force is halved.