A jet pilot loops the loop in a vertical circle as illustrated. The speed of the

Question

A jet pilot loops the loop in a vertical circle as illustrated. The speed of the plane is constant and the radius of the circle is 500m. At the top of the loop, the normal (contact) force exerted on the pilot by his/her seat is EQUAL to the pilot's body weight FW . At the bottom of the loop, the normal force exerted on the pilot by his/her seat is THREE TIMES the pilot's body weight.

1.) Find the magnitude of the centripetal force acting on the pilot at the top of the loop in terms of the pilot's body wieight as an expression of FW .

2.)Calculate the speed of the plane in m/s

Explanation / Answer

1.

If the normal force = Weight (down)
and gravitational force = Weight (down),
then the centripetal force must be 2xWeight (up).

2.

If the centripetal force = 2xWeight, then
the centripetal acceleration = 2x g = 19.6 m/s²
(so we don't need to know his mass!)
a = 19.6m/s² = v² / r = v² / 500m
v = 99 m/s

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