A jet pilot puts an aircraft with a constant speed into a vertical circular loop

Question

A jet pilot puts an aircraft with a constant speed into a vertical circular loop.
(a) Which is greater, the normal force exerted on the seat by the pilot at the bottom of the loop or that at the top of the loop?
the normal force exerted on the seat by the pilot at the bottom of the loop
the normal force exerted on the seat by the pilot at the top of the loop


Why?

Score: 0.25 out of 0.25
Comment:

(b) If the speed of the aircraft is 600 km/h and the radius of the circle is 1.8 km, calculate the normal forces exerted on the seat by the pilot at the bottom and top of the loop. Express your answer in terms of the pilot's weight mg.
at the bottom

mg
at the top

mg

Explanation / Answer

Well, the problem does not give the pilots mass (or weight in normal gravity), but the problem can be solved and stated in terms of m (the pilot's mass). When the jet is at the bottom of the loop, a free-body diagram shows the centripetal force acting upward toward the center of the loop, and the normal force of the seat an the pilot also upward. The pilot's weight (mg) is downward. From Newton's second law: ?F(c) = ma(c) = n - mg n = mg + ma(c) = m[g + a(c)] Since centripetal acceleration equals v² / r, the equation becomes: n = m[g + (v² / r)]

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