A pilot performs a vertical manoeuvre around a circle with a radius R. Which of the following is true about the pilot’s apparent weight?

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BlackTom AI · Accepted Answer

Consider the vertical circular motion and what the pilot feels as apparent weight, which is the normal force exerted by the seat on the pilot.
Option 1: It decreases when he moves from the lowest to the highest point of the circle. At the bottom, the centripetal force requirement m v^2 / R is provided by N - mg, so N = m v^2 / R + mg, which is large. At the top, N + mg = m v^2 / R, so N = m v^2 / R - mg, which is smaller. As the pilot moves upward from bottom to top, the normal force (apparent weight) decreases. This option is consistent with the standard result for vertical circular motion.
Option 2: It increases when he moves from the lowest to the highest point of the circle. This contradicts the force balance equations above, since the top requires N to be less than at the bottom for the same speed, assuming speed is not drastically changing. Therefore this is incorrect.
Option 3: It decreases when he moves from the highest to the lowest point of the circle. This would imply the weight is lighter at the bottom, which is opposite to the actual behavior where the bottom exerts a larger normal force due to the need to provide centripetal acceleration upward along with supporting weight. Hence this is false.
Option 4: Remains constant at all points. In a vertical circle with gravity, the weight component and the required centripetal force change with position, so the normal force cannot be the same at top and bottom unless v changes in just the right way. In general, this option is incorrect.

SPHY001 Graded Quiz 3 (Unit 5 and Unit 6)- Requires Respondus LockDown Browser

A pilot performs a vertical manoeuvre around a circle with a radius R. Which of the following is true about the pilot’s apparent weight?

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