Consider a person in an airplane at the top of a looping, circular trajectory, like the KH-135 "Vomit Comet". At this point, the person's ...

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BlackTom AI · Accepted Answer

The scenario concerns a person at the top of a vertical circular motion (in a looping trajectory) where the only forces on the person are gravity and the normal force from the seat, as interpreted by the apparent weight.
Option a: 'apparent weight is equal to his or her true weight.' At the top of a loop, the centripetal requirement is provided by the combination of gravity and normal force. The normal force can drop, and in fact for a tight loop it can decrease to zero; thus the apparent weight need not remain equal to the true weight. This statement ignores the centripetal condition and how normal force can change in such motion, making it incorrect in general.
Option b: 'true weight is zero.' The true weight is the gravitational force mg acting downward on the person, which is not zero unless gravity were absent. In the Earth’s gravity field, true weight is nonzero, so this option misidentifies the physical quantity and is false.
Option c: 'apparent weight can be zero.' Indeed, when the normal force from the seat drops to zero, the only downward force is gravity, but the centripetal acceleration required for circular motion can be supplied entirely by gravity, leading to zero contact force and thus zero apparent weight. This is the classic scenario at the top of a vertical circle where the rider briefly experiences weightlessness.
Option d: 'apparent weight can be a negative value.' Apparent weight is the normal reaction force between the person and the seat; it cannot be negative because the seat cannot pull on the person toward the center beyond what it already provides via the constraint. In rigid contact, the normal force is compressive and zero or positive; a negative apparent weight would imply the seat pulling on the person, which is not the case here. Therefore, this option is not physically possible in this setup.

MUF0121 Physics Unit 1 - Semester 2, 2025 8.15 Vertical circular motion

Consider a person in an airplane at the top of a looping, circular trajectory, like the KH-135 "Vomit Comet". At this point, the person's ...

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