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

Centripetal acceleration at the top of the loop is directed downward, and it must be provided by the sum of the weight (mg) and the normal force N from the seat. Apparent weight is the normal force the person feels (magnitude of N). 1) Relevant concepts: - True weight = mg (gravitational force) — always downward and nonzero near Earth. - Apparent weight = normal (contact) force from seat; this is what you feel. - For circular motion of radius r and speed v, required centripetal force = m v^2 / r directed toward the center (downward at the top). 2) Complete reasoning and equations: Take downward as positive at the top. Sum of forces toward center: mg + N = m v^2 / r. Solve for the normal force N: N = m v^2 / r - mg. 3) Intermediate steps / cases: - If m v^2 / r = mg, then N = 0. That is the critical speed v_crit = sqrt(g r). At this speed the seat exerts no normal force and the person is weightless (apparent weight zero). - If m v^2 / r > mg, then N > 0: the seat pushes the person toward the seat and apparent weight is greater than zero. - If m v^2 / r < mg, the equation gives N < 0 (negative in our sign convention), which would mean the seat would have to pull the person toward the seat. In practice a seat cannot "pull" unless there is a harness; contact is lost and the normal force goes to zero — the person becomes weightless or separates. Thus apparent weight (the contact force) cannot be negative. 4) Why the correct answer is correct: Because at the top of the loop there exists a speed where mg exactly supplies the required centripetal force and the normal force is zero, so apparent weight can be zero. 5) Why other options are incorrect: - (a) True weight is zero: false — true weight mg is not zero near Earth. - (b) Apparent weight can be negative: false for normal/contact force; negative solution just indicates loss of contact, not a negative contact force. - (d) Apparent weight equals true weight: only true if no net acceleration (v=0), not generally at the top of a loop. 6) Conclusion: Therefore the correct choice is c. apparent weight can be zero.

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 ...单项选择题

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