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 ...

Question

BlackTom AI · Accepted Answer

Apparent weight is the normal force the seat exerts on the person. At the top of a vertical circular loop the required centripetal acceleration is downward, so the vertical force balance toward the center gives the relation between weight, normal force, and centripetal requirement.

1) Relevant concepts:
- True weight = mg (gravitational force, always downward near Earth's surface).
- Apparent weight = normal force N (what a scale or seat reads).
- Centripetal acceleration a_c = v^2 / r, directed toward the center of the circle (downward at the top).

2) Step-by-step reasoning and algebra:
Take downward as positive toward the center. Sum of forces toward center: mg + N = m a_c = m(v^2 / r).
Solve for the normal force (apparent weight):
N = m(v^2 / r) - mg = m( v^2 / r - g ).

3) Intermediate steps / condition for N = 0:
Set N = 0:
0 = m( v^2 / r - g ) → v^2 / r = g → v = sqrt(g r).
Thus when the plane’s speed at the top satisfies v^2 = g r, the normal force is zero and the person is in free fall relative to the seat (apparent weight zero). Example: if r = 100 m, v = sqrt(9.8·100) ≈ 31.3 m/s gives N = 0.

4) Why the correct answer is correct:
Because apparent weight equals N and N can be zero when the centripetal acceleration exactly equals g. That is exactly the free-fall condition produced intentionally in parabolic flights like the “Vomit Comet.”

5) Why the other choices are incorrect:
a) “Apparent weight can be a negative value.” Normal force measured by a scale cannot be negative unless the seat/strap actively pulls upward; if the simple seat loses contact the actual N becomes zero (not negative). So negative apparent weight is not the usual outcome. 
b) “True weight is zero.” True weight mg is due to gravity and is not zero near Earth’s surface. 
d) “Apparent weight equals true weight.” That would require no net acceleration (a=0); at the top of a looping trajectory there is centripetal acceleration, so in general N ≠ mg.

6) Conclusion:
Therefore the correct choice is c. apparent weight can be zero. This matches the provided answer.

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