A Monash College student of mass70 kg standing in an elevator briefly experiences a constant upward vertical speed of 2 m/s as he moves from level 2 to level 6. What is apparent weight of the student at this moment?

Question

BlackTom AI · Accepted Answer

Apparent weight equals the normal contact force (N) from the floor or scale. For an object of mass m in a vertical situation, Newton’s second law gives: sum of forces = ma. Here the only vertical forces are the upward normal force N and the downward gravitational force mg.

Step-by-step reasoning and calculation:
1. Identify forces: upward N, downward mg (where m = 70 kg and g ≈ 9.8 m/s^2).
2. Because the elevator moves with a constant upward speed (2 m/s), its acceleration a = 0 (constant velocity → zero acceleration).
3. Apply Newton’s second law in the vertical direction: ΣF = ma → N − mg = m·0 = 0.
4. Solve for the normal force: N = mg.
5. Compute the numerical value: N = 70 kg × 9.8 m/s^2 = 686 N.

Why this answer is correct:
- With zero acceleration, net force must be zero, so the normal force must exactly balance the weight. The apparent weight is what you feel or what a scale reads, i.e., the normal force, so it equals the gravitational weight force (mg = 686 N) in this situation.

Why the other options are incorrect:
- Option b (less than gravitational weight): would be true only if the elevator were accelerating downward (a < 0), so N < mg. That is not the case here.
- Option c (greater than gravitational weight): would be true only if the elevator were accelerating upward (a > 0). Here the elevator has zero acceleration despite moving upward at constant speed, so N is not greater.

Conclusion: The apparent weight equals the gravitational weight force (option a), and numerically N = 686 N, which matches the provided correct answer.

A Monash College student of mass70 kg standing in an elevator briefly experiences a constant upward vertical speed of 2 m/s as he moves from level 2 to level 6. What is apparent weight of the student at this moment?多项选择题

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