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

1. Relevant knowledge points and concepts Constant velocity (even if upward) means acceleration a = 0. Apparent weight is the normal force N that the floor (or a scale) exerts on the person. Apply Newton’s second law in the vertical direction: sum of forces = m a. The two vertical forces are the normal force N (upward) and gravitational weight mg (downward). 2. Complete reasoning process, step by step Set upward as positive. The forces give: N − mg = m a. Because the elevator’s vertical speed is constant at 2 m/s, the acceleration a = 0. Substitute a = 0 into the equation to find N. 3. Calculations with all intermediate steps Equation: N − mg = m a With a = 0: N − mg = 0 Therefore: N = mg Numerical substitution: m = 70 kg, g ≈ 9.8 m/s^2 N = 70 kg × 9.8 m/s^2 = 686 N (If using g = 9.81 m/s^2, N ≈ 686.7 N; both show N ≈ 6.86 × 10^2 N.) 4. Why the correct answer is correct Since the acceleration is zero, there is no net force required to change the motion. The normal force must exactly balance the gravitational force, so the apparent weight (the normal force) equals the gravitational weight mg. 5. Why the other options are incorrect a. "Less than the gravitational weight force" would be true only if the elevator/person were accelerating downward (a < 0), so N = mg + m a < mg. That is not the case here. b. "Greater than the gravitational weight force" would be true only if the elevator/person were accelerating upward (a > 0), so N = mg + m a > mg. Constant upward speed implies a = 0, not a > 0. 6. Conclusion confirming the final answer Because the elevator moves upward at constant speed (a = 0), the apparent weight equals the gravitational weight mg = 686 N, so option c ("Equal to the gravitational weight force") is correct.

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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