A Monash College student of mass 69.1 kg standing in an elevator briefly experiences a constant upward acceleration of 1.9 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 force: N = m(g + a) for upward acceleration.

1) Relevant knowledge points and concepts
- True weight (gravitational force) = mg.
- Apparent weight is the normal force the scale (or elevator floor) exerts on the person.
- When an object accelerates upward with acceleration a, Newton’s second law gives N − mg = ma, so N = m(g + a).

2) Step-by-step reasoning
- Given mass m = 69.1 kg and upward acceleration a = 1.9 m/s^2.
- Use standard gravitational acceleration g = 9.81 m/s^2.
- Plug into N = m(g + a).

3) All intermediate calculation steps
- g + a = 9.81 + 1.9 = 11.71 (m/s^2).
- N = 69.1 × 11.71.
- Break multiplication: 69.1 × 11.71 = 69.1 × (11 + 0.71) = 69.1×11 + 69.1×0.71.
- 69.1 × 11 = 760.1.
- 69.1 × 0.71 = 49.061.
- Sum: 760.1 + 49.061 = 809.161 N ≈ 809.16 N.

4) Why the correct answer is correct
- The apparent weight is larger than the true weight because the elevator’s upward acceleration requires an extra upward normal force to produce the upward net acceleration ma. The formula N = m(g + a) directly yields 809.16 N for the given numbers.

5) Why the other options are incorrect
- b. 546.58 N corresponds to N = m(g − a) (i.e., if the elevator accelerated downward at 1.9 m/s^2).
- c. 131.29 N equals m a (the net upward force required), not the apparent weight (normal force).
- d. 677.87 N equals mg (the weight when the elevator is stationary or moving at constant velocity), not the increased apparent weight during upward acceleration.

6) Conclusion
Using N = m(g + a) with m = 69.1 kg, g = 9.81 m/s^2 and a = 1.9 m/s^2 gives N ≈ 809.16 N, which confirms the provided answer.

A Monash College student of mass 69.1 kg standing in an elevator briefly experiences a constant upward acceleration of 1.9 as he moves from level 2 to level 6. What is apparent weight of the student at this moment?数值题

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