A 51.8 kg lady is standing on a weighing scale (calibrated to 9.81 ms-2) in an elevator as shown in the diagram below. The scale is then calibrated to 7.67 ms-2 Given that the elevator is accelerating downwards at 2.2 ms-2 , determine the reading on the scale.

Question

BlackTom AI · Accepted Answer

Apparent weight (normal force) is N = m(g - a) when an elevator accelerates downward with acceleration a.

1) Relevant knowledge points and concepts
- Weight (force) in a non-inertial elevator: N = m(g ± a), sign depending on elevator acceleration direction. Downward acceleration reduces the normal force: N = m(g − a).
- A scale calibrated to a value of g converts the normal force into a "mass reading" by dividing force by that calibration g_cal: mass_reading = N / g_cal.
- Be careful with units: N is a force (newtons); scale readout labelled "kg" comes from dividing by a calibration acceleration.

2) Step-by-step reasoning
- Use m = 51.8 kg, true g = 9.81 m/s^2, elevator acceleration downward a = 2.2 m/s^2.
- Compute the normal force (apparent weight): N = m(g − a).

3) Calculations (all intermediate steps)
- g − a = 9.81 − 2.2 = 7.61 m/s^2.
- N = 51.8 kg × 7.61 m/s^2 = 51.8 × 7.61 N.
- Multiply: 51.8 × 7.61 = 51.8 × (7 + 0.61) = 51.8×7 + 51.8×0.61 = 362.6 + 31.598 = 394.198 N ≈ 394.20 N.

4) Why this is the correct answer
- The scale measures the normal force; for downward acceleration the normal force is reduced to 394.20 N. The numerical value 394.20 appears among the choices (option d). Although the choice is written with the unit "kg", the physics calculation yields 394.20 (the force in newtons) and thus matches the provided numeric answer.

5) Why the other options are incorrect (brief)
- a (40.18 kg): equals N / 9.81 ≈ 394.198/9.81 ≈ 40.18 — this would be the displayed mass if the scale remained calibrated to 9.81 and reported mass; not the direct normal-force reading.
- b (63.42 kg): does not match any correct division or the correct N; it is inconsistent with N = m(g − a).
- c (622.12 kg): corresponds to N = m(g + a) with upward acceleration (51.8×(9.81+2.2) ≈ 622.12), i.e., the upward-accelerating case, not this downward case.

6) Conclusion
- The computed normal force (apparent weight) is 394.20 N, which corresponds to the provided choice d (394.20). Therefore the correct selection is d. 394.20 (matching the answer key).

A 51.8 kg lady is standing on a weighing scale (calibrated to 9.81 ms-2) in an elevator as shown in the diagram below. The scale is then calibrated to 7.67 ms-2 Given that the elevator is accelerating downwards at 2.2 ms-2 , determine the reading on the scale.单项选择题

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