A person with mass 54.2 kg stands on a bathroom scale while riding an elevator. If the elevator has an upward acceleration of magnitude 2.00 m/s2, what is the reading on the scale?

Question

BlackTom AI · Accepted Answer

The scale measures the normal force N. For an elevator accelerating upward with acceleration a, Newton’s second law gives N − mg = ma, so N = m(g + a).

1) Relevant knowledge points and concepts
- Newton’s second law (ΣF = ma) applied in the vertical direction.
- Apparent weight equals the normal force from the scale.
- For upward acceleration, the normal force exceeds mg by an amount m a.

2) Complete reasoning process step by step
- Write forces: upward normal force N, downward gravitational force mg.
- Sum forces: N − mg = m a (positive a upward).
- Solve for N: N = m(g + a).

3) Calculations with intermediate steps
- Given m = 54.2 kg, a = 2.00 m/s^2, take g = 9.80 m/s^2.
- g + a = 9.80 + 2.00 = 11.80 m/s^2.
- N = 54.2 kg × 11.80 m/s^2.
- Multiply: 54.2 × 11.80 = 54.2 × (10 + 1.8) = 542.0 + 97.56 = 639.56 N.
- Rounding to three significant figures gives N ≈ 640 N.

4) Why the correct answer is correct
Because the elevator accelerates upward, the normal force must support both gravity and provide the upward acceleration. The formula N = m(g + a) yields 639.56 N, which rounds to 640 N — matching the listed correct choice.

5) Why the other options are incorrect
- 389 N is much smaller than mg (mg ≈ 54.2×9.80 = 531.2 N); 389 N would correspond to a large downward acceleration, not the given upward acceleration.
- 749 N is larger than the correct 640 N and would correspond to a much larger upward acceleration (about 4.0 m/s^2).
- 531 N equals approximately mg (no acceleration) — that would be the scale reading for zero acceleration, not for a = 2.00 m/s^2.
- 423 N is even less than mg and corresponds to downward acceleration of magnitude 2.00 m/s^2, the opposite of the stated motion.

6) Conclusion
The scale reading is N ≈ 640 N, which matches the provided correct answer (640 N).

A person with mass 54.2 kg stands on a bathroom scale while riding an elevator. If the elevator has an upward acceleration of magnitude 2.00 m/s2, what is the reading on the scale?单项选择题

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