You are standing on a bathroom scale in an elevator. In which of these situations must the scale read the same as when the elevator is at rest?

Question

BlackTom AI · Accepted Answer

Here is the scenario: you’re on a bathroom scale inside an elevator, and you’re asked in which situation the scale would read the same as when the elevator is at rest. The reading on the scale depends on the apparent weight, which is mass times the apparent acceleration felt by you (including the elevator’s motion). The formula for the apparent weight in an elevator accelerating upward is m(g + a), where a is the elevator’s vertical acceleration (positive when accelerating upward).

Option 1: In free fall (after the elevator cable has snapped).
In free fall, the elevator and you both accelerate downward at g. The apparent acceleration a is -g, so the scale reads m(g + (-g)) = 0. That means you would feel weightless and the scale would read zero, not the same as at rest. This option is not correct for a normal scale reading.

Option 2: Moving up at constant speed.
If the elevator is moving upward at constant speed, its acceleration is zero (a = 0). The apparent weight becomes m(g + 0) = mg, exactly the same as your weight when the elevator is at rest. There is no extra force from acceleration, so the scale reads your usual weight. This option matches the condition of reading the same as at rest.

Option 3: Moving up with increasing speed.
Increasing speed means the elevator is accelerating upward (a > 0). The apparent weight becomes m(g + a) > mg. The scale would read greater than your normal weight. This option would not match the rest condition.

Option 4: Moving up with decreasing speed.
If the speed is decreasing while moving upward, the elevator is accelerating downward (a < 0). The apparent weight becomes m(g + a), where a is negative, so the reading is less than mg. The scale would read less than your normal weight, not the same as at rest. This option is also not the same as at rest.

In summary, only the scenario with zero acceleration—moving up at constant speed—produces the same scale reading as when the elevator is stationary, because there is no net force change on you beyond gravity. The other options involve upward or downward acceleration, which alters the apparent weight on the scale.

You are standing on a bathroom scale in an elevator. In which of these situations must the scale read the same as when the elevator is at rest? 单项选择题

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