Question

An elevator accelerates upward at 3m/s^2 for a brief time. A 500 N woman standing on bathroom scales notices the reading is not what she expected. What do the scales read?

Answer 1

The Task:

An elevator accelerates upward at $3\mathrm{m}/\mathrm{s}^2$ for a brief time. A 500 N woman standing on bathroom scales notices the reading is not what she expected. What do the scales read?

Solution:

The gravitational acceleration of the Earth $g = 9.8 \, m/s^2$ acts on a woman when she is on the ground, and it gives her a weight $P_0 = 500 \, N$. So we can find a mass $m$ of the woman:

$$m = \frac{P_0}{g} = \frac{500 \, N}{9.8 \, m/s^2} = 51 \, kg$$

When a woman is standing on the elevator, it gives her to the acceleration of gravity additional acceleration $a = 3 \, m/s^2$, and thus her weight increases:

$$P = m(g + a) = 51 \cdot (9.8 + 3) = 653 \, N$$

The Answer: P=653 N