In an accelerating elevator, a person’s weight on Earth is 700 N. If the elevator accelerates upward with the same magnitude as Earth’s gravitational acceleration (a = g), what is the person’s apparent weight?

What “apparent weight” means in an elevator

Your true weight is the gravitational force $mg$.

A scale in an elevator measures the normal force $N$ from the floor on you, and that normal force is what we call your apparent weight.

Setting up the forces and using Newton’s 2nd law

Take upward as positive. Forces on you:

• Upward: normal force $N$
• Downward: weight $mg$

Newton’s 2nd law gives: $$N - mg = ma$$ So, $$N = m(g+a)$$

Plug in the given numbers

You are told your weight on Earth is $700\,\text{N}$, so: $$mg = 700\,\text{N}$$ And the elevator’s upward acceleration is $a=g$, so: $$N = m(g+g)=2mg=2(700\,\text{N})=1400\,\text{N}$$

Quick check

Because the elevator accelerates upward, you should feel heavier than normal, so a value bigger than $700\,\text{N}$ makes sense.