# Inertial Force Vs. Weight

What if, while coming down in an accelerated elevator, the inertial force acting on us is greater than our own weight? Would we fly upwards?

• What is the inertial force? When descenting in an elevator, your weight pulls down and a normal force of the floor holds you up. When accelerating downwards, the size of this normal force changes. There are no other forces. What did you mean with an inertial force? – Steeven Dec 11 '17 at 14:13

## 1 Answer

When the elevator accelerates downwards with acceleration $\vec{a}$, the apparent weight of the person will be:

$$W_{a}=W-ma=m\left(g-a\right)$$

If the elevator is in free fall, meaning that $(a=g)$, the person will feel weightless.

In order to make the elevator go down with an acceleration greater than $g$, an external force must act upon it in the downward direction. In this case the person will be pushed upwards - (accelerated upwards relative to the floor of the elevator).

• "pushed upwards" Do you mean accelerated upwards relative to the floor of the elevator? – Bill N Dec 11 '17 at 16:52
• @BillN, Exactly! – Andrei Geanta Dec 11 '17 at 21:08