Would you weigh less in an elevator? - Carol Hedden

Transcriber: Tom Carter
Reviewer: Bedirhan Cinar

You step into an elevator. It starts going down, fast. What would happen if you jumped right when it started going down? Would the ceiling hit your head? Ouch! Do you stay suspended in the air while the elevator plummets down? Let's examine the elevator problem one step at a time.

First, consider a scale. You know, the kind of scale you weigh yourself on. When you step on a scale to weigh yourself, there are two forces involved. One, gravity pulls you down. Two, the scale pushes you up. What? You didn't know a scale could push? Of course it can! If it didn't push up on you, you would go crashing through the floor. This upward push is called the normal force, and yes, it is normally there.

Since you're just standing there on the scale, you're not moving. Therefore, you're not accelerating. Newton's second law of motion -- net force equals mass times acceleration -- tells us that if the acceleration equals zero, the net force must equal zero. Which means that the force of gravity pulling you down must be equal to the force of the scale pushing you up.

Now let's suppose you're standing on that scale in an elevator. At first, the elevator is standing still, so you and the scale are standing still. The two forces on you are equal and opposite. You can read how hard the scale is pushing by looking at it. We call that your weight. Then, the elevator starts falling down. You and the scale are in the elevator, so you are falling down too, faster and faster. That means you are accelerating downward.

Now there is a net force in the same direction as the acceleration -- down. Since gravity hasn't changed, that must mean the scale isn't pushing up as hard. So the scale is reading a smaller number. The faster the elevator accelerates, the less the scale pushes up.

What if you jumped? Would you stop falling? Would the elevator hit your head? Well, what's pulling the elevator down? Gravity. Is gravity pulling on you? Of course. So your relative position in the elevator will stay the same. The ceiling will only hit you if you can jump up to the ceiling.

Now consider: what would happen if the elevator accelerated upward and, even more frightening, if someone snuck in and cut the cable holding the elevator, what would happen then? Think about it.