Investigate

Find yourself an elevator that’s reliable and, ideally, not too busy. Actually, the “too busy” part isn’t that important. It’s more fun to do this when others are watching.

Bring a standard bathroom scale on an elevator. The scale should be able to show you a continuous readout, so typically the scales with the old fashioned, analog dial are best. Stand on the scale while riding the elevator, in particular paying attention to the following conditions:

• Stopped, before any motion has occured
• Just starting to go upwards
• Going upwards, in between floors
• Coming to a stop as the elevator is going upwards
• Just starting to go downwards
• Going downwards, in between floors
• Coming to a stop as the elevator is going downwards

(In case you’re not in the vicinity of an elevator and/or you don’t have a bathroom scale or something similar, I’ve created this for you.)

Before you actually set off and make these observations, imagine what will be happening and think about what you expect will happen to the value on the scale.

When you’re on the elevator, make notes about what you observe and when you observe them, paying attention to the value that the scale reads under the different conditions, as well as any other oddities.

Reflect on your data and think about what these mean. Did the scale reading change in the way you were expecting? What do those scale readings actually mean — if they’re changing at all, it’s probably not due to your weight actually changing.

Debrief

When I first started teaching in the 6-story lab building of our campus, I quickly realized the potential in the infrastructure of the building. There are classic hypothetical problems and thought experiments about elevators, but it isn’t often that we actually put the absurd case studies to a test.

I love to put students on elevators, armed with their notebooks and a careful eye for what’s happening. And, they shoudl also be standing on scales. Alternatively, they could have a cart along with a grocery scale or perhaps a spring scale with a mass hanging from it. But the ideal is to be actually standing on the scale because this is the situation that we use to imagine the actual forces involved in going up and down.

When I first did this with a group of students early in my career, I had one who came back to me, dissatisfied and dismayed. He told me there was something wrong with the measurements: After they’d initially started, the weight he was reading was the same as his actual weight, even while the elevator was heading upwards. What did they do wrong, he wondered? If you’ve done the investigation, you realize that this is (hopefully) exactly the same result that you experienced. What does it mean?

The scale doesn’t necessarily tell you your “weight.” Rather, it tells you how much force the scale is pushing up with. When you’re at home weighing yourself, these two forces exactly balance one another, so you are assured that the reading on the scale is the same as your weight. This also holds true when you are moving at a constant velocity. It turns out, moving at a constant pace either in the upward or downward direction, that no extra forces are needed — the scale has the same reading as your weight. This tells us that constant velocity motion is natural, just as Newton’s 1st Law states. You don’t need any extra force pushing you in one direction or the other. Once you’re moving, you only need the force that’s necessary to balance your weight.

(This should feel counterintuitive in some ways. Go ahead and wrestle with it.)

However, in the elevator, there are instances where your motion changes. When the elevator slows down, speeds up, comes to a stop, or starts up, you have changes in the motion. It’s in these cases that an extra, net force is required. The scale has to push a little harder in the upward direction — more than just your weight — to produce changes in that direction. There is an upward change when you are just starting to go upward, but also when you are heading downward and coming to a stop. (Even if your motion is downward, you can still be changing towards the upward direction, just as you can pay money towards a loan but still be in debt.) The scale pushes with less force than your weight if the change in your motion is downward — as you’re heading upward and coming to a stop, or as you just start to head in the downward direction.

Elevators are an interesting case to me because many use them on a regular basis, but we still might not pay attention to how they’re exerting forces. I love the ridiculousness of standing on a scale in an elevator, but I especially like the simplicity of using the scale as a scientific instrument. It tells us something fundamental about motion, as well as about what conditions an extra force is required.