Why can’t you change seats on an empty plane?

It’s the last one flight of the day and the plane is quite empty. So you think, maaaybe you just have to move a few rows, where there is a nice window seat with a view that is not obstructed by the wing.

Not so fast, buster. The flight attendant says it’s not. You have to stay in your assigned seat or you will throw off the weight distribution of the plane. Really? Would moving a normal sized human make a difference? Yes, you know where this is going: Answering this question requires a lot of awesome physics. So let’s go!

Mass center

People often say that the center of mass of the object is the place where all the gravitational force acts. It’s a fair working definition, and you can use it to solve many physics problems, but it’s not really true. In fact, the gravitational force pulls everyone part of an object, not just a point.

(A quick side note: We’re actually going to watch the center of gravitynot the center of mass, but in a constant gravitational field like here on Earth, they are the same.)

If you really want to understand the center of mass, you need to think torque. Looking back at Newton’s second law, it states that a net force changes the motion of an object (F_net = mass × acceleration). So if the net force is zero, the motion of an object does not change. If it moves with a certain speed, it will continue to do so. If it is at rest, it will continue to rest.

Here’s a little experiment: Place a pencil on a flat table and then, take your two index fingers, push from the opposite sides, right to the center. Just stop there, right? Because they apply equal and opposite forces, the net force is zero. But what if you push like this:

Pencil pusherGraphics: Rhett Allain