How Do You Pour Water Up Into a Glass?
BY RHETT ALLAIN09.12.138:24 AM
What the heck? Did gravity reverse itself to make this water flow UP? No, not quite. But this trick is indeed impressive. I’ve looked at this same phenomena before, but let’s go over it again. (I saw the above image on Richard Wiseman’s blog.)
Does the Water Fall Up?
No. In fact, the water is falling down. Yes, I know it doesn’t look like it’s falling. That’s because the camera is in an accelerating reference frame of the plane. If you take a little piece of water (a drop) and let go, it will accelerate towards the Earth with an acceleration of 9.8 m/s2. However, the plane is also accelerating downward with an acceleration greater than 9.8 m/s2. Maybe this diagram will help.
If you could just see the water from a stationary reference frame (maybe a floating hot air balloon), you would see the water indeed falling down. Now, I remember that I said “falling down” and not “moving down”. The water actually might be moving up. The key is that even though it is moving up, it is accelerating down. The plane also is accelerating down. As long as the downward acceleration of the plane is greater than the water, the water will move into the cup above it.
What if the acceleration of the plane and the water were the same? Then the water and the cup wouldn’t get any closer. It would look similar to this dog in a plane that is accelerating down.
Yup. Weightless. You can read more about weightlessness in space in this post.
So, the plane is flying straight down? No. You have to be careful here. The plane is ACCELERATING down. Most likely the plane is flying in a vertical circle. And yes, flying in a circle is an acceleration towards the center of the circle.
What About Fake Forces?
There is another way to look at this problem. We like to think of the momentum principle when dealing with forces (some people would call this Newton’s second Law – but I think that is archaic terminology). This says that a force changes the momentum of an object and I can write it like this:
However, there is a catch. This momentum principle only works if the reference frame (or view point if you wish) is not accelerating itself. But fear not. There is a way to cheat so that we can still use the momentum principle IN an accelerating reference frame (which we physicists call a non-inertial reference frame). The cheat code for this case is a fake force.
Consider a tossed ball in an upward accelerating elevator. Here are the two ways I could look at that ball.
In both views, the ball is in the air for the same time and reaches the same distance from the top of the elevator. To make this work with a fake force, the fake force must be in the opposite direction as the acceleration of the reference frame.
La te xi t 1
Wouldn’t it be cool if you could actually look at a tossed ball both inside and outside an accelerating elevator at the same time? Oh, you can. Even better – I did this a while back.
Back to the case of the upside-down airplane, I can draw this diagram for the pouring water.
As long as the fake force is greater than the gravitational force, the water will “fall up” (in the reference frame of the plane).
If fake forces are so useful, why don’t introductory physics textbooks use them? The answer is simple. Although fake forces can be used for accelerating frames, they are also a bit dangerous. One of the problems introductory students (and normal people too) have is that they like to make up extra forces. The current teaching strategy is to always associate each force due to an interaction with another object. When you add in fake forces, this isn’t as clear. So, the best bet is to stick with “real” forces.