The old James Bond movie From Russia With Love features one of my favorite physics demos. Here is the non-spoiler version: 007 is being all cool and stuff and meeting with this dude in Turkey (I think it’s Turkey). The dude has someone bring coffee into the meeting, then Blam! Physics.
The demo is the swinging drink tray. How does it work?
Swinging Tray Physics
Let’s start with a non-swinging tray. Suppose I have a tray with a drink on it. In this case, a tasty blue liquid. What happens as I bring this tray to a sudden stop? Here it is in slo-mo:
What happens here and how can we stop it? Let me start with one of my favorite physics ideas: fake forces. Of course, to understand fake forces you must first look at the nature of forces and motion. In general, when a net force acts on an object that object will accelerate. You might like to call this Newton’s Second Law but it doesn’t matter. As an equation, it looks like this:
Yes, both the net force and the acceleration are vector quantities. This means that their direction matters–but for now, just realize that this force-motion equation works. Well, it works if you measure the acceleration from a stationary (technically at least a non-accelerating) reference frame.
If you try to use the force-motion law in an accelerating frame, it doesn’t work. How about an example? Suppose you are in your car and the car is just sitting there at rest. Your acceleration is zero and the net force on you also is zero. This zero net force is the sum of the gravitational force pulling down and the seat pushing up. Not too complicated.
But what happens when the car accelerates? You also are accelerating. If you could view yourself from outside the car in a stationary reference frame, everything would make sense. The only difference in force from the stationary car is that the seat now pushes up and forward. There is no other force pushing backward so that there is net force forward and thus a forward acceleration. The view is different inside the car. From this inside reference frame it seems like you are not accelerating (because you are stationary relative to the car). This means there must be a net-force of zero–but how? The only way is to add a fake force that pushes you into the seat to counteract the seat pushing you forward. You feel this force whenever you accelerate–so, in a sense it’s not so fake.
In physics, forces are interactions between objects (like between me and the Earth–we call this the gravitational force). Fake forces are different. They are not an interaction between two objects. They are just a force that we can add so that the force-motion law works again. The magnitude of this fake force depends on the acceleration of the reference frame and the mass of the object. We can write it as:
Let’s look back at the drink on the serving tray. First, from a stationary view, only three forces act on the cup–gravity, the tray pushing up, and a frictional force pushing to the left. The result of the horizontal force is to give the cup an acceleration to the left. But since the cup is moving to the right, this means the cup continues to move to the right as it slows. Unfortunately, the cup takes longer to slow than the tray, so it slides off. Oops.
Look at the cup from the frame of the accelerating tray and you must add a fake force. The tray is slowing down to the left so that this fake force is to the right. In this frame, the fake force pushes the cup off the tray.
As you can see, you don’t need fake forces to figure out why you would spill your drinks on this normal serving tray. You could easily use the stationary frame to explain the spill. Oh, just let me point out that you could also do the same analysis for the liquid in the cup. Notice that as the cup accelerates (by slowing down), the liquid moves up to the right. For the liquid, it might be easier to consider the fake forces that push it up the side.
OK, now for the swinging tray. Here are three drinks, because three is cooler than one, that don’t spill.
In this case the drinks and tray are also slowing down, but there is no spilled blue liquid. The key to this demo is the string supporting the tray. There is something special about string–it can only exert a force in the direction of the string and you can’t push with it. Since the string is perpendicular to the tray, the string can only exert a force in this direction.
Let’s look at the forces on these cups from the reference frame of the accelerating tray as it swings.
The string accelerates the tray perpendicular to the tray, creating a fake force that pushes the drinks into the tray. If you were on this tray, you would feel heavier–you wouldn’t feel any forces pushing you sideways. This is why the drinks don’t spill. Oh, but what about the gravitational force? That is not perpendicular to the tray. Yes, but gravity is sort of special. It’s not a contact force so that it pulls on all parts of the cup and liquid. Since gravity acts on all parts of the drink equally, there is no method to slosh the drinks out of the cup.
Make your own swinging tray
There are some key elements that make a demo great.
- The result should be surprising. If everyone knows what will happen, it’s not much fun.
- The demo should use simple items. It shouldn’t need super high end scientific equipment.
- Although it appears to be a skillful demo, it shouldn’t require any skill. This is the most important part–it means I look cool without actually being cool.
This swinging tray is easy to make. You just need a sturdy board and some string. I used a small section of tileboard–the same stuff you buy at the hardware store to make your own (cheap) white boards. The key is making the strings so the tray will swing perpendicular to the main string. I did this by drilling holes in the corners of the board and running one loop of string through all four holes. I used a quick link to attach this loop to the main support string. I like this design because it’s adjustable.
Here is a closer look.
Now for the demo. Put your drinks on the tray and just start moving.
If you are brave, you can even swing the tray in a circle.
But wait! It’s not all fun and games. There are three ways you can mess up this demo (I have done them all at one point).
- Don’t let the tray hit another object. If you are swinging the tray and it hits a table, this will exert a force parallel to the tray. The drinks will fly off and spill.
- It might seem cool to swing the tray in a vertical circle, but the tension in the string gets large. If the string breaks, bad things happen. The drinks will fly off and spill.
- You must keep tension in the string. If you let the string go slack, the drinks will fall and spill.
Here is an example of that last failure. At least I was outside.
But really, this is one of my favorite demos. You should probably try this one yourself.