Why Does the Balloon Move Forward in an Accelerating Car?

 

I love this experiment. It’s a classic really. Also, Destin (from Smarter Every Day) does a great job making it interesting to everyone.

 

Using Fake Forces

Let me point out one minor complaint. You have to be very careful with the words “move” and “fast”. Does the balloon lean forward when the car is going very fast? Not always. If the car is traveling at a constant speed of 100 mph, the balloon should just point straight up. If the car is going at a very fast speed of 100 mph and then slams on the brakes to reduce the speed to 80 mph (still very fast), the balloon would lean back. The key here isn’t speed at all. The key is the acceleration.

So, the car is accelerating forward and the balloon also leans forward. Why? Well, Destin gives a very nice explanation focusing on the air in the van. The air in the car has a higher density in the back of the vehicle than it does in the front. This means that the net force on the balloon due to collisions with the air will be in the forward direction.

Really, this is an interesting idea. Just think about gas in a stationary and non-accelerating car. The gravitational force pulls down on each molecule of nitrogen and oxygen. However, all the gas doesn’t just fall down to the floor because of collisions with other gas particles. In order to keep particles up at the top of the car, there needs to be more collisions at the bottom of the car in order to support both the lower and upper gas. This gives a greater gas density at the bottom.

Now consider an accelerating car. The back wall of the car will accelerate forward and push on the gas in the forward direction. This will cause more collisions in the forward direction with the rest of the gas. If you could look at individual gas molecules, it would look just like the car is tilted up a little bit in a slightly larger gravitational field.

This brings me to my favorite explanation of the balloon’s motion. Fake forces. What is a fake force? Well, you know about the momentum principle, right? It says that a net force changes the momentum of an object and forces are interactions between two objects (like the gravitational interaction between a ball and the Earth). However, this momentum principle only works if you are viewing the object from a non-accelerating reference frame (inertial reference frame). But what if you want to use the momentum principle in an accelerating mini-van? You can still do this, but you have to add a fake force. By fake, I mean that it isn’t a force between two interacting object. This fake force would have the form:

This fake force is what you feel when you are sitting in an accelerating car. Actually, that’s not true – you can’t feel this force because it’s fake. However, we humans can’t tell the difference between an acceleration and the gravitational force and this agrees with Einstein’s equivalence principle which says that a gravitational field is just like an acceleration.

Let’s start by looking at the forces on a chunk of air in this accelerating mini-van. Here is a view from the accelerating frame right when the car starts to accelerate (and the air has a normal distribution).

With this fake force in the horizontal direction, the piece of air will start to move towards the back of the vehicle. This air and other chunks of air will keep moving back until they interact with the back wall. Soon, there will be more air in the back of the car than in the front. This will change the distribution air and also the direction of the buoyancy force. The new buoyancy force will stop the chunks of air from accelerating with respect to the reference frame. Here is the new force diagram.

But what does this have to do with a balloon? The same buoyancy forces that push on the air push on the balloon (it’s the same air after all). That means the balloon would have forces like this:

Since the balloon has a low mass, it needs an extra force (the tension from the string) to keep it stationary (really, this is why balloons are so fun). But you can see, the balloon leans forward because of this buoyancy force.

Could You Use the Balloon Angle to Measure the Acceleration?

Yes. This would be a simple accelerometer – just like the one in your smart phone (except your smart phone doesn’t have a balloon inside it). You could also use a hanging weight to determine the acceleration, but this isn’t as nice. First, the hanging weight swings in the opposite direction as the acceleration and second, it won’t stop swinging. The balloon as a large drag force on it compared to its mass that prevents excessive swinging.

The balloon accelerometer isn’t very portable. Here is one you can build yourself. Take a clear jelly jar (or something like that) and attach a cork to a string. I then drilled a hole through the lid of the jar and mounted the string then sealed it with glue. After you fill the jar up with water, put the lid back on (all the way up with water with no air) and turn it upside down. Now, you should have a cork floating in water and held down by a string. Here is a picture.

You should build one of these. They are simple and very easy to use. It’s very fun to hold it in your hand while spinning in a circle. As the jar moves in a circle, it accelerates towards the center (towards you). The cork then leans in towards you also. Great personal demo for kids and adults.

But wait! How about an even more sophisticated version? Here is a plastic ball in a spherical flask (that probably has a technical name). The ball in this glass sphere can lean without hitting the wall. I had to add an anchor for the string so that the mounting point would be in the center of the sphere. Here is a picture.

But how can you use this to determine the acceleration? I’m not sure if it’s absolutely true (but it should be close) that the floating ball points in the direction of the vector sum of the negative of the gravitational field and the acceleration. I can draw that as:

If the acceleration vector is perpendicular to the gravitational field, then I can solve for the magnitude of the acceleration.

Or maybe you could put some marks on the glass sphere for an acceleration of 1/2 g at 26.6°, 1 g at 45°, 2 g’s at 63.4° and so on. Now you can go drive around and measure some accelerations.