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Q & A: Zooming balloons

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Most recent answer: 07/02/2018
When two inflated balloons of different sizes are taped to a straw which has been threaded onto a string which has been tied between two chairs, which one will travel the fastest?
- Daniel (age 10)
Williams Elementary, Glendora Ca USA

This old answer misses a key point, discussed in the next answer in the thread. For a related discussion see:

 Hi Daniel,

That’s a pretty tricky question! There are a lot of things that affect the speed of the balloons and there isn’t an easy answer. Let’s say for now that your balloons are identical. When you blow up a balloon, you stretch out the rubber. Balloon rubber is kind of like a spring; if you’ve ever played with springs before, you’ll notice that as you push or pull on the spring, it gets more and more difficult to continue pushing/pulling in that direction. In the same way, as you stretch out a balloon, it becomes more and more difficult to continue stretching it because the balloon wants to pull back on itself and become unstretched. In other words, the bigger balloon wants to pull back on itself more than the smaller balloon. [see below- that applies to stretching by hand but not to blowing up with air. The remainder of this paragraph is probably wrong.] When you let the balloons go, you let air escape out of the holes in the balloons. Because the bigger balloon wants to pull in more than the smaller balloon, it pushes out on the air with a greater force than the smaller balloon. Newton’s third law of motion states that for every action, there is an equal and opposite reaction. Therefore, if the balloons are pushing out on the air, the air is also pushing forwards on the balloons. The air is pushing forwards more on the bigger balloon than the smaller one, so this should make the bigger balloon move faster.

However, this is only part of the story! At the beginning, I said to assume that the two balloons were identical. In real life, it is impossible for two balloons to be *exactly* alike. So now let’s say that your two balloons are different; maybe you got them from two different companies. Just as different springs have different degrees of "springiness," balloon rubber can be of different stretchiness. Suppose you have one balloon (A) that is really hard to stretch out and another balloon (B) that is really easy to stretch out. Even if you blow up balloon B bigger than balloon A, there is a chance that the rubber in balloon A is pushing harder on the air than the rubber in balloon B, so balloon A might still move faster than balloon B. However, this all depends on to what extent the balloons differ in their stretchiness and how big you blow them up. For the most part, balloons that you buy are similar enough so that this won’t affect their speeds by much.

There is one other major factor that affects the speed of the balloons. This factor is air resistance. If you take a paper clip and a feather and drop them at the same time, you’ll see that the paper clip reaches the ground a lot faster than the feather. This is because air pushes on objects as they move, and since the feather has much more surface area than the paper clip, its motion is opposed by more air than the paper clip. Basically, the more surface area an object has, the more air resistance it has. (Air resistance also depends on how fast you are going -- if you are moving faster, you experience more air resistance.) That means that when you let your two balloons go, the bigger one will feel greater air resistance than the smaller one since it has more surface area. This would make the larger balloon travel slower. However, since most balloons travel for only a short period of time before the air runs out (unless you have a monster-sized balloon!), there is only a short time for them to accelerate. Chances are that in this time frame, they don’t reach speeds where the force of air resistance is large relative to the propulsion force (the force of the inside air pushing forward on the balloons).

Of course, given all these things that affect the speeds of the balloons, there is no way to figure all of this out exactly by sitting around and thinking about it; the best way to answer your question is to get balloons of different types and try it out!

(published on 10/22/2007)

Follow-Up #1: balloon stretchiness

In your answer, you say it becomes harder and harder to blow up a balloon, yet when I blow up a balloon, I notice that the first puff is the hardest and then each additional puff takes about the same force to force into the balloon - definitely not taking more lung power to fill it up. So, are balloons different than springs?
- George (age 55)
Long Valley, NJ, USA

You're right- balloons are only a little bit like springs.

There's a basic general complication that was missed in that old answer. Balloons are 3-D. The radius R is only is proportional to V1/3, where V is the volume.  If the energy of the stretch went as R (as would hold if the balloon material were like a siimple spring then the stretch energy would go as V2/3. The increase in energy from adding a given small volume of air (say 1cm3) then goes as V-1/3 i.e. it gets smaller as the balloon blows up more. So it would get easier to blow up as you went.

This is why when you connect two balloons they tend to get very unequal inflation. The one that is less inflated is squeezing harder on its air than the one that's more inflated, at least down to the point where it's not stretched much at all.

That brings up another complication as well:  the rubbery material is not always in the linear elastic range, meaning that doubling the stretch doesn't double the force or quadruple the energy. So that's a complication that requires more detailed knowledge about the balloons than I have. 

Mike W.

posted without vetting becuse I was in a hurry to correct the incorrect old answer.

(published on 07/02/2018)

Follow-up on this answer.