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. 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)