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One of the more memorable student course evaluations I've gotten in my years at Union was from a student in the introductory physics-for-engineers course who complained "They abstracted away all the interesting stuff, like air resistance." This strikes physicists as a weird thing to say, because air resistance is *annoying*-- if you abstract it away, you can solve a huge range of problems with a pencil and paper, getting elegant sets of equations you can write down and manipulate algebraically. When you include air resistance, though, you have basically no choice but to solve it numerically, writing some kind of computer simulation, and every time you want to change any of the parameters, you need to go back and run the whole simulation again. That's a big hassle.

Of course, that mostly reflects a fundamental difference in mindset between physicists and (proto-)engineers. Physicists are interested in fundamental laws and elegant equations, engineers are interested in building stuff. And when you're building stuff that's going to move around on the surface of the Earth, you need to worry about air resistance. Or, for that matter, *off* Earth, as air resistance is a big part of the plot of *The Martian*. So engineers tend get a little obsessive about it.

Of course, there is a tiny bit of common ground, thanks to the fact that the air resistance force isn't actually all that large. So the physicist's approach of ignoring air resistance works pretty well for a lot of cases involving everyday objects, particularly those with a large mass.

You might think this is because the air resistance force depends on the mass, but you'd be wrong-- it's exactly the opposite. Air resistance is insignificant for heavy objects precisely because it *doesn't* depend on the mass. This is because a force is just an interaction that tries to change the momentum of an object, and the momentum depends on the mass; the larger the mass, the larger the momentum, and the more force you need to change it. If the force also depends on the mass, the change in the velocity ends up being independent of mass-- this is why falling objects near the surface of the Earth all drop at the same rate, regardless of mass. Heavier objects experience a larger force of gravity, but they also have more momentum for a given velocity. The two effects exactly cancel each other out, and you end up with the same acceleration due to gravity for everything.

Air resistance, on the other hand, does *not* depend on mass, only on the density of air, the shape of the object, and the velocity of the object (or the square of the velocity, depending on the size and density-- air resistance is messy...). The force is the same for objects with the same shape and speed but different masses, but the momentum is different, and thus the *change* in velocity will be different. Specifically, the change in motion due to air resistance gets bigger as the mass gets smaller.

This is easy enough to demonstrate by throwing things around, and I shot some video the other day of me tossing the kids' toys in the air to illustrate the basic point:

There are three objects in the clip, all basically round: a small soccer ball (fairly heavy, around 200g), a big beach ball (mass around 65g), and a balloon left over from SteelyKid's birthday party a month and a half ago (mass about 7g). You can see the difference between these pretty clearly in the clip: the soccer ball flies smoothly, the beach ball floats a little, and the balloon really seems to hang in the air.

This is even more clear if you track the position of the objects over time, using something like Tracker Video Analysis. Which I did, because I'm a physics professor, and produced the following graph:

These look superficially similar in that they go up and come back down, but you can see a clear difference: the curve for the soccer ball looks the same coming down as going up, while the balloon clearly falls in a different way than it rose. Both the beach ball and the balloon take longer to rise and fall, reflecting the fact that air resistance slows them more significantly than the soccer ball.

We can see this even more clearly by trying to make these data points fit with the simple, elegant physics equation. In the absence of air resistance, an object falling near the surface of the Earth should trace out a parabola, with an acceleration of 9.8 m/s^{2} downward. If we fit a parabola to the soccer ball's flight, we can see that this works really well:

The line goes nicely through nearly all the points, and the value of acceleration you get from this is amazingly close to the expected result: 9.76+/-0.04m/s^{2}. Doing the same thing with the balloon, on the other hand...

That's clearly not a good fit, even though the goodness-of-fit parameter is R^{2}=0.976, a value to make economists drool (it's 0.9996 for the soccer ball). The line misses a bunch of the points on either side, and does so in a systematic way. That's because this curve isn't *really* a parabola at all-- it's pushed away from the elegant parabolic shape by the air resistance force, which produces an acceleration that's about 30 times greater for the balloon than the soccer ball.

In fact, if you look at the tail end of the balloon's flight, the points seem to fall along a straight line, not a parabola. (A straight-line fit works great (R^{2} of 0.9992), but isn't that visually interesting, so I won't include the graph...). This is the phenomenon of "terminal speed"-- since the air resistance force increases as speed increases, as gravity pulls the balloon down the air resistance force increases until it's just as big as the gravitational force. At which point, gravity pulling down and air resistance buoying the balloon up cancel each other out, and the balloon falls at a constant speed. This is critically important physics for things like skydiving or the re-entry of spacecraft coming down from orbit.

In fact, terminal velocity gives you a nice conceptual explanation of why spacecraft engineers have to work so hard to dissipate the tremendous heat generated by craft falling back to Earth. A falling object that reaches its terminal velocity does not increase its kinetic energy as it falls further (kinetic energy depends only on mass and speed), but *does* continue to lose potential energy due to gravity (which depends only on mass and height). That energy has to go somewhere, and it gets turned into heat.

(Actually, I'm not sure if re-entering spacecraft reach terminal velocity-- probably depends on the exact configuration... It gets the idea of why you *have* to have heat generated, though.)

So, what do we learn from all this? Well, first, that air resistance is annoying, but real . Second, that it's not all that significant for a lot of everyday situations involving objects with reasonably large masses, so the physicist's "ignoring air resistance" approach works pretty well. And third, video analysis of kids' toys can be entertaining and enlightening, at least if you're a physics nerd.