Wednesday, March 10, 2010

Physics, Visually

One of the things I enjoy about Newtonian Physics is that it's all about concrete, relatively human-scale phenomena - things that I can draw. I get a kick out of trying to put a little fun and realism in the sketches I make in my physics homework of the problems, almost all of which I start by drawing or diagramming.

A lot of intelligent people I know are intimidated or "don't get" higher math, but I think that the operations themselves are nothing those people couldn't do. I think the problem is the abstraction of describing things with numbers instead of as themselves. I think that a lot of physics can be done in a numberless, if somewhat tedious, way, using Euclidean geometry - until non-conservative forces like friction and air resistance are allowed to screw everything up, it's all about vector math and vector math is all about line segments and similar triangles. Most physics problems happen over time, something that can sometimes be problematic to describe well in words but often translates well to a series of pictures.

So I wondered if I could express Newtonian Physics in the format of a comic book, and it got me sketching. The following are attempts at Newton's three laws.

I knew I wanted a sense of motion in the picture, so I drew foreshortened arrows on a trajectory that would take the hockey puck out of the page and send it whizzing past the viewer. A lot of physics is less apparent in the real world because things like friction and air resistance screw it all up. A small object on ice experiences negligible friction and air resistance, so it's under those circumstances that one might see an object in motion tending to stay in motion. It's a mark of Newton's genius that he realized that that's the rule and overturned the previous idea that continuous application of force was needed to keep an object in motion.

In this panel, we see a tug boat pulling a barge. The tug exerts constant force, and the change in the barge's velocity is proportional to the force and happens in the same amount for any given period of time. As the amount of time approaches zero, the change in velocity becomes the rate of change, acceleration. It's actually quite difficult to find a "clean" example of this in real life. For example, the tug boat and the barge are in an environment in which the faster they go, the more counterforce is exerted against them by the water. At some point, they'll reach a speed at which the counterforce from drag and turbulence is equal to the force that the tug boat can develop. I suspect that the tug boat's propeller also develops less force as the speed of the water around it rises, but I haven't studied fluids yet.

Another example of this phenomenon is what happens when a stagehand leans against a heavy box with good casters. (I realize the good casters part almost never happens, but bear with me.) The box will begin to move. If the stagehand continues to lean on it, the box will accelerate. If the stagehand tries to keep up with the box while maintaining the same angle of lean, he'll continue to exert about the same force, the box will keep accelerating, and sooner or later he'll fall into the orchestra pit. I thought that tug boats might be more relatable than road cases, though.

Finally, this is Newton's Third Law. I was trying to think of a concrete example for a while, and nothing was coming. Then I realized that the calf stretch where you push against a wall has three matched pairs of external forces on the body of the person, here dressed as a superhero, doing the stretch. The wall pushes back with a force equal to the push, first of all. Otherwise either the person would fly backwards or put his hands through the wall. That push has to originate somewhere. That somewhere is his feet, pushing back against the ground. The ground pushes forward with static friction. Finally, the superhero has weight, pressing down into the ground. The ground pushes back with an equal force. That equal force is called the "Normal Force," denoted 'N.'

It occurred to me after the fact that I didn't really express that the forces in those pairs are equal. If I were to actually do this, I think I'd just use the little slashes used in Euclidean geometry.

I realize there are a lot of other people who've already had this same idea. I drew some inspiration from a proof my teacher did of something to do with elastic collisions. He proved it entirely with Euclidean geometry - aside from letters naming the line segments, there was no text and there were no numbers. I also had a friend turn me on to xkcd recently.

I've also heard there's a book that already sort-of does this, Larry Gonick's The Cartoon Guide to Physics. I've never seen it myself, and now I have to.

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