In the previous post, I arrogantly announced I could explain the classic experiment in which you drop a tennis ball and basketball together, and the tennis ball goes flying. Then, I got as far as examining a single bounce. Part way. This might take a while.
Today I’m going to keep talking about that single bounce. When you drop a basketball and see how high it bounces (assume it goes straight up-and-down), there are three possibilities:
- It bounces higher than you dropped it.
- It bounces back to the same height as you dropped it.
- It bounces lower than you dropped it (or does not bounce).
We’ve already said that the first one is impossible given that we can’t build a perpetual motion machine, and that a ball that bounces higher than it started would let us make a successful one. When we make the experiment, it turns out the basketball does not bounce back as high as it was dropped from. Today we’ll see why this is true.
On the face of it, bouncing back to exactly the same height seems a reasonable thing to do. After all, if the basketball is going to bounce to, say, 72% of the height it was dropped from, where does that number come from? Why not 71% instead? Bouncing back to exactly the same height is a sort of natural choice if the problem is very simple, because it’s a very simple answer. The problem, however, is not very simple.
Watch this remarkable video of a golf ball colliding with a wall at high speed.
This is clearly not simple! After bouncing off the wall, the motion of the golf ball is very different than before bouncing – all that vibrating and oscillating got added in. So it makes sense that the trip back up should be different than the trip down.
The oscillation of the ball is a form of motion, and if we had a ball oscillating the way it does in that video, we could find some way to use that to drive a cuckoo clock, if we were clever. So the ball can’t bounce to its original height because if it did, we could catch it there, damp the oscillations while driving the cuckoo clock, and drop it again.
Further, when the ball hits the ground, it makes some noise. The noise is motion of the air, and this motion could be used to drive a cuckoo clock. The wall the ball bounces off is shoved back during the collision – this too is a motion that could drive the clock. Additionally, the ball and wall both heat up a little in the collision. If you’ve ever driven a nail with a hammer and touched the nailhead immediately afterward, you’ve probably noticed this phenomenon. The difference in heat between the part of the wall that the ball hit and the rest of the wall could, in principle, drive the cuckoo clock as well.
I’m not interested in the details and mechanics of how the various types of motion I just mentioned could be converted into driving the cuckoo clock. The goal is to understand a bounce, and for now we simply need to know that when the bounce occurs, there’s a lot more going on than simply a ball changing direction. All that other stuff makes the sequence distinctly irreversible. We go from having the motion concentrated in once place – the overall movement of the ball – to many places – the oscillations of the ball, noise, heat, the movement of the wall, etc. As various other bits of the environment pick up motion (which, in general, we call “energy” in physics), the ball loses it, and can’t bounce to the same height again.
This brings up an interesting question. We know the ball doesn’t bounce as high as it was dropped because its motion gets spread out to other places. Does that mean that the process could, in principle, work the other way? Could various bits of the environment give motion to the ball, so that in fact it does bounce higher than it was dropped in that special case? For example, in the video, the ball oscillates after hitting the wall, but not before. What if we struck the ball to set it oscillating, then dropped it? Could it then work the other way, losing most of its oscillation when it bounces off the wall, but actually picking up speed and going higher than it was dropped?
That’s possible. It would be a difficult trick to pull. But notice it doesn’t violate our principle of no perpetual motion, because in order to make that scheme work you need to strike the ball and set up oscillations, which is against the “no outside influences” rule.
Another way to make the ball bounce back faster would be to move the wall it crashes into. If we push the wall forward to meet the ball, then the wall might give some of its energy to the ball, and the ball could bounce away quickly and go higher than dropped. This is what happens when a baseball player hits a pitch. The batted ball can travel much further than the pitcher could have thrown it, since the bat adds energy to the ball. This is what’s happening with the basketball and tennis ball. We’ll get more into it next time.
Before I go, check out this additional video of a much tamer golf ball collision. In the slower collision, the golf ball is still deformed, but not so severely. You can guess that if you want something to bounce up to nearly its original height, it’s better to drop it from a low height than a high one – and that’s true (try it).