## Tuesday, February 18, 2020

### Physics in the playground V: Swinging

What would a playground be without swings? Well, it don't mean a thing if it ain't got that swing (Doo wah, Doo wah, Doo wah).

The Walnut Hills playgrounds have swings (I was tempted to say, "got swings" but this blog is rated S for "science" so….)

Anyway, here are the swings.

My plan was to swing 10 times, first sitting as still as possible, then with my 10 pound pack (I weighed it with a full water bladder), then pumping it to get more energy into the swing, and then pumping it erratically.

This, I think, is our first adventure with a pendulum. It won't be our last because pendulums are surprising.

I recorded all four swingings on one recording. The phone was on the breast pocket of my overalls so the x direction is left-right, the y direction is up-down, and the z direction is forward-backward.

There wasn't a lot of motion left-right, but there was some. That's a problem with studying pendulum motion. You often want the pendulum to swing in only one direction but that's easier said than done. We'll have to deal with that later when we look closer at oscillatory motion.

The y direction shows the up and down motions. Let's look a little closer at that.

That's not what I expected. I thought I would see nice, smooth wave (sine waves, if you're into trigonometry) going from zero (no motion means no acceleration, right?) to maximum acceleration at the bottom of my swings. It's easy to separate the swings because I specifically counted ten.

The reason I never got to zero acceleration is because, even at rest (and, as we will see over and over, nothing is ever really at rest in the universe) gravity is accelerating me downward. Here's a question. Does my phone accelerometers measure the motion of the Earth around the sun, or the sun's gravitational acceleration, or the sun's motion around the Galaxy?

That little dip at the top is a reminder that, try as I might, I could not sit perfectly still on the swing. As the swing began slowing at the bottom of each swing, I wobbled a little. If you've ever seen a chaos pendulum, the crazy swinging was an amplification of the complex motions there in all pendulums.

Noticed that more weight increased the wobble as I tried to sit still against the inertia of my backpack.

When I pumped the swing, the wobble shifted to the top of each swing where I slowed to a stop. I was leaning forward at the end of the forward swing and back at the end of the backward swing with the motion of the pendulum. You can see how this pattern built up.

There was no build up here, but it's hard to separate the wobble from the swing. I was pumping the swing without any particular timing.

The front to back motions showed an interesting thing. Each trial was ten swings. Check the time for each on the line below.

The swings when I tried to sit still took 26.5 seconds. The swings with a ten pound backpack took 26.7 seconds. When I was pumping the swing, it took 28.1 seconds. And when I was pumping erratically, it took 20.7 seconds to complete ten swings.

The difference in measured time between 10 swings without and with a 10 pound backpack was only 2 tenths of a second - for each swing, only 2 hundredths of a second. That difference could have been due to anything: the wind, a nervous twitch. Basically, a difference of 10 pounds didn't make any difference at all.

Pumping the swing did make a difference. When I pumped in time with the swing, each oscillation was longer, so it took 1.3 seconds longer for 10 swings. Still, a tenth of a second (actually, 0.13 second) for each swing is surprisingly small. The swinging of a pendulum is very stable. That's why they used pendulums in clocks for so long.

Did you expect the erratic swinging to take longer? The jerky motion meant that I couldn't get more altitude, I didn't swing as far, so it took less time - 20.7 seconds instead of 26.5 seconds. It did wear me out more, though. Another thing I learned was how out-of-shape I was from sitting around the month before.

Keep in mind how little difference extra weight caused on the pendulum. We'll be looking at more pendulums later and that's an important issue.

Playgrounds are physics laboratories. If you have one nearby, check it out (just don't interfere with the kiddies fun.)

My heart can't handle the g-forces at an amusement park but, if you like the rides, you might take your smartphone and it's accelerometers for a wild ride. Let us know what you learn!