Wednesday, March 14, 2012

The last bowling ball pendulum post I promise

For safety's sake, I took down the pendulum balls last weekend. Thanks so much to all who helped!  It was inspiring to see so many people out together on such cold days to enjoy patterns in gravity and time. Even with all the cool things on youtube, there's nothing like the tactile world. What giant physics demo should we build next year?

Robin asked me to put up some of the final videos of the bowling ball pendulum after tuning. They are big files, so you may have to let them load for a bit or lower your youtube resolution settings if you have a slow connection.


This one, from the side, is in slow motion, and it shows a beautiful corkscrew motion as it goes:


Throughout the project, I was impressed by the idea that the patterns we see are equally in the math and in our minds. They are real patterns, but they come about from the relationship of separate objects.

A number of people have asked about the math that governs this project.  Here's a run-down:
  • The period (length of time for one back and forth) of a pendulum is governed only by the distance from the support to the center of mass of the pendulum. This is nearly the center of the ball in this case, but not quite, as the center of mass is shifted upwards by the mass of the hook-eye and cable. The mass of a pendulum doesn't affect the period.
  • The equation that governs the period is Time=2*pi*(length/acceleration due to gravity)^.5 
  • Once we set the longest pendulum's length, we could figure out how long it took to go 48 times back and forth. This is about 2 minutes, 40 seconds. We called that a "full cycle."
  • From there, we could take that "full cycle" time and back-calculate the necessary lengths so the next pendulum would go 49 times in the same full cycle time, the following one 50 times per cycle, etc.
  • You'll see that at the half-cycle point (about 1 minute, 20 seconds) there is a moment when every other ball is in line at the "to" and "fro" points; a very fast and brave superman could fly down the middle at this moment.
  • After that mid point, the patterns reverse, more or less, to reform a line that starts the original curve again at 2:40.
Though the math is very clean, Matt Tibbits, Theo and Eric Witherspoon, and many others and I spent a lot of time tuning this and trying to get the real thing right. It wasn't so easy, and it never was perfect.  However, it got good enough for us to feel satisfied, and we learned some of the limitations of our materials. Here are some things that complicate the tuning:
  • While the a ball's weight doesn't affect the period, it does affect the amplitude over time. That is, a heavier ball will start with more potential energy and thus will have more energy to work with in overcoming the friction in the hooks and air resistance.  So, for example, the very light red-orange ball doesn't swing out as far as the other balls over time.  I considered putting jam on the hooks for the heavy balls and olive oil on the light balls' hooks, but that started to sound messy.
  • The lighter the ball, the more a given amount of cable and eye hook weight would throw the center of mass off from the center of the ball.
  • The beam from which the balls were suspended flexed a little side to side, and we suspect this changed the balls' motions in some small and mind-boggling ways. We added a stiffener, but still there was some transfer of energy from ball to ball through the beam. 
  • The hooks started getting loose over time and added some wiggle to our already wiggly re-calculations. 

If you're still reading this, you are as much of a nerd as I, and you might be interested in the following equation that predicts where any two balls in the sequence will line up. This came up because we were using a ball-ball-comparison to tune the pendulums and started to see patterns. I include it mostly so I'll have a record of this for when Margot and I rebuild this in the woods below our house this summer:

  1. let x = number of swings per full cycle of a longer ball in any pair we're comparing. 
  2. let S = any integer or half integer representing a 0 velocity point (swing out, E = .5, back for the first period, E= 1, out for the second swing, E = 1.5 etc.) where the two balls might match up. 
  3. let n = the number of the comparison ball, if counting the first ball as 1 (i.e. n=2 for the neighboring ball, 3 for the third in the line, etc.) 
  4. let q= an integer representing the number of full periods ahead the second ball is that allows it to match the first 
The formula boils down to:    x=S(n-1)/q
and anything that satisfies this equation is a match.  If S is a half-integer, the match it on the out-swing, a full integer, the match is back at the starting side.

________

For those of you who haven't seen it, here is another video from Bev Hill, our bowling ball procurement expert:
Pendulum with Ground Level Observers

16 comments:

Robin Dreyer said...

Jeff,

Your persistence on this project was truly inspirational. The video is beautiful

curlyhairfreak said...

I am a student and I was very interested in this project. In my science lab, I designed and made a pendulum out of golf balls. Now to finus my project, I need to explain why the balls make th pattern. I was wondering if you could help me?

Alex Woo said...

How long did it take you to build this demonstration?

Karen said...

Jeff, What was hitting the pipes to make the chiming noise? I assume it was pipes on top of the wooden posts, but didn't think the balls could be hitting it or that would have affected the motion of the balls.
Thanks,
Karen

John said...

Will this work if each ball is on a separate beam.

Barbara Gardner said...

Awesome! I watched this about 10 times already.

Tarnished Rose said...

This has to be one of the coolest things I have ever seen. Just caught the video that was shared on FB.

Marilyn

Ziyon Monte Alto said...

Anyone tried already put sensors in each ball and recording all movement data? This pattern is telling us something...

Bman said...

Curious, are all the bowling balls the same weight?

Elf said...

Nice work! Beautiful to watch the action and the colors.

SJ Morris said...

Is there any way I could get the lengths or cable you used as I would LOVE to recreate this in my school to get the pupils interested in Physics and making links between other subjects.

Tomáš Konopásek said...

why are you excited in patterns in head. This is about capacity. Pendulum system doesnt show pattern. I dont get you

Monower hossain said...

A bowling ball is a piece of sporting equipment used to hit bowling pins in the sport ofbowling. Ten-pin bowling balls are typically hard spheres with three holes drilled in them, one each for the ring and middle fingers, and one for the thumb.

Mari Feline said...

What do you mean "for safety sake"? Were you afraid someone might touch it and get bonked with a bowling ball. Too bad. I was taught, and taught my children--If it isn't yours, DON'T TOUCH OR TAKE IT".

Helish Lawera said...

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Brooke said...

This is super cool, how long did it take you to build it? I needed a science project like this back in high school lol. Since you like bowling balls, I saw some really creative bowling sayings that you may really like, I'll share them here: Bowling Slogans