Comment on Chain Fountain videos

Chain Fountain 2 – Drill powered spool
https://www.youtube.com/watch?v=bcsb1xAv7XA

When the beads are in a jar, they have a vertical component of velocity to go up and over the rim, so the beads trajectory follows gravity. Since stress travels through the beads much faster than the beads themselves, the force of the faster beads in the downward flow is transmitted to the beads just starting out and up. It appears instantaneous, but it is not. As the whole string accelerates, the velocity of the whole string increases. The mass of the moving beads increases as more beads move.

When you draw the beads from this flat platform, they are launched in their trajectories with no upward velocity. Essentially shot horizontally and gravity takes over.

When you add additional velocity, by hand, at the beginning, he and you both give upward and outward (vertical and horizontal) velocity. Throwing the beads into an upward and outward path. Then gravity, and the stress transmitted from the whole downward moving string of beads takes over. The rate of lowering of the peak depends on the stiffness of the bond between beads. A rigid hoop would rotate if you gave it velocity. Mercury or water flowing through a pipe stays at a nearly constant velocity, but it can be calculated (tedious).

The mass of the moving beads is the mass already off the table or off the surface of the pile of beads. The downward force on the peak bead is just the component of the force pulling down at an angle toward the beads rising plus the component of the force from the falling beads falling. That angle (and the associated horizontal and vertical components of the stress force plus the gravity force) depends on the radius of curvature and stiffness of the string or force joining the beads.

“Fountain” is relevant. The force holding a water jet together as it rises from the surface to a peak and then falls is the same. Except water only holds together slightly. Your compatriot would have fun using jello or sticky beads or magnetic beads.  Or beads with rubber bands.

Your videos could be run faster and then count the beads below the peak, or just track all of them. Find their positions over time and calculate the horizontal and vertical velocity and acceleration. The beads do fall with gravity, those are the ones past the peak of their trajectory – pulled by vertical gravity, and by vertical and horizontal accelerations.

I really appreciate your efforts. This is a fascinating problem, and you helped make it clearer. But it needs measurement (video is good) and it needs models (equations, data, calculations). There are lots of cameras that can run at hundreds of frames per second. You said 40 frames (30 fps?) so a second to rise a few inches. The vertical velocity of the beads just leaving the surface can be estimated from (1/2) M*V^2 = M*g*h, or V = sqrt(2*g*h). Or measure the velocity and it should be closely related to the peak height.

10 inches is 0.254 meters. V = sqrt(2*9.8 meters/secondSquared*0.254 meters) = 2.23 meters/second. Your video should tell you the bead horizontal velocity at the peak.

Thanks again. Sorry I have to use words. Even a system of equations is clumsy. But you might try writing the forces on the beads, the mass of the rising beads, the mass of the falling beads, the peak bead which can be rising or falling, and all the velocities and accelerations involved. As a classroom experiment video is the easiest.

HTML5 javascript does allow video processing for machine vision and changing pixels in video frames. But it is Sooo! clumsy. The browser companies don’t really try very hard to take their global training responsibilities seriously. All the developers work in their groups or alone, with no standards or goals. No wonder the Internet never improves, except slowly in fits and starts and many failures.

Put some cardboard circles on your spool and the chain won’t fall off so easily. Don’t hold it and wave it around. Keep it fixed, duct tape and string and rubber bands should work. Some people love hot glue. You could use silk thread to pull the first bead.

Richard Collins, Director, The Internet Foundation

If you close the loop of beads, you can have a pile of beads on the ground, and launch them with a spool or other means of accelerating them. Then you can run it continuously. An infinite loop of beads. Launch them at an angle just like shooting a cannon. See how the trajectory changes based on the density of beads, their cohesive strength and ability to transmit stresses. Put the pile on the floor, use a spool to get them back up to the table. That should work, but it will require care.

When you lift a board from one end, the other end pushes down on the ground more. The mass of the board times the gravity is the force. and the surface area determines the pressures (stresses) involved. The angle of the force you apply mimics the force the outgoing bead chain exerts on the “just rising” bead. It has horizontal and vertical components.

Two rotating elements on either side of the bead, pressing inward, probably rubber or something soft, can accelerate a chain at a given angle and speed. It is “speed” along the trajectory, and then “components of velocity” when using x y z or R theta phi coordinates. Those baseball and tennis ball throwers are something like that.  Use the initial velocity and angle to estimate the peak and how far away it will be.  You could make one large and fast enough to have a chain circle the earth, or reach to orbit. Then it would be a launcher and you would probably want to not lose any energy as the chain comes down again.

Thank you for your interesting videos. But try to limit talking head frames. I would like to see the beads and their data.  If you and ElectroBoom work together, there are 1.92 Billion first time learners in the world now from 5 to 20 years old. They need inexpensive and globally stable experiments, ways of sharing and collaborating. It is vastly wasteful for billions of people to all reinvent and relearn basic physics. Let the computers and intelligent algorithms remember that, and let people put together the pieces in different ways.

Richard Collins, Director, The Internet Foundation