An impressive ping-pong ball cannon can be made by placing a bottle of liquid nitrogen at the bottom of a container and quickly covering it with, say, 1500 ping-pong balls. The liquid turns rapidly into a gas whose mounting pressure explodes the bottle, sending a swarm of balls upward out of the container. Surprisingly, the container also moves upward. This is a counterintuitive effect because the balance of forces, that is, Newton's third law does not seem to allow the container to move upwards. We explain the effect as a consequence of granular jamming in combination with Coulomb's friction law.

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See supplementary material at https://doi.org/10.1119/1.5088805 for animated sequences of the simulation Movie M1.mp4 shows a numerical simulation of the ping-pong balls cannon. In quantitative agreement with the experiment, the barrel jumps to a height of approximately 0.9 m. Movie M2.mp4 shows the formation of the force network (plug formation) during the first 600μs after the beginning of the explosion and its later decay. The left side shows a cut through the barrel and details of the modeling of the explosion. The force network is shown right where the forces are represented by bars whose color codes the shear forces. The movie therefore shows the vertical forces transmitted between ping-pong balls in contact with the barrel responsible for the acceleration of the barrel. Movie M3.mp4 shows a numerical simulation of idealized systems where either the friction between ping-pong balls (left) or the friction between ping-pong balls and the barrel (right) is omitted. The first case suppresses jamming, the second case does not allow transfer of momentum in the vertical direction between the plug and the barrel. In both cases the barrel remains in contact with the floor while the ping-pong balls leave the barrel at high velocity. Movie M4.mp4 shows a numerical simulations of the system in the absence of gravity and a solid floor. In this case, the total momentum is conserved due to the absence of external forces. Left: frictional walls and frictional particles; right: no friction at the wall. In the latter case, the terminal relative velocity between the center of mass of the balls and the barrel is smaller since friction between the plug of particles and the vertical walls decelerates the relative motion; <https://mss.cbi.fau.de/sup/ping-pong-cannon/>.
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Supplementary Material

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