Ping pong ball physics

What happens when a row of PPBs (Ping pong balls) roll on inclined wide tracks?

 
 
Usually they roll nicely, but sometimes the balls won't start up. Especially when the inclination is small and the tracks wide. 

The cause lies in the friction between the balls where they touch. To start rolling, the first ball has to overcome the friction between the balls. When rolling on wide tracks, a ball has to rotate many revolutions to cover a given distance. The force available to overcome the friction will be small, and the direction of movement at the friction point will be quite close to parallel to the touching surfaces. This makes start-up difficult. 

When rolling on narrow tracks (or a single track), the ball needs not rotate so fast. The force available to overcome the friction will be correspondingly greater. The direction of movement at the friction point will also be less parallel to the surfaces, easing start-up even more. 

Other factors can also play a part. Static electricity will make the balls repel each other, easing start-up. Rough surfaces on balls or tracks will obviously do no good. 
 

 Static electricity

 
PPBs are easily charged statically, especially in cold weather, when the indoor humidity is low. When charged, the balls repell each other. This can cause balls resting on a slightly inclined plane to stay away from each other. I have been trobled by two effects caused by this behaviour. 
  • When the balls do not rest closely together on a tilting arm, the arm may tilt too early, before the last ball has arrived.
  • When the balls roll off a tilting arm, the repelling forces can cause extra spacing between the balls when they roll. This can cause the arm to tilt back to normal position before all balls have left it.
A good remedy against static electricity is ordinary clothes softener. I wash the balls in a solution about 5 times stronger then normal. The antistatic of a washing of the Vitensenteret clock has now lasted for several months. 
 

Lifting PPBs by fans

A PPB weights 2.5 g, and has a diameter of 38 mm. When pushed up in a tube of the right diameter, theoretically a pressure of 22 Pa (Pascal) or 0.00022 atmospheres is enough to lift it. According to a catalogue I have got, small axial fans of the type used in PC power supplies can deliver from 10 to 200 Pa (probably at zero flow) depending on size, price etc. Thus such fans are good for lifting PPBs. 
 
I use plexiglass tubes with an inner diameter of 40 mm, which is 2 mm more than the ball diameter. Thus the air leakage around the ball is small. The dimensioning point however is where the balls enter the tube, where the leakage will be much greater. What counts is usually not the maximum pressure of the fan, but how large air flow it can deliver to overcome the leakage. 

A tennis ball on the other hand weights 58 g and has a diameter of 65 mm. Theoretically it needs a pressure of 175 Pa. For ttennis balls may be a vacuum cleaner is better as a fan. 

If you generate the pressure using a piston arrangement a piston with a weight of 1.75 g per square cm (1.75 cm height of water) should theoretically  generate enough pressure to lift a tennis ball (and 0.22 g per square cm, 2.2 mm of water,  should lift a PPB). Thus the piston arrangement should be good for both, and in addition has the advantage of requiring audience activity, which has appeal at least for children.
 
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Last modified 15.05.98