M-EngMom3: Nearly elastic collisions; example: steel collision or impact balls

PIRA: 1N30.10

Equipment: Standard set of steel impact balls supported by bifilar suspension. Ten balls have same mass; one ball has three times the mass of each of the others. The equipment is located at Set 9, Cabinet 1, Shelf 1.

Procedure: The equipment consists of a standard set of impact balls. Cups at the top allow the balls to be stored when so desired. In general, keep the large ball stored in its cup.

If one ball is removed from the end of the line of similar balls and allowed to swing a short distance to strike the line, only one ball flies off the far end. Two balls at one end, two at the other. Seven at one end (there are only ten), seven at the other, etc. Configurations dropped at one end, such as three-space-one, come off the other, in this example, three-space-one. That is, almost! If the input swings are too vigorous it is soon obvious that the results are not so simple. Early explanations quoted simultaneous conservation of momentum and energy.

The success of the experiment as described depends upon the balls not touching each other at the time of the first impact. In such a case there follows a rapid succession of two-body collisions, and the outcome is as described (see reference 2). If the balls are in contact at the outset (because of the supporting cords not in vertical planes, because balls are magnetized, or because surface film of oil causing one ball to adhere to adjacent one), the outcome is quite different (see references 1 and 3).

The large ball in this set has three times the mass of each other ball. It should not be used in the multiple ball experiment except to show the complexity of the result. However, an interesting experiment can be performed with the large ball and the smaller ball adjacent to it, the other balls being put in the cups on top. The small ball is allowed to swing into the larger stationary ball. Both bounce back equal distances from the larger impact point. When they fall together from this configuration the large ball stops dead and the small ball returns to the position from which it was originally dropped. From here the small ball swings into the stationary large ball, and the cycle is repeated.

Maintenance: Do not allow the balls to be magnetized! If the balls get rusty specks on the surface, these can be buffed off with rouge and a buffing wheel. If the climate is so humid that rust is a real problem, coat the balls with a good machine oil that will not rust them (some oils do); then before use wash the balls a couple of times in acetone and wipe with dry clean cloth or Kleenex. (Do not breath acetone vapor).

References: (1) Chapman, Seville: Some Interesting Aspects of Impact Ball Apparatus. American. Journal. of Physics: 9: 357-360 (1941)

(2) Kline, John V.: The Case of the Counting Balls. American. Journal.

of Physics: 28: 102-103 (1960)

(3) Chapman, Seville: Misconceptions Concerning the Dynamics of the

Impact Ball Apparatus. American Journal. of Physics: 28: 705-711 (1960)