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Newton's cradle or Newton's balls, named after Sir Isaac Newton is a device that in prinicipla demonstrates conservation of momentum and energy, although this it is not enough to explain the result.

Description and purpose

It is constructed from a series of pendulums (usually five in number) abutting one another. Each pendulum is attached to a frame by two strings of equal length angled away from each other. If these strings are not same in length, the balls would then be unbalanced. This string arrangement restricts the pendulums' movements to the same plane.

The behaviour of the pendulum follows from the conservation of momentum and energy only in the case of two pendula. Indeed, if there are r pendula there are also r unknown velocities to be calculated from the initial conditions. An additional condition for the observed outcome is that a shock wave has to propagate dispersion free through the chain.

The principle demonstrated by the device, the law of impacts between bodies, was first demonstrated by the French physicist, Abbé Mariotte in the 17th century. [1] [2] Sir Isaac Newton acknowledged Mariotte's work, among that of others, in his Principia.

In pedagogic settings, a cradle device is sometimes used to present the concept of "action-reaction" (Newton's third law), with the words said to the cadence of the clacking pendulums as they execute a single cycle of swinging and clacking oscillation. This is not a very clear presentation of action-reaction. In fact, the conservation laws can be easily derived from Newton's second and third laws.

k=1,2,3,4,5 ;

Conservation of Momentum (1)

Conservation of Energy (2)

( Simplification : v1r = v2r =....= vkr = vr )

(1), (2) =>

Solution (n/k) = 1

Invention and design

Newton's Cradle has been a popular executive toy since being first named and produced in 1967 by English-born actor Simon Prebble. His original wooden frame version was first sold by Harrods of London and later a chrome design for the Carnaby Street store Gear was created by the sculptor and future film director Richard Loncraine. The popular clackers toy of the early 70's is believed to have been manufactured in Spain using a plastic injection moulding originally made for the Newton's Cradle manufacturer, Scientific Demonstrations Ltd, just before the company went into self liquidation. Due to the scarcity and high cost of steel ballbearings, the company intended to use high density plastic balls instead.

The largest cradle device in the world was designed by Chris Boden and is owned by The Geek Group in Kalamazoo, Michigan. It is on public display and is used for science and technology demonstrations. It consists of a set of 20 matched bowling balls each with a weight of 15 pounds (6.8 kilograms). These are suspended from cables from metal trusses in the ceiling. The cables have a length of 20 feet (6.1m) and the balls hang 3 feet (0.9m) off the floor.

References

1. ^ Harvard website page on Newton's Cradle. Retrieved on 2007-10-07.

2. ^ Catholic Encyclopedia: Edme Mariotte. Retrieved on 2007-10-07.

Literature

* F. Herrmann, P. Schmälzle: A simple explanation of a well-known collision experiment, Am. J. Phys. 49, 761 (1981)
* F. Herrmann, M. Seitz: How does the ball-chain work?, Am. J. Phys. 50, 977 (1982)

Physics Encyclopedia