Newton's cradle

The cradle in motion.

Newton's cradle, named after Sir Isaac Newton, is a device that demonstrates conservation of momentum and energy.

Construction

The animated image above shows a typical Newton's cradle; a series of identically sized metal balls suspended in a metal frame so that they are just touching each other at rest. Each ball is attached to the frame by two wires of equal length angled away from each other. This restricts the pendulums' movements to the same plane.

Action

If one ball is pulled away and released, it falls and appears to come to a dead stop on hitting the other balls. The ball on the opposite side of the series appears to instantly acquire the speed of the first ball and swings in an arc that one would expect of the first ball. Again, the animated image shows this better than words can do.

The first time observer may find this visually intriguing and counter-intuitive. If a person charged into one end of a row of adjacent people then one would intuitively expect the whole row of people to be moved, rather then the last person in the row to acquire the kinetic energy.

The intermediate balls appear stationary. In fact, the cradle continues to work even if the intermediate balls are physically clamped still. This is also counter intuitive - transmitting motion without moving.

What actually happens is that the first impact produces a shock wave that propagates through the intermediate balls. A hard material such as steel is very good at doing this, where common objects like people in a bus queue are not.

The shock wave travels at the speed of sound in the medium. The speed of sound in steel is much faster (around 4699 m/s) than in air (around 300 m/s). The time to travel a few centimetres is too small for human perception, and so is the physical distortion of the balls as the shock wave passes through them.

In the real world, none of these processes have perfect efficiency. Energy is lost in the suspending wires, friction of the surrounding air, and sound. The last is obvious as we can hear the clicking of the balls. Toward the end of oscillation, even the intermediate balls are jiggling a bit.

Further intrigue is provided by starting more than one ball in motion. With two balls, exactly two balls on the opposite side swing out and back. While this is satisfyingly symmetrical, why could not one opposite ball swing out twice as fast, or four balls at quarter speed? Having the same number of balls swing on each side conserves both energy and momentum.

More than half the balls can be set in motion - for example 3 of 5 will result in the central ball swinging without abrupt cessation or resumption of motion.

Further Physics

The behaviour of a pendulum follows from the conservation of momentum and kinetic energy only in the case of two pendulums. Indeed, if there are r pendulums 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 without dispersion 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. Newton acknowledged Mariotte's work, among that of others, in his Principia.

In academic 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.

Applications

The most common application is that of a desktop executive toy. A less common use is as an educational aid, where a tutor explains what is happening or challenges students to do so.

Invention and design

There is much confusion over the origins of the modern 'Newton's Cradle'. An unknown designer in Canada has been credited, without any substantiating evidence, as being the first to name and make this popular executive toy. However in early 1967, an English actor, Simon Prebble, coined the name 'Newton's Cradle', (now used generically) for his iconic wooden version manufactured by his company, Scientific Demonstrations Ltd . After some initial resistance from uncomprehending retailers, they were first sold by Harrods of London thus creating the start of an enduring market for executive toys. Later a very successful chrome design for the Carnaby Street store Gear was created by the sculptor and future film director Richard Loncraine.

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.

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)

External links

• iPhone example with touch and tilt simulation
• Java Applet moving example
• Largest Newton's cradle in the world
• Further explanation
• Newton's Cradle Applet by found in EJS 4.1 user/murcia/fem/mechanics