Comment fonctionnent les berceaux de Newton

Vous avez probablement déjà vu cet engin auparavant : cinq petites boules d'argent sont suspendues en une ligne parfaitement droite par de fins fils qui les attachent à deux barres horizontales parallèles, qui sont à leur tour attachées à une base. Ils sont assis sur des bureaux dans le monde entier.

Si vous tirez une balle vers le haut et que vous la relâchez, elle retombe et entre en collision avec les autres avec un clic fort. Ensuite, au lieu que les quatre balles restantes se balancent, seule la balle à l'extrémité opposée saute vers l'avant, laissant ses camarades derrière, immobiles. Cette balle ralentit jusqu'à s'arrêter puis retombe, et les cinq sont brièvement réunies avant que la première balle ne soit à nouveau repoussée du groupe.

Il s'agit d'un berceau de Newton, également appelé bascule de Newton ou cliqueur de balle. Il a été nommé ainsi en 1967 par l'acteur anglais Simon Prebble, en l'honneur de son compatriote et physicien révolutionnaire Isaac Newton.

Malgré sa conception apparemment simple, le berceau du Newton et ses boules qui se balancent et cliquent ne sont pas seulement un jouet de bureau ordinaire. Il s'agit en fait d'une démonstration élégante de certaines des lois les plus fondamentales de la physique et de la mécanique.

Le jouet illustre les trois principaux principes de physique à l'œuvre : la conservation de l'énergie, la conservation de la quantité de mouvement et le frottement. Dans cet article, nous examinerons ces principes, les collisions élastiques et inélastiques, ainsi que l'énergie cinétique et potentielle. Nous examinerons également le travail de grands penseurs tels que René Descartes, Christiaan Huygens et Isaac Newton lui-même.

1. Histoire du berceau de Newton
2. Conception et construction du berceau de Newton
3. Composition de boules dans un berceau de Newton
4. Conservation d'énergie
5. Conservation de l'élan
6. Collisions et frottements élastiques

Étant donné qu'Isaac Newton a été l'un des premiers fondateurs de la physique et de la mécanique modernes, il est parfaitement logique qu'il invente quelque chose comme le berceau, qui démontre si simplement et élégamment certaines des lois fondamentales du mouvement qu'il a contribué à décrire.

Mais il ne l'a pas fait.

Malgré son nom, le berceau de Newton n'est pas une invention d'Isaac Newton, et en fait la science derrière l'appareil est antérieure à la carrière de Newton en physique. John Wallis, Christopher Wren et Christiaan Huygens ont tous présenté des articles à la Royal Society en 1662, décrivant les principes théoriques à l'œuvre dans le berceau de Newton. C'est Huygens en particulier qui a noté la conservation de la quantité de mouvement et de l'énergie cinétique [source : Hutzler, etal ]. Huygens n'a cependant pas utilisé le terme "énergie cinétique", car l'expression ne serait pas inventée avant près d'un autre siècle; il a plutôt fait référence à "une quantité proportionnelle à la masse et à la vitesse au carré" [source : Hutzler, et al. ].

La conservation de la quantité de mouvement avait été suggérée pour la première fois par le philosophe français René Descartes (1596 - 1650), mais il n'a pas été en mesure de résoudre complètement le problème - sa formulation était que la quantité de mouvement était égale à la masse multipliée par la vitesse (p=mv). Bien que cela fonctionnait dans certaines situations, cela ne fonctionnait pas dans le cas de collisions entre objets [source : Fowler ].

C'est Huygens qui a suggéré de changer "speed" en "velocity" dans la formule, ce qui a résolu le problème. Contrairement à la vitesse, la vitesse implique une direction de mouvement, de sorte que la quantité de mouvement de deux objets de même taille voyageant à la même vitesse dans des directions opposées serait égale à zéro.

Même s'il n'a pas développé la science derrière le berceau, Newton est reconnu pour deux raisons principales. Premièrement, la loi de conservation de la quantité de mouvement peut être dérivée de sa deuxième loi du mouvement (la force est égale à la masse multipliée par l'accélération, ou F = ma). Ironiquement, les lois du mouvement de Newton ont été publiées en 1687, 25 ans après que Huygens ait fourni la loi de conservation de la quantité de mouvement. Deuxièmement, Newton a eu un impact global plus important sur le monde de la physique et donc plus de renommée que Huygens.

Bien qu'il puisse y avoir de nombreuses modifications esthétiques, un berceau de Newton normal a une configuration très simple : plusieurs balles sont suspendues en ligne à partir de deux barres transversales parallèles à la ligne des balles. Ces barres transversales sont montées sur une base lourde pour plus de stabilité.

On small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all.

All the balls are, ideally, exactly the same size, weight, mass and density. Different-sized balls would still work, but would make the demonstration of the physical principles much less clear. The cradle is meant to show the conservation of energy and momentum, both of which involve mass. The impact of one ball will move another ball of the same mass the same distance at the same speed. In other words, it'll do the same amount of work on the second ball as gravity did on the first one. A larger ball requires more energy to move the same distance -- so while the cradle will still work, it makes it more difficult to see the equivalence.

As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best. If the balls hit each other at some other point, energy and momentum is lost by being sent in a different direction. There's usually an odd number of balls, five and seven being the most common, though any number will work.

So now that we've covered how the balls are set up, let's look at what they're made of and why.

In a Newton's Cradle, ideal balls are made out of a material that is very elastic and of uniform density. Elasticity is the measure of a material's ability to deform and then return to its original shape without losing energy; very elastic materials lose little energy, inelastic materials lose more energy. A Newton's cradle will move for longer with balls made of a more elastic material. A good rule of thumb is that the better something bounces, the higher its elasticity.

Stainless steel is a common material for Newton's cradle balls because it's both highly elastic and relatively cheap. Other elastic metals like titanium would also work well, but are rather expensive.

It may not look like the balls in the cradle deform very much on impact. That's true -- they don't. A stainless steel ball may only compress by a few microns when it's hit by another ball, but the cradle still functions because steel rebounds without losing much energy.

The density of the balls should be the same to ensure that energy is transferred through them with as little interference as possible. Changing the density of a material will change the way energy is transferred through it. Consider the transmission of vibration through air and through steel; because steel is much denser than air, the vibration will carry farther through steel than it will through air, given that the same amount of energy is applied in the beginning. So, if a Newton's cradle ball is, for example, more dense on one side than the other, the energy it transfers out the less-dense side might be different from the energy it received on the more-dense side, with the difference lost to friction.

Other types of balls commonly used in Newton's cradles, particularly ones meant more for demonstration than display, are billiard balls and bowling balls , both of which are made of various types of very hard resins.

Alloy There!

Amorphous metals are a new kind of highly elastic alloy. During manufacturing, molten metal is cooled very quickly so it solidifies with its molecules in random alignment, rather than in crystals like normal metals. This makes them stronger than crystalline metals, because there are no ready-made shear points. Amorphous metals would work very well in Newton's cradles, but they're currently very expensive to manufacture.

The law of conservation of energy states that energy -- the ability to do work -- can't be created or destroyed. Energy can, however, change forms, which the Newton's Cradle takes advantage of -- particularly the conversion of potential energy to kinetic energy and vice versa. Potential energy is energy objects have stored either by virtue of gravity or of their elasticity. Kinetic energy is energy objects have by being in motion.

Let's number the balls one through five. When all five are at rest, each has zero potential energy because they cannot move down any further and zero kinetic energy because they aren't moving. When the first ball is lifted up and out, its kinetic energy remains zero, but its potential energy is greater, because gravity can make it fall. After the ball is released, its potential energy is converted into kinetic energy during its fall because of the work gravity does on it.

When the ball has reached its lowest point, its potential energy is zero, and its kinetic energy is greater. Because energy can't be destroyed, the ball's greatest potential energy is equal to its greatest kinetic energy. When Ball One hits Ball Two, it stops immediately, its kinetic and potential energy back to zero again. But the energy must go somewhere -- into Ball Two.

Ball One's energy is transferred into Ball Two as potential energy as it compresses under the force of the impact. As Ball Two returns to its original shape, it converts its potential energy into kinetic energy again, transferring that energy into Ball Three by compressing it. The ball essentially functions as a spring.

This transfer of energy continues on down the line until it reaches Ball Five, the last in the line. When it returns to its original shape, it doesn't have another ball in line to compress. Instead, its kinetic energy pushes on Ball Four, and so Ball Five swings out. Because of the conservation of energy, Ball Five will have the same amount of kinetic energy as Ball One, and so will swing out with the same speed that Ball One had when it hit.

One falling ball imparts enough energy to move one other ball the same distance it fell at the same velocity it fell. Similarly, two balls impart enough energy to move two balls, and so on.

But why doesn't the ball just bounce back the way it came? Why does the motion continue on in only one direction? That's where momentum comes into play.

Momentum is the force of objects in motion; everything that moves has momentum equal to its mass multiplied by its velocity. Like energy , momentum is conserved. It's important to note that momentum is a vector quantity, meaning that the direction of the force is part of its definition; it's not enough to say an object has momentum, you have to say in which direction that momentum is acting.

When Ball One hits Ball Two, it's traveling in a specific direction -- let's say east to west. This means that its momentum is moving west as well. Any change in direction of the motion would be a change in the momentum, which cannot happen without the influence of an outside force. That is why Ball One doesn't simply bounce off Ball Two -- the momentum carries the energy through all the balls in a westward direction.

But wait. The ball comes to a brief but definite stop at the top of its arc; if momentum requires motion, how is it conserved? It seems like the cradle is breaking an unbreakable law. The reason it's not, though, is that the law of conservation only works in a closed system, which is one that is free from any external force -- and the Newton's cradle is not a closed system. As Ball Five swings out away from the rest of the balls, it also swings up. As it does so, it's affected by the force of gravity, which works to slow the ball down.

A more accurate analogy of a closed system is pool balls : On impact, the first ball stops and the second continues in a straight line, as Newton's cradle balls would if they weren't tethered. (In practical terms, a closed system is impossible, because gravity and friction will always be factors. In this example, gravity is irrelevant, because it's acting perpendicular to the motion of the balls, and so does not affect their speed or direction of motion.)

The horizontal line of balls at rest functions as a closed system, free from any influence of any force other than gravity. It's here, in the small time between the first ball's impact and the end ball's swinging out, that momentum is conserved.

When the ball reaches its peak, it's back to having only potential energy, and its kinetic energy and momentum are reduced to zero. Gravity then begins pulling the ball downward, starting the cycle again.

There are two final things at play here, and the first is the elastic collision. An elastic collision occurs when two objects run into each other, and the combined kinetic energy of the objects is the same before and after the collision. Imagine for a moment a Newton's cradle with only two balls. If Ball One had 10 joules of energy and it hit Ball Two in an elastic collision, Ball Two would swing away with 10 joules. The balls in a Newton's cradle hit each other in a series of elastic collisions, transferring the energy of Ball One through the line on to Ball Five, losing no energy along the way.

At least, that's how it would work in an "ideal" Newton's cradle, which is to say, one in an environment where only energy, momentum and gravity are acting on the balls, all the collisions are perfectly elastic, and the construction of the cradle is perfect. In that situation, the balls would continue to swing forever.

But it's impossible to have an ideal Newton's cradle, because one force will always conspire to slow things to a stop: friction . Friction robs the system of energy, slowly bringing the balls to a standstill.

Though a small amount of friction comes from air resistance, the main source is from within the balls themselves. So what you see in a Newton's cradle aren't really elastic collisions but rather inelastic collisions, in which the kinetic energy after the collision is less than the kinetic energy beforehand. This happens because the balls themselves are not perfectly elastic -- they can't escape the effect of friction. But due to the conservation of energy, the total amount of energy stays the same. As the balls are compressed and return to their original shape, the friction between the molecules inside the ball converts the kinetic energy into heat. The balls also vibrate, which dissipates energy into the air and creates the clicking sound that is the signature of the Newton's cradle.

Imperfections in the construction of the cradle also slow the balls. If the balls aren't perfectly aligned or aren't exactly the same density, that will change the amount of energy it takes to move a given ball. These deviations from the ideal Newton's cradle slow down the swinging of the balls on either end, and eventually result in all the balls swinging together, in unison.

For more details on Newton's cradles, physics, metals and other related subjects, take a look at the links that follow.

Originally Published: Jan 17, 2012

What is Newton's cradle used for?

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Can a Newton's cradle only work with certain materials?

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