In Newton’s cradle, when the ball on one side strikes the subsequent stationary balls, the ball on the end side propels outwards. How is that possible?
Newton’s cradle, also known as Newton’s balls, is an educational tool which works based on conservation laws of energy and momentum. On the one hand, Newton’s cradle relieves stress and is found on every successful person’s desk and the other hand, it is an appealing distraction to many people.
Newton’s cradle was named in 1967 by an English actor Simon Prebble, in honour of Isaac Newton. This device is also known as Newton’s rocker, Newton’s balls and Newton’s pendulum.
History of Newton’s Cradle
Despite its name, the theoretical principles of Newton’s cradle were presented in papers to the Royal Society in 1962 by John Wallis, Christiaan Huygens & Christopher Wren. In particular, it was Huygens to note the conservation of kinetic energy and momentum. Since the term, kinetic energy wasn’t introduced for nearly another century, Huygens referred to the principle behind it as a quantity proportional to mass velocity squared.
Rene Descartes, a French philosopher suggested the idea of conservation but failed to solve the problem completely. According to this philosopher,
Momentum = Mass x Speed
This worked only for some situations, but not for collisions between objects.
Later Huygens suggested a change which solved the problem. Huygens suggested replacing speed with velocity because velocity implies the direction of motion, therefore the momentum of two objects of same size travelling with the same velocity in the opposite directions will be equal to zero.
Why Does Newton Get Name Credit?
Newton gets the name credit mainly because of the following two reasons –
- Newton’s second law of motion derives the law of momentum conservation. Interestingly, Newton published his laws of motion in 1687, twenty-five years after Huygens gave the law of momentum conservation.
- Newton was more famous than Huygens and also, his overall impact on the Physics world was much greater than anyone.
Newton’s Cradle Design
There are several artistic modifications of Newton’s cradle, but the basic setup consists of several balls hung in a line from two crossbars, parallel to the line of the balls. For stability, the crossbars are attached to a heavy base. The balls are hung by light wires, forming an inverted triangle.
All the balls are of the same size and possess the same weight, mass and density.
Balls can be of any size, weight and mass as long as they all are of the same size, weight and mass. The alignment of the balls to the crossbars is equally important. Though any number of balls would work, it has the odd number of balls usually.
What Are These Balls Made Of?
The balls are made of the material with high elasticity and uniform density. As we know, a material with high elasticity bounces more, therefore, high elasticity of the material allows the balls to move for a longer time. Commonly, stainless steel is used for Newton’s cradle balls. Titanium can be used as well, but it’s expensive.
Stainless steel doesn’t deform but compresses by a few microns when it hits the next ball.
The same density of the balls maintains the energy transferred between the balls without much interference.
The new kind of high elastic alloy used to manufacture Newton’s cradle is Amorphous metal. But since they are expensive to manufacture, they aren’t currently used. These have no ready-made shear points as the molten metal is cooled rapidly to obtain random molecular alignment, unlike normal metals which have crystal-like alignment.
Working Principles of Newton’s Cradle
As mentioned earlier, this cradle works based on the laws of energy and momentum conservation.
The law of energy conservation says that energy can neither be created nor destroyed, but converted from one form to another. The law of momentum conservation says that when two objects within an isolated system collide, the momentum remains the same i.e. conserved before and after the collision.
- Height, h = 0
- v = 0
- Potential energy = mgh = 0
- Kinetic energy = (1/2)mv2 = 0
- Momentum = mv = 0
When the first ball is lifted,
- Height increases
- Gravitational potential energy increases
- Kinetic energy = o
When the ball is released,
- Height decreases
- Potential energy converts into kinetic energy
- Ball gains momentum
At the bottom of the swing,
- Entire potential energy is transformed into Kinetic energy
- Ball attains maximum momentum
Impact on the next ball,
- The first ball loses its entire energy
- Transfers energy and momentum to the next ball it strikes.
- The second ball compresses slightly, signifying the transfer of energy in the form of potential energy
- The second ball regains its actual shapes, converting potential energy into kinetic energy while transferring it to the next ball.
The process of compression and decompression continues until the last ball.
The Final Sphere
- It decompresses.
- No energy transfer, as no subsequent ball is present.
- No energy loss
- Shoots up with speed equivalent to the released speed of the first ball, conserving the momentum
- The rising height of the final ball = the dropping height of the first ball.
What if you release more than one ball?
Since we know each ball transfers enough energy to move one other ball, the number of balls propelling to the air will be equal to the number of balls released. Also, we know
Momentum = Mass X Velocity
To conserve the momentum, if the mass of the balls is equal, the speed will remain the same as well.
Newton’s Cradle work based on the laws of energy & momentum conservation. Newton’s cradle is a stress reliever and is found on the desktop of every Fortun 500 CEO.