The Physics Behind Newton's Cradle

This is an object you've probably seen before, maybe as a desk toy or at an institute—whatever, the point is you've seen it. Five metal spheres in a straight line that hang from thin metal wires, it is known as Newton's Cradle and is perhaps one of the greatest objects to display the laws of physics.

It works like this—there are five metal spheres hanging from thin metal wires all lined up. When you lift the sphere at the end and release it, it stops at the next metal sphere but that does not move. Neither does the third, neither does the fourth, but the fifth sphere moves up and then comes down and hits the metal sphere next to it, but again the last sphere moves up and the spheres in the middle don't. This process continues in a cycle but eventually stops. It has a very odd way of moving but also has a very elegant way to display certain laws of physics.

Okay, so let's see what physics Newton's Cradle actually displays. If you haven't figured it out yet, Newton's Cradle displays the laws of Conservation of Momentum and Conservation of Energy.

Okay, now moving on to the actual physics.

So what happens when you raise one sphere is that its gravitational potential energy increases. Potential energy is basically the energy to go into motion—that is a very blunt definition. The mathematical form is much more simplified, PE = mgh, where m = mass, g = gravitational acceleration, h = height. So when the sphere is released the potential energy converts to kinetic energy which is basically the energy during motion. This also has broader meaning—its mathematical form is as follows: KE= 1/2 MV ^ 2. Continuing, the sphere then, in its state of kinetic energy, strikes the sphere next to it and transfers the energy up until the last sphere which has no sphere to give energy to so it moves up, gaining potential energy and decreasing kinetic energy in the process. This displays the Laws of Conservation of Energy, which states that energy cannot be created nor destroyed. Basically what you put in is the exact same that you get out. There is nothing extra.

Now the second aspect of the Newtonian Cradle's movement: when the sphere moves, it gains momentum, which is basically the product of mass and velocity; p=mv is the mathematical form. When a Newton's Cradle moves, you notice that both the spheres at both ends reach the same height while moving. This displays the Law of Conservation of Momentum which states that the initial momentum of an object will always be equal to the final momentum of an object. The masses of both objects are the same, because of the Law of Conservation of Momentum. While moving their velocities remain the same as well. And with that, we learn the two principles of physics displayed in the Newton’s Cradle.

But now let us learn why two spheres can't be displaced when one sphere is released.

Let us prove this mathematically,

When the sphere is released at first, its momentum is p =mv.

If two spheres were displaced, then the momentum would be p =2mv

Due to the Law of Conservation of Momentum,

Mv =2mv

But this isn’t possible as the mass is doubled on the right hand side of the equation. Therefore mv cannot be equal to 2mv, so therefore two spheres cannot be displaced in the cradle.

I'm not exactly sure how to end articles like these so I'll just say I hope you learnt something from this and have a nice day.