Newton's cradle, named after Sir Isaac Newton, is a device that demonstrates conservation of and energy using a series of swinging spheres. When one on the end is lifted and released, it strikes the stationary spheres; a force is transmitted through the stationary spheres and pushes the last one upward. The device is also known as Newton's balls or Executive Ball Clicker.
The conservation of momentum (mass × velocity) and kinetic energy (0.5 × mass × velocity^2) can be used to find the resulting velocities for two colliding perfectly elastic objects. These two equations are used to determine the resulting velocities of the two objects. For the case of two balls constrained to a straight path by the strings in the cradle, the velocities are a single number instead of a 3D vector for 3D space, so the math requires only two equations to solve for two unknowns. When the two objects weigh the same, the solution is very simple: the moving object stops relative to the stationary one and the stationary one picks up all the other's initial velocity. This assumes perfectly elastic objects, so we do not need to account for heat and sound energy losses. Steel does not compress much, but its elasticity is very efficient which means it does not cause much waste heat. The simple effect from two same-weight efficiently elastic colliding objects constrained to a straight path is the basis of the interesting effect seen in the cradle and gives an approximate solution to all its action.
For a sequence of same-weight elastic objects constrained to a straight path, the effect continues to each successive object. For example, when two balls are dropped to strike three stationary balls in a cradle, there is an unnoticed but crucial small distance between the two dropped balls and the action is as follows: The first moving ball that strikes the first stationary ball (the 2nd ball striking the 3rd ball) transfers all its velocity to the 3rd ball and stops. The 3rd ball then transfers the velocity to the 4th ball and stops, and then the 4th to the 5th ball. Right behind this sequence is the 1st ball transferring its velocity to the 2nd ball that had just been stopped, and the sequence repeats immediately and imperceptibly behind the first sequence, ejecting the 4th ball right behind the 5th ball with the same small separation that was between the two initial striking balls. If they are simply touching when they strike the 3rd ball, the more complete solution described below is necessary in order to be precise.
Using an efficiently elastic material other than steel such as rubber or glass, larger or smaller balls, or flattening the surface at the contact points will not change the action (final velocities) of the cradle as long as the same change is made in each ball. This is clear from the simple solution for when the balls only collide in pairs. It is also true for the complete solution because the compressibility of the surfaces relative to each other (not the actual amount of compression) determines the percent of kinetic energy transferred to each ball and therefore the final velocities. Steel is better than most materials because it allows the simple solution to apply more often in subsequent collisions. Hollow thin-shell spheres or objects with traditional springs on their surfaces will have a smaller exponent than the Hertzian 1.5 value which will cause their action to be a different, further away from the ideal simple solution if their surfaces are initially touching.
In order for the simple solution to precisely predict the action, no pair in the midst of colliding may touch a third ball because the presence of the 3rd ball effectively makes the ball being struck appear heavier. Applying the two conservation equations to solve the final velocities of three or more balls in a single collision results in many possible solutions, so these two principles are not enough to determine resulting action.
Even when there is a small initial separation, a third ball may become involved in the collision if the initial separation is not large enough. When this occurs, the complete solution method described below must be used.
Small steel balls work well because they remain efficiently elastic with little heat loss under strong strikes and do not compress much (up to about 30 µm in a small Newton's cradle). The small, stiff compressions mean they occur rapidly, less than 200 microseconds, so steel balls are more likely to complete a collision before touching a nearby third ball. Softer elastic balls require a larger separation in order to maximize the effect from pair-wise collisions.