Newton's Cradle

Newton's cradle is a clear visual example of the conservation of both momentum (mass x velocity) and kinetic energy (0.5 x mass x velocity^2) in a mechanical system. When the cradle only has two balls, these two principles are sufficient to specify its behaviour; i.e. there is no way of conserving momentum and energy when the first ball strikes the second other than for the first to stop and the second to move off at the same speed as the first.

However, these two principles alone are not sufficient to explain the behaviour of a cradle having three or more balls. For example, if the balls each have a mass of 1 and the first ball strikes the other two stationary balls with a velocity of 1, the initial momentum of the system is 1 x 1 = 1 and the kinetic energy is 0.5 x 1 x 1^2 = 0.5. If the first balls stops and the third ball moves off with a velocity of 1 (which is what actually happens), the momentum remains 1 and the kinetic energy remains 0.5. However, if the first ball were to bounce backwards with a velocity of -1/3 and the second and third balls were to move forward each at a velocity of 2/3, the momentum would be 1 x (-1/3 + 2/3 + 2/3) = 1 and the kinetic energy 0.5 x 1 x ((-1/3)^2 + (2/3)^2 + (2/3)^2) = 0.5; i.e. this would also preserve both momentum and kinetic energy; however, it is not what happens. There must therefore be an additional constraint at work. This additional condition relates to a shock wave, which has to propagate through the line of balls without dispersion.

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.[8] [9] Newton acknowledged Mariotte's work, among that of others, in his Principia