Steel does not compress much, but its elasticity is very efficient, so it does not cause much waste heat. This assumes perfectly elastic objects, so there is no need to account for heat and sound energy losses. When the two objects weigh the same, the solution is simple: the moving object stops relative to the stationary one and the stationary one picks up all the other's initial velocity. 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. These two equations are used to determine the resulting velocities of the two objects.
The conservation of momentum (mass × velocity) and kinetic energy ( 1/ 2 × mass × velocity 2) can be used to find the resulting velocities for two colliding perfectly elastic objects. All the animations in this article show idealized action (simple solution) that only occurs if the balls are not touching initially and only collide in pairs. For example, in a real Newton's cradle the fourth has some movement and the first ball has a slight reverse movement. If one ball strikes four stationary balls that are already touching, these simple equations can not explain the resulting movements in all five balls, which are not due to friction losses. Newton's cradle can be modeled fairly accurately with simple mathematical equations with the assumption that the balls always collide in pairs. The central ball swings without any apparent interruption. Newton's cradle three-ball swing in a five-ball system. However, if the colliding balls behave as described above with the same mass possessing the same velocity before and after the collisions, then any function of mass and velocity is conserved in such an event. Some say that this behavior demonstrates the conservation of momentum and kinetic energy in elastic collisions.
When two (or three) balls are dropped, the two (or three) balls on the opposite side swing out. There are slight movements in all the balls after the initial strike but the last ball receives most of the initial energy from the impact of the first ball. Any efficiently elastic material such as steel does this, as long as the kinetic energy is temporarily stored as potential energy in the compression of the material rather than being lost as heat. The impact produces a compression wave that propagates through the intermediate balls. This shows that the last ball receives most of the energy and momentum of the first ball. The ball on the opposite side acquires most of the velocity of the first ball and swings in an arc almost as high as the release height of the first ball. When it is let go, it strikes the second ball and comes to nearly a dead stop. When one of the end balls ("the first") is pulled sideways, the attached string makes it follow an upward arc.
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