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Elasticity is the ability to deform, with complete reversibility — the capability of bouncing back to a shape or state equivalent to the one before an applied force incrementally deformed the object or body. One example of an elastic body that at least approximately meets that description is a billiard cue ball, which following a collision with another billiard ball regains its original shape. Another example of an elastic body is a spring, or a spandex waistband. These regain their shape after undergoing a compressing or a stretching. The physics principle involved is Hooke's law.
Relating to linear elasticity, Hooke's law states that a force applied to what is equivalent to a spring is equal to the negative product of the spring or rate constant times the coordinate change for the dimension in which the force is applied. For a spring deformed along the x-direction from its point of rest, Hooke’s law is written F = ‒kx. Since it is comparable to an elastic body, when the force is cut off, the spring, if massless, returns to its point of relaxation. If, on the other hand, a mass is attached to the spring, the object, when released, travels beyond the relaxation point, oscillating back and forth, until internal friction ends the process. Objects in the real world can easily be pressed beyond their limit of elasticity.
When an elastic body collides with another elastic body, deformations in both bodies are momentary and kinetic energy is conserved. In such a collision, if both objects have the same mass, and object #1 with velocity V1, strikes object #2 with velocity V2, object #1 will come to a complete stop and all of its momentum will be transferred to object #2. A classic demonstration of this is a group of pendulums made of strings tied at the same point above and attached to metal balls of equal mass at their bottom, each touching the other. If the left-most pendulum is swung, when it strikes the next ball, all its momentum is transferred to it, which transfers to the third upon striking it, and so on. Finally, the last ball is seen moving to the right, with all the energy of the first pendulum; this exhibition is known as Newton’s cradle.
Another demonstration of elasticity is to bounce an ivory ball on a very hard, flat surface that has been rubbed with oil. Ivory has an unusually high coefficient of elasticity. The ball will bounce very nearly to its former height, illustrating its minimal loss of kinetic energy in the process. An object that is forced beyond its elastic limit may exhibit plastic deformation, whereby changes are permanent. In metals, such permanent deformations often involve atomic dislocations in the crystal matrix.
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