Elasticity is the ability to deform and return to its original shape. Examples include billiard balls, springs, and spandex belts. Hooke’s law explains linear elasticity. Elastic collisions conserve kinetic energy, demonstrated by Newton’s cradle. Ivory balls have high elasticity, exhibiting minimal loss of kinetic energy when bounced. Objects pushed beyond their elastic limit can exhibit permanent changes.
Elasticity is the ability to deform, with complete reversibility: the ability to return to a shape or state equivalent to that before an applied force incrementally deformed the object or body. An example of an elastic body that at least approximately satisfies this description is a billiard ball, which upon collision with another billiard ball regains its original shape. Another example of an elastic body is a spring or spandex belt. These regain their shape after being compressed or stretched. The physical principle involved is Hooke’s law.
Regarding 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 change in coordinates times the dimension in which the force is applied. For a spring strained along the x direction from its rest point, Hooke’s law is written F = ‒kx. Being comparable to an elastic body, when the force is interrupted, the spring, if devoid of mass, returns to its point of relaxation. However, if a mass is attached to the spring, the object, once released, travels past the point of relaxation, rocking back and forth, until internal friction terminates the process. Objects in the real world can easily be pushed beyond their elastic limit.
When an elastic body collides with another elastic body, the deformations in both bodies are momentary and the kinetic energy is conserved. In such a collision, if both objects have the same mass and object n. 1 with velocity V1, hits object no. 2 with speed V2, object no. 1 will come to a complete stop and all of its momentum will be transferred to object No. . 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 bottoms, each touching the other. If the leftmost pendulum is swung, when he hits the next ball, all of his momentum is transferred to it, which transfers to the third after hitting it, and so on. Finally, we see the last ball moving to the right, with all the energy of the first pendulum; this exhibit is known as Newton’s cradle.
Another demonstration of elasticity is bouncing an ivory ball off a very hard flat surface that has been rubbed with oil. Ivory has an unusually high coefficient of elasticity. The ball will bounce very close to its previous height, illustrating its minimal loss of kinetic energy in the process. An object forced beyond its elastic limit can exhibit plastic deformation, so the changes are permanent. In metals, such permanent deformations often involve atomic dislocations in the crystalline matrix.
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