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Question
What exactly is meant by coefficient of elasticity? And is it the same as coefficient of restitution?
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Solution
Elasticity is the property of solid materials to return to their original shape and size after the forces deforming them have been removed. Recall Hooke's law
F = − kΔx
This is Hooke's law for a spring — a simple object that's essentially one-dimensional. Hooke's law can be generalized to…
Stress is proportional to strain.
where strain refers to a change in some spatial dimension (length, angle, or volume) compared to its original value and stress refers to the cause of the change (a force applied to a surface).
The coefficient that relates a particular type of stress to the strain that results is called an elastic modulus (plural, moduli). Elastic moduli are properties of materials, not objects.
The coefficient of restitution is defined as the ratio of the final velocity to the initial velocity between two objects after their collision. Another way of saying this is that the coefficient of restitution is the ratio of the velocity components along the normal plane of contact after and before the collision.
As its name signifies, the coefficient of restitution is actually a measure of the “restitution” (i.e., what you give back) of a collision between two objects, or in other words, how much of the kinetic energy remains after two objects collide.
From this it is clear that coefficient of elasticity and restitution are not the same.
F = − kΔx
This is Hooke's law for a spring — a simple object that's essentially one-dimensional. Hooke's law can be generalized to…
Stress is proportional to strain.
where strain refers to a change in some spatial dimension (length, angle, or volume) compared to its original value and stress refers to the cause of the change (a force applied to a surface).
The coefficient that relates a particular type of stress to the strain that results is called an elastic modulus (plural, moduli). Elastic moduli are properties of materials, not objects.
The coefficient of restitution is defined as the ratio of the final velocity to the initial velocity between two objects after their collision. Another way of saying this is that the coefficient of restitution is the ratio of the velocity components along the normal plane of contact after and before the collision.
As its name signifies, the coefficient of restitution is actually a measure of the “restitution” (i.e., what you give back) of a collision between two objects, or in other words, how much of the kinetic energy remains after two objects collide.
From this it is clear that coefficient of elasticity and restitution are not the same.
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