elasticity

Examples of elasticity in the following topics:

• Hooke's Law

  • Hooke's law of elasticity is an approximation that states that the extension of a spring is directly proportional to the load applied to it.
  • In mechanics (physics), Hooke's law is an approximation of the response of elastic (i.e., springlike) bodies.
  • Many materials obey this law of elasticity as long as the load does not exceed the material's elastic limit.
  • Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.
  • A brief overview of springs, Hooke's Law, and elastic potential energy for algebra-based physics students.

• Elastic Collisions in One Dimension

  • An elastic collision is a collision between two or more bodies in which kinetic energy is conserved.
  • An elastic collision will not occur if kinetic energy is converted into other forms of energy.
  • It important to understand how elastic collisions work, because atoms often undergo essentially elastic collisions when they collide.
  • On the other hand, molecules do not undergo elastic collisions when they collide .
  • The mathematics of an elastic collision is best demonstrated through an example.

• Fracture

  • Fracture is caused by a strain placed on an object such that it deforms beyond its elastic limit and breaks.
  • When a strain is applied to a material it deforms elastically proportional to the force applied.
  • The zone in which it bends under strain is called the elastic region.
  • For larger forces, the graph is curved but the deformation is still elastic—L will return to zero if the force is removed.

• Elastic Potential Energy

  • If a force results in only deformation, with no thermal, sound, or kinetic energy, the work done is stored as elastic potential energy.
  • A mouse trap stores elastic potential energy by twisting a piece of metal; this energy is released when the mouse steps into it.
  • where k is the elastic constant and x is the displacement.
  • This energy can also produce macroscopic vibrations sufficiently lacking in randomization to lead to oscillations that are merely the exchange between (elastic) potential energy within the object and the kinetic energy of motion of the object as a whole.
  • Express elastic energy stored in a spring in a mathematical form

• Elastic Collisions in Multiple Dimensions

  • To solve a two dimensional elastic collision problem, decompose the velocity components of the masses along perpendicular axes.
  • As stated previously, there is conservation of total kinetic energy before and after an elastic collision.
  • If an elastic collision occurs in two dimensions, the colliding masses can travel side to side after the collision (not just along the same line as in a one dimensional collision).
  • We also know that because the collision is elastic that there must be conservation of kinetic energy before and after the collision.
  • In this illustration, we see the initial and final configurations of two masses that undergo an elastic collision in two dimensions.

• Elasticity, Stress, and Strain

  • First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations.
  • Very elastic materials like rubber have small $k$ and thus will stretch a lot with only a small force.

• Stress and Strain

  • First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations.
  • Stress and strain are related to each other by a constant called Young's Modulus or the elastic modulus which varies depending on the material.
  • A material with a high elastic modulus is said to have high tensile strength.

• Glancing Collisions

  • Collisions can either be elastic, meaning they conserve both momentum and kinetic energy, or inelastic, meaning they conserve momentum but not kinetic energy.
  • The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution, a value that generally ranges between zero and one.
  • A perfectly elastic collision has a coefficient of restitution of one; a perfectly-inelastic collision has a coefficient of restitution of zero.

• Linear Momentum

  • Linear momentum is the product of the mass and velocity of an object, it is conserved in elastic and inelastic collisions.
  • Momentum is conserved in both inelastic and elastic collisions.
  • (Kinetic energy is not conserved in inelastic collisions but is conserved in elastic collisions. ) It important to note that if the collision takes place on a surface with friction, or if there is air resistance, we would need to account for the momentum of the bodies that would be transferred to the surface and/or air.

• Inelastic Collisions in One Dimension

  • Collisions may be classified as either inelastic or elastic collisions based on how energy is conserved in the collision.
  • This is in contrast to an elastic collision in which conservation of total kinetic energy applies.