elastic collision

Examples of elastic collision in the following topics:

• 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 is a collision between two or more bodies in which the total kinetic energy of the bodies before the collision is equal to the total kinetic energy of the bodies after the collision.
  • 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.

• 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.

• Inelastic Collisions in One Dimension

  • Collisions may be classified as either inelastic or elastic collisions based on how energy is conserved in the collision.
  • In an inelastic collision the total kinetic energy after the collision is not equal to the total kinetic energy before the collision.
  • This is in contrast to an elastic collision in which conservation of total kinetic energy applies.
  • While inelastic collisions may not conserve total kinetic energy, they do conserve total momentum.
  • In such a collision, the colliding particles stick together.

• Glancing Collisions

  • Collision at glancing angle is called "glancing collision".
  • Collisions can either be elastic, meaning they conserve both momentum and kinetic energy, or inelastic, meaning they conserve momentum but not kinetic energy.
  • An inelastic collision is sometimes also called a plastic collision.
  • 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.

• The Compton Effect

  • Still, the origin of the effect can be considered as an elastic collision between a photon and an electron.

• Equations of State

  • In an ideal gas, there is no molecule-molecule interaction, and only elastic collisions are allowed.

• Temperature

  • Also, we assume elastic collisions when molecules hit the wall of the container, as illustrated in .

• Internal vs. External Forces

  • There are mainly three kinds of forces: Gravity, normal force (between ice & pucks), and frictional forces during the collision between the pucks
  • In the previous example, it is worthwhile to note that we didn't assume anything about the nature of the collision between the two pucks.
  • Without knowing anything about the internal forces (frictional forces during contact), we learned that the total momentum of the system is a conserved quantity (p1 and p2 are momentum vectors of the pucks. ) In fact, this relation holds true both in elastic or inelastic collisions.
  • Contrast the effects of external and internal forces on linear momentum and collisions

• Inelastic Collisions in Multiple Dimensions

  • At this point we will expand our discussion of inelastic collisions in one dimension to inelastic collisions in multiple dimensions.
  • It is still true that the total kinetic energy after the collision is not equal to the total kinetic energy before the collision.
  • After this, we will calculate whether this collision was inelastic or not.
  • As these values are not the same, we know this was an inelastic collision.
  • Relate inelastic collision multiple dimension equations to the one dimension collisions you learned earlier