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 Effect of the Finite Volume

  • Ideal gases are assumed to be composed of point masses whose interactions are restricted to perfectly elastic collisions; in other words, a gas particles' volume is considered negligible compared to the container's total volume.
  • Ideal gases are assumed to be composed of point masses that interact via elastic collisions.

• The Effect of Intermolecular Forces

  • This equation assumes that gas molecules interact with their neighbors solely through perfectly elastic collisions, and that particles exert no intermolecular forces upon each other.
  • At low temperatures, gas particles have less kinetic energy, and therefore move more slowly; at slower speeds, they are much more likely to interact (attracting or repelling one another) upon collision.
  • Ideal gases are assumed to interact via perfectly elastic collisions in which no energy is lost.

• Van der Waals Equation

  • The Ideal Gas Law is based on the assumptions that gases are composed of point masses that undergo perfectly elastic collisions. 
  • The gas particles are affected by the intermolecular forces acting on them, which leads to inelastic collisions between them. 
  • This leads to fewer collisions with the container and a lower pressure than what is expected from an ideal gas.
  • Attractive forces between molecules decrease the pressure of a real gas, slowing the molecules and reducing collisions with the walls.

• 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

• Kinetic Molecular Theory and Gas Laws

  • The collisions exhibited by gas particles are completely elastic; when two molecules collide, total kinetic energy is conserved.
  • If the reaction is kept at constant pressure, they must stay farther apart, and an increase in volume will compensate for the increase in particle collision with the surface of the container.
  • If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; the number of collisions against the container will increase, and, by extension, the pressure will increase as well.