Elastic and Inelastic Collision

For an elastic collision it is characteristic that the sum of the kinetic energies of the involved bodies is constant

In an inelastic collision, however, both bodies have the same velocity; the sum of their kinetic energies is reduced, compared with the initial value, because a part of it has changed into internal energy

Inelastic collisions occur when the colliding bodies deform or stick together

Have you ever smashed a toy car into a wall? Before the collision, the car was moving fast and had lots of kinetic energy - and afterward, it just sat there with zero kinetic energy

An inelastic collision is one where the total kinetic energy of the colliding particles is not the same after the collision as it was before

Energy and momentum are conserved in elastic collisions. In the game of billiards, elastic collisions occur between balls of equal mass. However, elastic collisions can occur between objects of very different mass. This difference in mass creates different outcomes for the collisions

Have you ever seen a basketball bounce off a backboard? It comes back with the same level of kinetic energy as it had when it hit, which means it was an elastic collision.

The total momentum of the involved bodies is conserved, regardless whether the collision is elastic or inelastic

Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy.

Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic.

Head-on Elastic Collisions

For a head-on collision with a stationary object of equal mass, the projectile will come to rest and the target will move off with equal velocity, like a head-on shot with the cue ball on a pool table. This may be generalized to say that for a head-on elastic collision of equal masses, the velocities will always exchange.

In a head-on elastic collision where the projectile is much more massive than the target, the velocity of the target particle after the collision will be about twice that of the projectile and the projectile velocity will be essentially unchanged.

For a non-head-on elastic collision between equal masses, the angle between the velocities after the collision will always be 90 degrees. The spot on a pool table is placed so that a collision with a ball on the spot which sends it to a corner pocket will send the cue ball to the other corner pocket.

For non-head-on collisions, the angle between projectile and target is always less than 90 degrees. This was important in the analysis of the original Rutherford scattering experiment.

This case implies that a train moving at 60 miles/hr which hits a small rock on the track could send that rock forward at 120 miles/hr if the collision were head-on and perfectly elastic. It also implies that if the speed of the head of your golf club is 110 miles/hr, the limiting speed on the golf ball off the tee is 220 miles/hr in the ideal case. That is, the limiting speed of the ball depends strictly on the clubhead speed, and not on how much muscle power you put into the swing.

In a head-on elastic collision between a small projectile and a much more massive target, the projectile will bounce back with essentially the same speed and the massive target will be given a very small velocity. One example is a ball bouncing back from the Earth when we throw it down.

In the case of a non-head on elastic collision, the angle of the projectiles path after the collision will be more than 90 degrees away from the targets motion.

Inelastic Collision Examples Most ordinary collisions are classified as inelastic collisions because some of their kinetic energy is converted to other forms such as internal energy. Links to some examples are provided.

Example of Force on Car

                                                                                                                                

Inelastic CollisionsPerfectly elastic collisions are those in which no kinetic energy is lost in the collision. Macroscopic collisions are generally inelastic and do not conserve kinetic energy, though of course the total energy is conserved. The extreme inelastic collision is one in which the colliding objects stick together after the collision, and this case may be analyzed in general terms:

                                                                            

K.E. Lost in Inelastic Collision

Non-Stretching SeatbeltStretching Seatbelt

Airplane and Duck

Ballistic Pendulum The ballistic pendulum is a classic example of a dissipative collision in which conservation of momentum can be used for analysis, but conservation of energy during the collision cannot be invoked because the energy goes into inaccessible forms such as internal energy. After the collision, conservation of energy can be used in the swing of the combined masses upward, since the gravitational potential energy is conservative.

The Air Track

http://www.walter-fendt.de/ph11e/collision.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/colcon.html#c1