Elastic and inelastic collisions

[member 529879]

I was looking up elastic and inelastic collisions and found that and elastic collision is a collision where kinetic energy isn't lost to other forms of energy or heat while an inelastic collision is just the opposite. In physics class we were taught that an elastic collision was a collision of two object without any sticking while an inelastic collision is a collision of two object where they stick together and become one mass. What is the relation between these two things?

 

[Matterwave]

Can you show that if the two objects stick together, given that momentum is conserved, they can't possibly conserve Kinetic energy? Only if the two objects bounce off each other, is it possible to conserve both kinetic energy and momentum.

 

[member 529879]

Oh okay that makes sense, but what if two masses of the same value move toward each other at the same velocity and then bounce off of each other going at a lower speed. In this situation, the kinetic energy decreases but the two objects don't stick together. Would this be an elastic or inelastic collision?

 

[axmls]

Collisions (macroscopic ones, that is) are never perfectly elastic (for instance, if you can hear it, then some of the energy has been converted to sound energy). An inelastic collision is simply a collision in which kinetic energy is not conserved. The objects sticking together is not a requirement. The case you describe is inelastic, as kinetic energy is not conserved. A collision in which the two bodies stick together is actually called a perfectly inelastic collision.

 

[Bystander]

same velocity and then bounce off of each other going at a lower speed

You are thinking perhaps of the Mythbusters episode in which wrecking balls were used as a large version of Newton's Cradle? This is an inelastic collision. Some of the original energy has been dissipated in the permanent deformation of the wrecking balls due to the forces in the collision exceeding the elastic limit of the rather pedestrian iron alloy of the wrecking balls.

 

[mathman]

Another example. Serious car crashes are inelastic, while slight bumps (no damage) are elastic.

 

[Quantum Defect]

Physical chemists/chemical physicists talk about inelastic collisions between molecules, atoms, etc.

For example, He + H2 (v=0, J=0) ----> He + H2 (v=1, J=2)
There is no sticking, but the internal energy of H2 has changed. You can also see this in atomic systems, and in nuclear collisions. In all of these cases, translational motion/energy has been converted into internal energy of one of the collision partners (or vice versa). In the H2 case above, vibrational and rotational energy of the H2 has changed.

An elastic collision for the example above would be He + H2 (v=0, J=0) ---> He + H2 (v=0, J=0) [no change of internal state of the H2]

 

[Matterwave]

Oh okay that makes sense, but what if two masses of the same value move toward each other at the same velocity and then bounce off of each other going at a lower speed. In this situation, the kinetic energy decreases but the two objects don't stick together. Would this be an elastic or inelastic collision?

There are varying degrees of "elastic" or "inelastic". A "perfectly elastic" collision would be one in which NO kinetic energy was lost to other forms of energy. A "perfectly inelastic" collision is one where the two objects stick together and the maximum amount of kinetic energy is lost (can you show that this is the maximum, given momentum must be conserved? There's a trick to make this easier). In the situation described, the collision would be "not perfectly elastic". But it is not "perfectly inelastic" either. It is somewhere in between. Terminology wise, we probably would call it an "inelastic collision" because a good amount of kinetic energy was lost.

 

[Bystander]

"not perfectly elastic". But it is not "perfectly inelastic" either

A distinction too often overlooked in the heat of helping.

 

[member 529879]

Oh ok I got it now, thanks. I do have one final question though. What determines how much kinetic energy will be lost in a collision and how the object will be moving after the collision given the momentum of the objects? Is it the material that the colliding objects are made of?

 

[A.T.]

Is it the material that the colliding objects are made of?

Material but also internal structure and general shape. So there is no simple way to compute this in general. Usually empirically determined coefficients are used:
http://en.wikipedia.org/wiki/Coefficient_of_restitution