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inelastic collision

Definition/Summary
A collision is said to be inelastic if the total kinetic energy of all the bodies involved in the collision changes.

So conservation of kinetic energy does not apply.

But conservation of momentum, and of angular momentum, does apply to all unrestrained collisions.

For restrained collisions, conservation of momentum applies in any direction along which there is no impulsive restraining force, and conservation of angular momentum applies about any axis about which there is no impulsive restraining torque.

Most collisions are inelastic.

Equations
Click to see the LaTeX code for this image

e is the coefficient of restitution.

Click to see the LaTeX code for this image is the scalar final velocity of the first object after impact.

Click to see the LaTeX code for this image is the scalar final velocity of the second object after impact.

Click to see the LaTeX code for this image is the scalar initial velocity of the first object before impact.

Click to see the LaTeX code for this image is the scalar initial velocity of the second object before impact.

Conservation of momentum:
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If an object is bounced of a stationary object:

Click to see the LaTeX code for this image
Where h is the height of the bounce
And H is the height the object was dropped from.
Click to see the LaTeX code for this image
Click to see the LaTeX code for this image

Scientists

Recent forum threads on inelastic collision
 
Breakdown
Physics
> Classical Mechanics
>> Newtonian Dynamics

See Also
elastic collisions

Images

Extended explanation
In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy, such as heat sound and vibration.

Of the two principles which suffice to describe an elastic collision (conservation of kinetic energy and conservation of momentum), only conservation of momentum is available for an inelastic collision.

Therefore some other information is needed, and this is often available in the form of a Coefficient of Restitution.

Explosions:

An explosion can be treated as an inelastic collision.

Centre of mass:

In all collisions, momentum is conserved, and therefore the velocity of the centre of mass of the bodies in a collision is always the same just after the collision as it was just before.
In other words: the centre of mass instantaneously obeys Newton's first law.

For example, the trajectory of a rocket in which there is a tremendous explosion which is contained inside the rocket will not be altered by the explosion.

Commentary

tiny-tim @ 05:02 PM Aug29-08
Added reference to restrained collisions, and to angular momentum.

tiny-tim @ 01:08 PM Jun27-08
Added explosions, and centre of mass.

tiny-tim @ 03:45 PM Jun14-08
Harmonised with entry on elastic collisions.


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