Describe one elastic collisions and one inelastic collisions that you observed in your daily activities. in the inelastic collision explain where did the lost energy (with mathematical expressions) go, in the elastic collision explain what energy (include mathematical expressions) is conserved.

A typical example of an elastic collision that can be observed is the collision of billiard balls, while an inelastic collision is presented in cars collisions.

Explanation:

In an inelastic collision, the energy system is lost in making the permanent deformation over car's structures due to the impact. As can be stated below, the final and initial kinetic energy are expressed:

[tex] Ei =0.5*m1.v1_{i}^2+m2.v2_{i}^2[/text]  

[tex] Ef =0.5*m1.v1_{f}^2+m2.v2_{f}^2[/text]  

Where the subscripts 1 and 2 relate to each car. In the final energy equation Ef, the car's final velocity will be lower than the respective initial velocities.

[tex] v1_{f}<v1_{i}[/text]  

[tex] v2_{f}<v2_{i}[/text]  

Take into account that car's masses still being the same after the collision, therefore the energy losses are always because of cars velocities changes:

[tex] Ef<Ei[/text]

In the elastic collision, there will be little or negligible deformations and that won't make energy losses. But this statement doesn't affirm that billiard balls velocities will be the same. In fact, could happen that one ball increases its velocities if the other ball decreases its velocity, but taking into account that the energy will always conserve.

[tex] v2_{f}>v2_{i}[/text] if [tex] v1_{f}<v1_{i}[/text]

or  

[tex] v1_{f}>v1_{i}[/text] if [tex] v2_{f}<v2_{i}[/text]

Under the assumption that balls masses still being the same:

[tex] Ef=Ei[/text]

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