: Why is the outcome of two object colliding is determined by momentum 1 = momentum 2, instead of Kinetic energy 1 = kinetic energy 2?

Question

I think i’m missing something. When two object is colliding and no energy is lost why is the outcome determined by the total momentum formula? (m1v1 +m2v2 = m1v1′ + m2v2′)

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Why is it not total kinetic energy ? (¹/² m1.v1² + ¹/² m2.v2² = ¹/² m1.v1²’ + ¹/² m2.v2²’)

Why do we say momentum is conserved, instead of total energy is conserved?

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Answer 1

>Why do we say momentum is conserved, instead of total energy is conserved?

Total energy is conserved, however total **kinetic** energy is not always conserved. Energy can be transformed into other forms, if you throw two blobs of clay at each other then a large amount of their energy upon collision will go into deforming the blobs for example. Here kinetic energy has been transferred into the materials and will eventually end up as heat.

There are cases where the kinetic energy is also conserved, and we call these collisions elastic or perfectly elastic, and in those cases we can use both conservation of momentum and conservation of kinetic energy. In other cases we can still use kinetic energy to determine what happens, but we need to take into account how much energy gets lost.