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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Kinetic energy isn’t conserved because it can be transferred to other forms of energy. If two objects head straight towards each other and collide, bringing them to a stop, they start with a lot of kinetic energy and end with none.
Momentum, however, is conserved.
Mathematically the key difference is that kinetic energy comes from velocity squared, whereas momentum is just velocity.
Consider the example above. Two vehicles with equal velocity in opposite directions. So, one will have mv, one has – mv. If their masses are also equal, we can work out that their total momentum is 0, so after collision it will also be 0.
If you used kinetic energy, you wouldn’t get that, because the minus sign disappears when you square it, so they no longer sum to zero.
Basically, squaring velocity means you lose information about its direction
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