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 can’t be conserved in a collision. Consider filming a head on collision between two hard spheres that are moving toward each other. The spheres each have mass and velocity and therefore positive kinetic energy. Kinetic energy is always positive because the direction of motion doesn’t matter as the velocity is squared. If you were to observe the balls after the collision they would be moving in opposite directions. But for an object to initially be moving in one direction and later be moving in the opposite direction, there must have been a moment when the velocity was zero. The same is true for the other sphere. At the moment of the collision the kinetic energy dropped to zero. This means that kinetic energy is not conserved. The energy didn’t vanish, it changed form. When the spheres are at rest, acoustic, elastic and thermal energies were present. The electric energy can be converted back into kinetic energy in the next moments as the spheres rebound, but the acoustic and thermal energy won’t be converted to kinetic energy. So even though the balls are moving after the collision, they have less kinetic energy than before the collision.
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