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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If you take two identical balls and throw them at each other at the same speed, the first ball has positive momentum, and the second ball, moving in the opposite direction, has negative momentum. When they collide the net momentum is still zero, meaning they exit the collision in opposite directions and moving the same speed. If they hit off center they can each go off at a right angle to their initial path.
Depending on the material properties of the ball though, some of that energy gets turned into heat. If you have two perfectly bouncy balls, they rebound at the same speed they started, but if you have two balls of dough that stick together, all that kinetic energy gets turned into heat. This is the difference between an elastic collision and an inelastic collision.
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