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The law of momentum conservation is all about comparing the total momentum of the system before the collision to the total momentum of the system after the collision. The total momentum of the system is the sum of both objects' momentum. In the diagram, the individual momentum values are listed. If you add these two values together before the collision and do the same after the collision, then you will be able to tell if the total amount is conserved. Since the momentum direction is rightward in each case, there is no need to consider the +/- nature or vector nature of momentum when summing individual values. (See Know the Law section.)
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The Law of Momentum Conservation:
If a collision occurs between object 1 and object 2 in an isolated system, then the momentum change of object 1 is equal in magnitude and opposite in direction to the momentum change of object 2. In equation form
m1 • ∆v1 = - m2 • ∆v2
The total momentum of the system before the collision (p1 + p2) is the same as the total momentum of the system of two objects after the collision (p1' + p2'). That is
p1 + p2 = p1' + p2'
Total system momentum is said to be conserved for any collision occurring in an isolated system.
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