Q:

# When is the only time the momentum of a system is conserved?

A:

The momentum of a system is conserved in elastic collisions between system objects. The system must be isolated, indicating that it is free from the influence of a net, external altering force that affects collision processes, such as gravity.

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According to the law of conservation of momentum, when two objects collide in an isolated system, the sum of their momenta before must be equal to the sum of their momenta afterwards. The loss of momentum by the first object is accompanied by an equal and opposite gain in momentum by the second object. This conservation stems from Newton’s third law, which states that the force acted by each body is accompanied by an equal and opposite reaction force in the other body. Impulse is defined as the momentum acted upon by each body on the other and is the product of force and time.

If the two bodies contact one another for the same time during collision, this must mean their momenta are also equal and opposite. Momentum can also be expressed as the product of mass and velocity, so the velocities of each colliding body after collision can be determined if their masses are known. For non-linear collisions, this involves vectorial analysis of each of the components of the velocities.

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