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In a perfectly elastic collision, the total momentum of the system is conserved before and after the collision.

In physics, a perfectly elastic collision is one in which both momentum and kinetic energy are conserved. This means that the total momentum of the system (the sum of the momenta of the individual objects involved) remains constant before and after the collision. This principle is a direct consequence of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

To understand this concept better, let's consider a simple example of two objects colliding. Before the collision, each object has a certain momentum, which is the product of its mass and velocity. When the two objects collide, they exert forces on each other, causing their velocities, and hence their momenta, to change. However, because the forces are equal and opposite, the changes in momentum cancel each other out, resulting in no net change in the total momentum of the system.

In a perfectly elastic collision, not only is momentum conserved, but kinetic energy is also conserved. This is different from an inelastic collision, where kinetic energy is not conserved and some of it is converted into other forms of energy, such as heat or sound. In a perfectly elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. This is because the objects 'bounce' off each other without any loss of speed, due to the absence of any energy-dissipating forces.

In summary, in a perfectly elastic collision, the total momentum of the system is conserved, meaning it remains constant before and after the collision. This is a fundamental principle in physics and is a direct consequence of Newton's third law of motion. Additionally, in a perfectly elastic collision, kinetic energy is also conserved, distinguishing it from inelastic collisions where kinetic energy is not conserved.

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