Conservation of Momentum
In an earlier lecture, we learned from Newton's 3rd Law of Motion that for every action, there is an equal and opposite reaction. One consequence of this law is that if two objects collide the force applied from the first object to the second will be equal and opposite of the force applied from the second object to the first. The result is that the total momentum (p) of all of the objects in the system is the same before and after the collision. This principle is known as the Conservation of Momentum.
In the animation below we have two objects approaching each other on a collision course. The 10kg red ball is moving at +1m/s and the 5kg blue ball is moving at −1 m/s. The total momentum within the system is therefore:
p = mredvred +
mbluevblue
p = (10kg)(1m/s) + (5kg)(−1m/s) = 5 kg·m/s
If the red ball rebounds at a velocity of −1 m/s, the blue ball must rebound with a velocity of +3 m/s to keep the total momentum of the system at 5 kg·m/s, because:
p = (10kg)(−1m/s) + (5kg)(3m/s) = 5 kg·m/s
The Conservation of Momentum assumes a closed system in which there are no other forces interacting with the two objects. If there is an external force, it will cause a change in momentum in the entire system. For example, the momentum will be changed by the force of friction, eventually leading to complete loss of velocity and momentum.