when a body collides with another moving body of equal mass and moving with equal velocity, explain what happens in terms of force and momentum
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Answer:
At this point, we introduce some further concepts that will prove useful in describing motion. The first of these, momentum, was actually introduced by the French scientist and philosopher Descartes before Newton. Descartes’ idea is best understood by considering a simple example: think first about someone (weighing say 45 kg) standing motionless on high quality (frictionless) rollerskates on a level smooth floor. A 5 kg medicine ball is thrown directly at her by someone standing in front of her, and only a short distance away, so that we can take the ball’s flight to be close to horizontal. She catches and holds it, and because of its impact begins to roll backwards. Notice we’ve chosen her weight so that, conveniently, she plus the ball weigh just ten times what the ball weighs by itself. What is found on doing this experiment carefully is that after the catch, she plus the ball roll backwards at just one-tenth the speed the ball was moving just before she caught it, so if the ball was thrown at 5 meters per second, she will roll backwards at one-half meter per second after the catch. It is tempting to conclude that the “total amount of motion” is the same before and after her catching the ball, since we end up with ten times the mass moving at one-tenth the speed.
Considerations and experiments like this led Descartes to invent the concept of “momentum”, meaning “amount of motion”, and to state that for a moving body the momentum was just the product of the mass of the body and its speed. Momentum is traditionally labeled by the letter p, so his definition was:
momentum = p = mv
for a body having mass m and moving at speed v. It is then obvious that in the above scenario of the woman catching the medicine ball, total “momentum” is the same before and after the catch. Initially, only the ball had momentum, an amount 5x5 = 25 in suitable units, since its mass is 5kg and its speed is 5 meters per second. After the catch, there is a total mass of 50kg moving at a speed of 0.5 meters per second, so the final momentum is 0.5x50 = 25, the total final amount is equal to the total initial amount.