But if we take a isolated system and take a ball A of mass 1 kg and a ball B of mass 1 kg moving in opposite direction with a velocity of 100000m/s . And we have to find final velocity . ~ By applying the law of conversation it will come 0. ~But it should not be true in reality as they have high velocity so they would deflect each other and would have non zero velocity.
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Answer:
We have used the concepts of mass and velocity to describe the motion of objects. Imagine two objects, one with a small mass and one with a large mass; consider, for instance, a tennis ball (less massive) and a medicine ball (more massive). Now, imagine the two objects being thrown at you at some speed v; obviously, getting hit by a tennis ball traveling at speed v sounds much less painful than getting hit by a medicine ball traveling at speed v. Consider also the medicine ball traveling at two different speeds: a slower speed, s, and a faster speed, f. Trying to catch a medicine ball traveling at speed s (the slower speed) certainly sounds easier than trying to catch one traveling at a faster speed f! We tend to think of a larger object traveling at a particular speed as having more momentum than a smaller object traveling at that speed. Likewise, we think of one object traveling at a fast speed as having more momentum than that object traveling at a lower speed. Momentum, therefore, increases with increasing speed as well as increasing mass. This situation fits logically, then, with the definition of momentum in physics. The momentum p of an object of mass m and velocity v is defined according to the following relationship:
p = mv
Notice that momentum, like velocity, is a vector with both magnitude and direction. As the mass or velocity of an object increase, so does the momentum.
The Relationship Between Momentum and Force
Recall that acceleration is simply the time rate of change of velocity. Thus (on average), we can write the following:
Let's substitute this into our force expression from Newton's second law of motion:
Assuming the mass m remains constant, we can make the following change:
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Note that because mv appears in the net force expression, we can write it in terms of momentum p. The net force on an object is therefore the time rate of change of The momentum, p, of the object is simply the product of its mass and its velocity: p = mv. Because no direction is specified, we are only interested in determining the magnitude of p, or p. Thus,
Note the units in the result--we can also express the units in terms of newton seconds.
Let's now consider some arbitrary number of objects; the total momentum P of the system of objects is simply the sum of all the individual momenta: . In the same manner, following Newton's second law, we'll call Ftot the sum of all the forces acting on the objects. But this sum, Ftot, is simply the sum of all external forces acting on the system of objects. Then,
And if no external forces are acting on the system of objects,
In other words, the time rate of change of the total momentum of the system of objects is zero in this case; this is simply a statement of the law of conservation of linear momentum for a closed and isolated system. That is to say, the total momentum is constant for a given system of objects on which no external force acts. This conclusion is extremely useful for problems involving, for instance, collisions of objects. The following practice problems allow you to explore the implications of this result.