Momentum Vectors: Adding or Subtracting in Isolated Systems

[boris16]

hi

If a person on a train moving at speed 100 km per hour is moving in opossite direction with speed of 10 km per hour, then person's speed is 90 km per hour. Adding or substracting velocity vectors makes perfect sense. But adding or substracting momentums doesn't, if it means adding or substracting two momentums that each belong to two DIFFERENT objects in an isolated system.


If in isolated system two balls are approaching each other from opposite directions ( friction is negligible ), one on the left with momentum of 160 and the one on the right with momentum 100, then since momentum is vector quantity the resultant momentum will be 60 and its direction will be to the left.

I know the two balls together represent a system, but at the end of the day they are still two distinctive balls each with its own momentum, so to me substracting the two momentums belonging to DIFFERENT objects is like ... I don't know ... apples and oranges.

I know that when they collide their individual momentums will change but total momentum will stay the same!
So is perhaps the main reason why we add or substract momentums of different objects ( like in the above example ) because system has net momentum of 60 even in a case where objects at collision experience impulse that equals the smaller of the two momentums ( that would be momentum of the ball going left -> M=100), the remaining momentum will still be 60?

thank you

 

[Hootenanny]

It depends what you call the system. The positive and negative sign is a crude way of indicating the direction of the vector. Summation of the vectors gives the net or resultant vector. Finding the magnitude would be something completely different.

 

[krab]

Adding or substracting velocity vectors makes perfect sense. But adding or substracting momentums doesn't,

This suggests that you don't really know what momentum is. If a system consists of two objects, one with momentum x and the other with momentum y, then the total momentum is x+y. Simple as that. I suspect that you are confusing momentum with energy. If y=-x, then the two objects can collide and as a result be at rest (say they are really sticky). Momentum is conserved. But the energy is a different matter; energy is not a vector, so the two objects had the same energy of motion to start with, and this energy must re-appear somewhere in the system. For example, the two objects stuck together could end at a higher temperature.