Problem A: 10kg mass moving at 1m/s strikes a 1kg stationary mass. If the collision is inelastic, the combined 11kg mass (calculated using conservation of momentum) continues moving at (10*1+1*0)/11 = about .91m/s. For the observer that was also moving at 1m/s, the collision mass is now moving at a relative velosity of 1-.91 = 0.09m/s. The initial kinetic energy (1/2 mv2) was 5 joules and the final ke is about 4.55 joules. The missing .45 joules was converted to heat.
Problem B: A 10kg stationary mass is struck by a 1kg mass moving at 1m/s. Agian, for and inelastic collision, the combined mass moves at (10*0+1*1)/11 = about 0.09m/s relative to the observer that was not moving. The kinetic energy was initially 10*0*0/2+1*1*1/2=0.5 and after the collision is 11*(0.09)2=0.05 joules again leaving 0.45 joules converted to heat.
To the observer, both collisions looked exactly the same. If you want, you can try the calculations for an elastic collision. In this case, the kinetic energy is conserved instead of being converted into heat.
I thought a bit before answering this, but I don't know if you could be more obtuse, Dan O.
Momentum is conserved, right? So the sum the momentum in one case is 10 times that of the other? Redistribute at collision time. There you go.
The fact that the final velocities of the combined masses are different doesn't matter, as long as the observer is satisfied concerning the relative velocities? They are different events, as events. You also have the observer "following" one mass or the other.
The collision is some thing that happens in the journey of the objects, there is no start or finish. There is no prior expectation of a result.
It is not a problem of maths, but of "the world" I really don't know why you make any distinction. Should those masses carry on, they may hit the surface of the planet with different effect. They have same mass but different initial velocities as they approach.
The collision happens. The observer can only ever witness it.
Collisions involve a larger level of momentum. They are different.
The effect will be manifest in the world. Stuff happens independently of the observer. Everything is relative, you say, but you impose an arbitrary observer?
Annihilation of a small mass at impact releases more energy than a little on of the same velocity. Observer or not.
Is this why you thing that there is a wind? That the nature of the objects and how they react can simply be abstracted to simple one-off events?
I notice this in this thread. Tests and machines are analysed from the middle, or some place of convenience.
Many magnetic over-unity devices forget the history of ,say, a steel ball.
They think only of it being pulled towards the magnet, but if they don't do exactly that again, then all is forgotten. It's free.