You first said the initial momentum was 50,000 kg km/hr. For a 1000 kg car, that means initial velocity is 50 km/hr.
Later you change things to suit your needs. Now your initial total momentum changes to zero? When did sleight of hand become part of physics?
MV before the collision. 50,000 kg km/hr. That means 1,250,000 kg km2/hr2 of energy - your numbers. Cars collide. You said, crumple zones, et al absorb energy.
1,250,000 must be smaller because you said energy is absorbed. Any number - the crumple zone absorbs 1,000,000. Now the car only has 250.000 kg km2/hr2 remaining.
E / .5 / mass = velocity squared.
250,000 / .5 / 1000 = 125 = velocity squared.
Due to energy absorbed in crumple zones, the new velocity is less. In this example, 11 km/hr. Where is your conservation of momentum?
MV for 50 km/hr is not equal to MV for 11 km/hr. Why? Because collisions are not elastic. Because crumple zones absorb energy. Since a crumple zone absorbed only 1,000,000 kg km2/hr2 of energy, the new velocity goes from 50 km/hr to 11 km/hr. Where is conservation of momentum?
The collision was not elastic. Cars are intentionally designed (for human safety) to be the least elastic. Conservation of momentum can only exist in elastic collisions. Your own numbers demonstrate that conservation of momentum does not exist.
Then you also invented an initial velocity of zero when your own numbers started with an initial velocity of 50.
I aggressively asked for numbers in every post from every poster. Now that you did, identified is where your numbers only make sense when conservation of momentum is disposed.
Using your own numbers, if a crash absorbs energy, then momentum is not conserved. I used your numbers. Crumple zones reduce velocity from 50 o any other numbers down to zero (ie 11 in the example). If velocity decreases, then conservation of momentum does not exist. We intentionally design cars to make inelastic collisions. To not conserve momentum.
Finally using your own numbers. First collision: each car at 50 km/hr has an energy content of 1,250,000 kg km2/hr2. Second collision: a car moving at 100 km/hr has an energy content of 5,000,000 kg km2/hr2. For a parked car: 0 kg km2/hr2
Total energy in the first collision: 2,500,000. Total energy in a 100 km/hr crash: 5,000,000. Energy numbers do not lie. A 100 km/hr car crash is twice as violent - your numbers.
And yet somehow you then spin those numbers to make 2,500,000 equal to 5,000,000. How? You ignored conservation of energy. You assumed a crash and crumpling zone absorbs no energy. Assume conservation of momentum exists. Let’s use your numbers.
Second collisioni: what happens when 5,000,000 kg km2/hr2 energy is applied to two 1000 kg cars? Do the numbers. Both cars are now moving at 70.7 km/hr.
E = .5 times mass of both cars times the velocity of both squared.
5,000,000 = .5 * 2000 Kg * velocity squared.= 5000
Velocity is 70.7 km/hr
What happened to your conservation of momentum? When did 1000 kg times 100 kg/hr become 2000 times 70.7 km/hr? It didn’t. Why. Conservation of momentum here is bogus. Conservation of energy says so.
But again, using your numbers. Everything works as long as conservation of momentum is bogus. You cannot have it both ways. Either you believe in conservation of energy. Or you believe in conservation of momentum. Both cannot exist – as demonstrated by your numbers.
How do you get 2000 kg times 50 km/hr to equal 1000 kg times 100 km/hr? Somehow you must change initial energy from 5,000,000 kg km2/hr2 to 2,500,000. How do you do that? Change initial velocity from 100 km/hr to 70.7 km/hr.
Changing initial conditions is the only way to make conservation of momentum work. But the initial conditions are 100 km/hr – not 70.7. You cannot change facts to justify a myth - ‘conservation of momentum’. Why? Because conservation of momentum does not apply to inelastic collisions. And because your own numbers said the incoming 100 km/hr car is 5,000,000 kg km2/hr2. Not 2,500,000 as your conservation of momentum claims.
Now that you have provided the numbers - finally - I can use your numbers to expose mistakes. Your own numbers says the energy of a 100 km/hr car is not equivalent to a collision of two 50 km/hr cars. And yet using a myth called conservation of momentum, you magically changed 5,000,000 kg km2/hr2 into 2,500,000 kg km2/hr2.
Again, either you have conservation of momentum OR conservation of energy. Your own numbers say both cannot exist. Your own numbers say the two collisions have vastly different energy. You even changed initial conditions from 50 km/hr to zero km/hr just to make a bogus ‘conservation of momentum’ work.