# Is momentum really conserved in a perfectly inelastic collision?

sophiecentaur
Science Advisor
Gold Member
2020 Award
I tried to deal with your question directly when I wrote that you have to deal with the very simplest system if you want to understand things like this.
Momentum is always conserved. That statement is always correct for any isolated system. If you want to introduce an outside influence then all bets are off - unless you include the new addition as part of the system.
Two equal masses collide, going in opposite directions (wrt an Earth frame of reference) and with the same intiial speeds. Total momentum was zero and ends up at zero. The KE, wrt the Earth frame , was two times half mvsquared and ends up as zero. The energy lost must go somewhere, of course, but net motion of the masses doesn't contribute.
You cannot introduce Potential Energy (except between the two masses) in your argument or the system is not isolated. Every interaction involves some Potential Energy (even the elastic deformation during collisions). If you hit an infinitely massive object then you cannot consider the Momentum rigorously because, somewhere along the line, you will end up dividing by infinity and be comparing one zero with another zero (very crude maths here, but I won't apologise)
Instead of trying to find loopholes, it might be better if you were to try to spot where your suggestions are flawed. They have to be!
Forget the "Mathematically" bit. Maths is only a tool for working things out and it tends to stick to the model you use (assuming it's the right model).

atyy
Science Advisor
Also, doesn't conserving momentum and not KINETIC energy break down mathematically at some point??

In some collisions, kinetic energy and momentum are lost.

However, it is mathematically exactly consistent to have loss of kinetic energy without any loss of momentum. Physically, you can think of it that the missing energy is carried away by particles you do not see. Consider the simple case in which there is a pair of unobserved particles. The pair of particles carries away kinetic energy, but because each particle moves in opposite directions, they carry away no net momentum. (Energy is a scalar, momentum is a vector.)

Last edited:
nasu
Gold Member
In addition to what sophiecentaur already explained, it seems that the OP is not aware of a significant difference in the effects of internal forces.

For an ISOLATED (100% isolated) system, the internal forces cannot change the total momentum but the same internal forces can change the kinetic energy of the system.
We don't need any mysterious or unmeasured particles to explain this. It just follows from Newton's laws for system of particles.