# Momentum conservation in perfectly inelastic collision

Dear Experts,

Total momentum of a system is said to be conserved in perfectly inelastic collisions also. I have a slight problem trying to comprehend a simple example regarding the same.

If a small mass 'm' , say a ball is thrown at a huge stationary mass 'M' , say a wall. If the collision is perfectly inelastic, both the bodies after collision is expected to follow the same speed. In this case, if the ball gets stuck on the wall the total momentum after collision would be 0. But, since the ball was moving before the collision, it has some finite momentum and hence, the total momentum before collision cannot be zero. What is it that i am missing or misinterpreting ?

Ken G
Gold Member
You are missing that momentum is only conserved in a closed system. If your system is closed, the speed of the wall will not be zero after the collision, unless the wall is infinitely massive, which it is not.

• NikhilRGS
Nugatory
Mentor
In this case, if the ball gets stuck on the wall the total momentum after collision would be 0.

The total momentum after the collision is not zero, because the "stationary" wall and the earth it is attached to do move very slightly in the collision. It's a good exercise to calculate just how much the speed of the earth changes as a result of an inelastic collision with a 1kg mass moving at 10 meters per second, compare that with the precision of our best available methods of measuring speeds.

• NikhilRGS
Thank you.

I am trying to understand it with the help of the idea that you suggested. But this is a regular phenomenon that we notice. If we throw something sticky on the wall, it tends to stick. So is it correct to assume that there is some velocity imparted to the massive body? And in that case, how far or by how much do we expect it to move after the impact.

And as it was suggested in the post just above this, i tried calculating the velocity at which both bodies would move.and it was found to be of the order of 10 to the power -25 m/s.

jbriggs444