Momentum conservation in perfectly inelastic collision

[NikhilRGS]

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]

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.

 

[Nugatory]

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]

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.

You ask "by how much do we expect it to move". You have calculated a velocity in the neighborhood of 10^-25 m/s. Assume that is correct. After 10²⁵ seconds, we could expect the larger body to have moved by how much?

That ignores the throw. Where did the ball get its initial velocity if not from the thrower? Where did the thrower get his or her initial velocity if not from the Earth? If you factor that in then the Earth could be considered to start at rest and stop at rest and to only be moving for the duration of the throw. If the ball is in the air for one second then how far would we expect the Earth to have moved while the ball is in flight?