# Conservation of momentum in a collision [duplicate]

Imagine I have an iron ball in vacuum and it is moving and it hits an iron wall. All the kinetic energy gets converted into heat, right?(since sound cannot be produced).Will there be any other energy conversion?

The ball does not bounce back and nor does the wall move. So,how is the momentum being conserved?

Energy can be conserved as the thermal energy is produced but since momentum is a vector,how do we know that the random motion of the particles of the ball and the wall all add up vector-ally to conserve momentum?

• The wall does move unless it is infinitely massive, which it is not. – tfb Oct 16 '17 at 15:21
• You cannot specify that neither of them move after the collision and remain in the realm of physics. That behavior moves you into the world of superhero comic books. As far as energy, there is some energy put into the permanent deformation of the two objects as potential energy. – Bill N Oct 16 '17 at 15:25
• Yeah but to conserve momentum it has to keep moving which it will not , even if it is not infinitely huge – spatialdelusion Oct 16 '17 at 15:25

The iron ball will not stick to the wall but will be rebounded back. This will conserve momentum minus the energy lost to deformation. Also, the wall will vibrate, making sound waves if there were an atmosphere. The vibration still occurs in a vacuum.

• how ?momentum in the two cases will be different right? – spatialdelusion Oct 16 '17 at 15:45
• momentum will be different only if energy is lost to deformation. Without that, the ball should rebound with same speed. – jmh Oct 16 '17 at 18:38

The ball does not bounce back and nor does the wall move.

is physically impossible.

If you consider the ball alone as the system then momentum would not be conserved because an external force (impulse) acts on the ball which originates from the wall (+ Earth).

If you consider the ball and the wall & Earth as the system then momentum is conserved as no external forces will be acing and the final momentum will be carried by the ball and the wall and the Earth.
Thus not all the kinetic energy is converted to other forms of energy but the amount of kinetic energy carried by the ball and the wall and the Earth will be very much smaller than the kinetic energy carried by the ball before the collision.

You can think of the problem as the centre of mass of the system carrying the momentum and having a finite but very small amount of kinetic energy compared with the kinetic energy of the ball before the collision.
Nothing that happens during the collision will change the motion of the centre of mass of the system because there are no external forces acting on the system.

The kinetic energy of the components of the system in the centre of mass frame can change.
The kinetic will not change if the collision is elastic, it could increase if there was an explosion when the ball impacted on the wall and that would be called a super-elastic collision.
In the case that you have asked about when the collision is inelastic the extreme of kinetic energy decrease would be that all the kinetic energy in the centre of mass frame is converted into other forms of energy ie in the centre of mass frame all the system components would be stationary.

Some of the kinetic energy is converted into heat by the collision causing the ball and the wall to vibrate.
Eventually all these vibrations would dissipate and the thermal kinetic energy of the wall and the ball would be larger - they become hotter.
There will also be permanent deformation of the wall and ball which means that work has been done to permanently break the bonds between the molecules and the energy to that comes from the kinetic energy that the ball had before the collision.