# In an inelastic collision momentum is conserved, but kinetic energy isn't?

student34
In an inelastic collision momentum is conserved, but kinetic energy isn't?

Here is a simple example about my issue with this. 1g ball (ball A) moving west at 10m/s hits another 1g ball (ball B) moving east at 10m/s. After the collision, ball A moves east at 3m/s, and ball B moves west at 3m/s.

My understanding is that momentum is conserved because the sum of momentum before the collision will equal the sum of momentum after the collision. If that is correct, then why doesn't it work that way with kinetic energy? Regarding the example above, isn't the net kinetic energy of the system 0m/s before the collision and 0m/s after the collision?

In other words, my stubborn intuition tells me that there should be no difference between a vector quantity and a scalar quantity in a two dimensional collision.

Mentor

Regarding the example above, isn't the net kinetic energy of the system 0m/s before the collision and 0m/s after the collision?
No, the KE of the system is the sum of the KEs of each ball. In your example, the KE is positive before and after the collision. KE doesn't have a direction and cannot 'cancel'.
In other words, my stubborn intuition tells me that there should be no difference between a vector quantity and a scalar quantity in a two dimensional collision.
I guess your intuition is way off!

phhoton

Hi,
in an inelastic collision momentum and KE aren't conserved because the system isn't considered as isolated.

Mentor

Hi,
in an inelastic collision momentum and KE aren't conserved because the system isn't considered as isolated.
No, there's nothing about an inelastic collision that implies that the system isn't isolated. Inelastic just means that KE isn't conserved; momentum still is.

phhoton

I know that four-momentum is conserved but I didn't know momentum is conserved too.

phhoton

I'm sorry. I forgot that momentum means "quantité de mouvement". I thought that momentum means moment. Excuse me.

mickybob

Here is a simple example about my issue with this. 1g ball (ball A) moving west at 10m/s hits another 1g ball (ball B) moving east at 10m/s. After the collision, ball A moves east at 3m/s, and ball B moves west at 3m/s.

My understanding is that momentum is conserved because the sum of momentum before the collision will equal the sum of momentum after the collision. If that is correct, then why doesn't it work that way with kinetic energy? Regarding the example above, isn't the net kinetic energy of the system 0m/s before the collision and 0m/s after the collision?

In other words, my stubborn intuition tells me that there should be no difference between a vector quantity and a scalar quantity in a two dimensional collision.

Okay, first I guess you actually mean a 1D collision, not a 2D collision.

Vector quantities do not becomes the same as scalar quantities in 1D situations. There is still a direction, it's just that there are only two options : moving left or moving right.

The momentum of a ball moving to the left at 3 m/s is not the same as the momentum of the ball moving to the right at 3 m/s: they are equal but opposite. The kinetic energy is, of course, the same, since that does not depend on direction.

Kinetic energy isn't conserved because there is a transfer of energy from one type to another - from kinetic to thermal/sound. That is the very definition of an inelastic collision. Total energy is, of course, conserved.