Does Energy Conservation Apply to Linear Momentum Collisions?

[John Pang]

Just a conceptual question :
During a collision of two objects say A and B with the same mass, is the object with a higher velocity before collision never has its velocity increased after the collision, while the object with a lower initial velocity never has its velocity further decreased after the collision?

 

[John Pang]

Suddenly i realize that it is not correct :p. Thanks anyway

 

[John Pang]

What is actually confusing me is about the transfer of kinetic energy.
Theorectically, atoms with greater kinetic energy should transfer kinetic energy to atoms with lower kinetic energy,which is done through collisions. However, as an atom with a higher velocity and thus higher kinetic theory may even has its velocity（in terms of magnitude but not direction) increased after colliding with another atom with a lower initial velocity , then it may seem to violate the fact that kinetic energy is transferred from hotter objects to colder objects.

 

[A.T.]

However, as an atom with a higher velocity and thus higher kinetic theory may even has its velocity（in terms of magnitude but not direction) increased after colliding with another atom with a lower initial velocity , then it may seem to violate the fact that kinetic energy is transferred from hotter objects to colder objects.

Temperature is a statistical quantity. You have to consider which type of collision is more likely, to determine the net energy flow.

 

[John Pang]

Sorry I can't understand it.
So is it possible that, during a head-on elastic collision of two atoms with equal mass, is it possible that the atom with a higher initial velocity has its velocity increases in terms of magnitude after the collision, while the atom with a lower initial velocity has its velocity further decreased in terms of magnitude after the collision?
I am still not quite sure about it.

 

[John Pang]

And is it true that heat is transferred from hotter objects to colder objects through collisions?

 

[lonelypancreas]

So is it possible that, during a head-on elastic collision of two atoms with equal mass, is it possible that the atom with a higher initial velocity has its velocity increases in terms of magnitude after the collision, while the atom with a lower initial velocity has its velocity further decreased in terms of magnitude after the collision?

No, it is not possible.
During an elastic collision, linear momentum is conserved as well as the total kinetic energy of the system before and after the collision so after an elastic collision, the kinetic energy will also be conserved. Upon contact, energy will be transferred. Therefore, the atom with the larger velocity (hence w/ the larger KE) transfers energy into the other atom. Upon transferring KE, it corresponds to a lost in its initial velocity. Therefore, the object with the higher velocity will transfer (lose velocity) energy to the other object while that other object will do the same: transfer energy (but gain velocity since it has lower KE initially) to the first object.

So no, it is not possible. The atom with the higher initial velocity relatively slows down upon collision while the atom with the lower initial velocity gains velocity upon collision.

 

[A.T.]

So no, it is not possible. The atom with the higher initial velocity relatively slows down upon collision while the atom with the lower initial velocity gains velocity upon collision.

This is wrong. With different masses or in more than 1 dimension, it is possible that the slower body slows down, while the faster gets even faster.

 

[John Pang]

This is wrong. With different masses or in more than 1 dimension, it is possible that the slower body slows down, while the faster gets even faster.

So is it true that, as far as the mass of the atoms is the same and the collision is only one dimensional, then the rule applies?

 

[A.T.]

So is it true that, as far as the mass of the atoms is the same and the collision is only one dimensional, then the rule applies?

Yes.

 

[John Pang]

Thank you. I get it :D

 

[John Pang]

I am sorry to raise further questions. Why ,in case of two dimensional elastic collisions, is it possible that a faster atom becomes faster while the slower gets even slower?
Btw, is the above the reason why evaporation, in which some atoms acquire more and more velocity, is possible?

 

[A.T.]

Why ,in case of two dimensional elastic collisions, is it possible that a faster atom becomes faster while the slower gets even slower?

Consider a slow particle hits a fast particle perpendicularly to the fast particle's velocity.

 

[John Pang]

I understand that the faster atom would attain greater velocity due to the addition of the y component.
But I don't understand what will be the effect on the slower atom? Would tge slower atom decreases in velocity and why?

 

[John Pang]

By the why, is this the reason why some atoms can attain greater velocities than the average atoms, leading to evaporation ?

 

[A.T.]

I understand that the faster atom would attain greater velocity due to the addition of the y component.
But I don't understand what will be the effect on the slower atom? Would tge slower atom decreases in velocity and why?

Energy conservation.