How Can Momentum Be Conserved When Kinetic Energy Is Lost?

[physea]

I read that kinetic energy may not be preserved, but momentum must always be preserved.

How can that be? If there's a loss in kinetic energy due to friction or heat, the velocities will be reduced thus momentum will be reduced?

 

[Dale]

If there's a loss in kinetic energy due to friction or heat, the velocities will be reduced thus momentum will be reduced?

Momentum is a vector, so it may be zero to begin with. For example two objects with same mass, one moving at v and the other at -v. If they collide and stick together then the KE reduces to zero whereas the momentum was always zero.

 

[physea]

Momentum is a vector, so it may be zero to begin with. For example two objects with same mass, one moving at v and the other at -v. If they collide and stick together then the KE reduces to zero whereas the momentum was always zero.

Obviously we are not talking about the exceptional situation that momentum is zero and remains zero...

 

[A.T.]

I read that kinetic energy may not be preserved, but momentum must always be preserved.

How can that be?

 

[Dale]

Obviously we are not talking about the exceptional situation that momentum is zero and remains zero...

It is not an exceptional situation. Any collision can be analyzed in the center of momentum frame. It is one of the most common strategies for solving collision problems in particle physics.

In any case, the rule you are questioning applies in this scenario.

 

[PeroK]

I read that kinetic energy may not be preserved, but momentum must always be preserved.

How can that be? If there's a loss in kinetic energy due to friction or heat, the velocities will be reduced thus momentum will be reduced?

If kinetic energy is lost to friction, then you do not have a closed system, so the lost momentum, like the lost energy is being transferred to another body outside the sys

 

[A.T.]

If kinetic energy is lost to friction, then you do not have a closed system, so the lost momentum, like the lost energy is being transferred to another body outside the sys

Why must the friction be with a body outside the system?

 

[physea]

View attachment 220850

What about an item crashing into another and they become one and this one aggregate moves very little?
Isn't that both energy and momentum loss?

 

[A.T.]

What about an item crashing into another and they become one and this one aggregate moves very little?
Isn't that both energy and momentum loss?

Where did the momentum go?

 

[russ_watters]

I read that kinetic energy may not be preserved, but momentum must always be preserved.

How can that be? If there's a loss in kinetic energy due to friction or heat, the velocities will be reduced thus momentum will be reduced?

Think about a collision between two identical objects that stick together, one starting stationary. The final speed is half the initial speed of the first object, momentum is conserved and energy is lost. The math to demonstrate this is straightforward...

[Edit...someone posted an animation of this...]

 

[mfig]

I read that kinetic energy may not be preserved, but momentum must always be preserved.

How can that be?

Internal forces can transform energy form one form to another, but cannot change momentum.

 

[Dale]

What about an item crashing into another and they become one and this one aggregate moves very little?
Isn't that both energy and momentum loss?

Work out the numbers. You will see, only KE is lost, not momentum.

 

[mfig]

What about an item crashing into another and they become one and this one aggregate moves very little?
Isn't that both energy and momentum loss?

The key is to consider the system to be composed of both items.