How Can Momentum Be Conserved When Kinetic Energy Is Lost?

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Discussion Overview

The discussion centers around the relationship between momentum and kinetic energy, particularly in scenarios where kinetic energy is lost, such as through friction or inelastic collisions. Participants explore the principles of conservation of momentum and the conditions under which kinetic energy may not be conserved, examining various examples and theoretical implications.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that while kinetic energy may not be conserved, momentum must always be conserved, questioning how this can be true in cases of energy loss.
  • Others illustrate scenarios where two objects collide and stick together, noting that while kinetic energy may decrease, momentum remains conserved.
  • A participant emphasizes that the conservation of momentum applies even in cases where kinetic energy is lost to friction, suggesting that the system must be closed for momentum conservation to hold.
  • Some participants challenge the assumption that friction must involve an external body, questioning the conditions under which momentum is considered lost.
  • There are discussions about specific collision scenarios, such as two identical objects colliding, where the final speed is reduced but momentum is conserved, highlighting the distinction between energy and momentum loss.
  • Participants mention the importance of defining the system when analyzing collisions, suggesting that both objects involved should be considered as part of the system to accurately assess momentum conservation.

Areas of Agreement / Disagreement

Participants express differing views on the implications of momentum conservation in the presence of kinetic energy loss. There is no consensus on the conditions under which momentum may be perceived as lost or transferred, and the discussion remains unresolved regarding the relationship between internal and external forces in these contexts.

Contextual Notes

Some arguments depend on the definitions of closed systems and the treatment of internal versus external forces. The discussion also highlights the need for careful consideration of the mathematical relationships involved in collisions and energy transformations.

physea
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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?
 
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physea said:
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.
 
Dale said:
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...
 
physea said:
I read that kinetic energy may not be preserved, but momentum must always be preserved.

How can that be?

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physea said:
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.
 
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physea said:
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
 
PeroK said:
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?
 
A.T. said:
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?
 
physea said:
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?
 
  • #10
physea said:
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...]
 
  • #11
physea said:
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.
 
  • #12
physea said:
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.
 
  • #13
physea said:
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.
 

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