Simple question on Conservation of Momentum and KE

Click For Summary

Discussion Overview

The discussion revolves around the concepts of conservation of momentum and kinetic energy (KE) in the context of inelastic collisions. Participants explore the relationship between these conservation laws and the implications of energy loss during such collisions.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how momentum can be conserved when kinetic energy is not conserved in an inelastic collision, given that both depend on mass and velocity.
  • Another participant clarifies that momentum conservation applies to the system as a whole, not to individual bodies, and notes the difference in how momentum and kinetic energy are calculated.
  • A further comment emphasizes that momentum conservation does not derive from energy conservation, highlighting their independence.
  • One participant acknowledges a misunderstanding, previously believing that momentum conservation was a consequence of energy conservation.
  • A later reply suggests that at a fundamental level, the laws of momentum and energy conservation are interconnected, but classical mechanics imposes specific conditions for their application.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement. While there is consensus on the independence of momentum and energy conservation, there is ongoing debate regarding the implications of these principles in inelastic collisions and the participant's understanding of their relationship.

Contextual Notes

Some participants note that the discussion hinges on the definitions of energy and momentum, as well as the conditions under which these conservation laws apply, particularly in the context of dissipative forces.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics seeking to understand the nuances of conservation laws in mechanics, particularly in the context of collisions.

Crumbles
Messages
142
Reaction score
0
I am having a bit of a conceptual problem with the conservation laws.

Consider a system of two bodies of mass m each. One moving at speed V1 towards the second body which is at rest.

For the case of an inelastic collision, I understand that the total kinetic energy of the system is not conserved but the total momentum of the system is.

What is bugging me is how can this be if both KE and the momentum, P depend on the mass and velocity of the body.

If the KE before and after the collision is different, how can the momentum which also depends on m and v be the same?

In the case of an inelastic collision, energy is lost to the surroundings: if momentum conservation stems from the conservation of energy, how can the momentum be conserved?
 
Physics news on Phys.org
Nope,conservation of momentum is a direct consequence of Newton's principles applied to isolated systems.However,the conservation on energy is true only for a restrained class of systems,namely conservative systems,for which the interaction forces are derived from a potential field...Dissipative forces are not derived from a potential field.

Daniel.
 
Crumbles said:
For the case of an inelastic collision, I understand that the total kinetic energy of the system is not conserved but the total momentum of the system is.
Right.

What is bugging me is how can this be if both KE and the momentum, P depend on the mass and velocity of the body.
Two comments: (1) It's the momentum of the system that's conserved, not the momenta of each body. (2) KE and momentum depend on the velocites in very different ways: momentum is a vector while KE is a scalar. To find the momentum of a system of two bodies you need to add the individual momentum vectors of each; if they point in opposite directions, they can cancel each other. But to find the KE of a system of two bodies, just add the KE of each; they always add, never cancel.

If the KE before and after the collision is different, how can the momentum which also depends on m and v be the same?
See above.

In the case of an inelastic collision, energy is lost to the surroundings: if momentum conservation stems from the conservation of energy, how can the momentum be conserved?
Two more comments: (1) In an inelastic collision between two bodies, mechanical energy is "lost" to thermal energy, deformation, sound, etc. (2) Conservation of momentum does not stem from conservation of energy! They are independent.
 
Thanks for explaining this. I always thought that the law of conservation of momentum was from the law of conservation of energy.
 
At fundamental level (elementary particles) these laws go hand in hand,though...But classically,there are certain conditions which must be fulfilled.

Daniel.
 

Similar threads

High School Why is KE not conserved when momentum is?
  • · Replies 53 ·
2
Replies
53
Views
6K
High School K Energy & Momentum: Driving Force or Lost Heat?
  • · Replies 12 ·
Replies
12
Views
2K
High School Ignoring the motion of the Earth for energy vs. momentum conservation
  • · Replies 21 ·
Replies
21
Views
2K
High School Why Do Objects Bounce? Exploring Momentum and Energy Conservation
  • · Replies 6 ·
Replies
6
Views
3K
High School Conservation of momentum in a closed system
  • · Replies 3 ·
Replies
3
Views
2K
High School Conservation of Momentum for system of particles
  • · Replies 52 ·
2
Replies
52
Views
4K
High School Conservation of momentum and conservation of energy details
  • · Replies 30 ·
2
Replies
30
Views
4K
Undergrad Why momentum is conserved when a gun fires? (conceptual question)
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad How momentum is conserved in an inelastic collision
  • · Replies 25 ·
Replies
25
Views
4K
Undergrad Conservation of angular momentum during collisions
  • · Replies 3 ·
Replies
3
Views
4K