Conservation of linear momentum when friction is present

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Discussion Overview

The discussion revolves around the conservation of linear momentum in scenarios where friction is present, particularly during inelastic collisions. Participants explore whether momentum can be considered conserved despite external forces acting on the system, and how the inclusion of the Earth as part of the system affects this conservation.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants argue that momentum is not conserved due to the presence of external frictional forces acting on the system.
  • Others suggest that during the collision, the friction force is non-impulsive and acts for such a short duration that its effect can be ignored, allowing for momentum conservation during the collision.
  • There is a discussion about whether considering the Earth along with blocks A and B as the system changes the analysis of momentum conservation.
  • One participant points out that while momentum is technically conserved, the change in the Earth's momentum is negligible and cannot be measured, making it seem as though momentum is "lost" in practical terms.
  • Another participant questions the analogy of ignoring the Earth's momentum, indicating a lack of agreement on this point.
  • There is a mention of the work-energy theorem as an alternative approach when momentum is not conserved after the collision.

Areas of Agreement / Disagreement

Participants express differing views on the conservation of momentum in the presence of friction, with no consensus reached. Some believe momentum can be considered conserved during the collision, while others argue that it is not due to external forces.

Contextual Notes

Participants highlight the limitations of their arguments, including the dependence on the assumptions made about the system and the effects of external forces like friction. There is also mention of measurement thresholds affecting the practical observation of momentum changes.

zorro
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See the figure-

attachment.php?attachmentid=32890&stc=1&d=1299618716.jpg


The block A collides inelastically with the block B. I have seen in 2 of my books that they apply conservation of momentum in such problems along x-direction. According to me, since there is an external frictional force acting, the linear momentum is not conserved.

Is it that they consider Earth + A + B to be the system and ignore the velocity of the Earth ?
Please throw some light on this.
 

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The friction does transfer some of the momentum to the table (or whatever). Simpler experiment - put a book on the table and give it a push (impart momentum) and it will soon stop (momentum transferred to table).
 
Hi Abdul! :smile:
Abdul Quadeer said:
The block A collides inelastically with the block B. I have seen in 2 of my books that they apply conservation of momentum in such problems along x-direction. According to me, since there is an external frictional force acting, the linear momentum is not conserved.

As you know, momentum is not conserved after the collision, and we have to use the work energy theorem instead.

But during the collision, the friction force is non-impulsive, ie it acts for such a short time that its effect can be ignored …

it has no effect on the sudden change in momentum …

so momentum is conserved. :smile:
 
tiny-tim said:
But during the collision, the friction force is non-impulsive, ie it acts for such a short time that its effect can be ignored …

So ideally the momentum is not conserved?
 
Abdul Quadeer said:
So ideally the momentum is not conserved?

Yes, but well below the threshold of accuracy with which you could measure the velocities. :wink:
 
Is this approximation same as the situation when we ignore the momentum of the Earth by considering A+B+Earth as our system?
 
I don't think so (I don't really see the analogy :redface:).
 
But that would violate mathematical laws. You must get the same equation by two different methods. Otherwise either one of them is wrong.
 
Momentum is conserved. You change the momentum of the Earth itself. But that amount is so small compared to Earth's total momentum that you could never measure it. So for all practical purposes the momentum is treated as "lost". Think of it this way. If you pour a glass of water into the ocean you increase its volume. But if you go to any station that measures sea level you will never ever observe a change in sea level because of your action. It is the same with the momentum of a sliding object on the Earth. The momentum is still there, you just can't measure it.
 

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