Can you verify if there is a error in the notes or i am just stupid.

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Discussion Overview

The discussion revolves around the application of conservation of momentum in a scenario involving two masses connected by a string and the presence of external forces. Participants are examining the validity of the assumptions made in the example provided, particularly regarding whether momentum can be considered conserved under the given conditions.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the use of conservation of momentum due to the presence of external forces acting on the system.
  • Another participant argues that momentum can be considered conserved because the tension in the string is uniform, allowing the two masses to exert equal and opposite forces on each other, thus ignoring external forces during the short duration of impulse.
  • Several participants assert that momentum is not conserved in "normal" coordinates, emphasizing that the forces acting on the masses are equal but not opposite, which complicates the conservation argument.
  • There is a consensus among some that the textbook's explanation is insufficient and fails to clarify the assumptions regarding momentum conservation adequately.
  • One participant suggests that while the result in the attachment is correct, the justification for conservation of momentum requires more thorough explanation.

Areas of Agreement / Disagreement

Participants express disagreement regarding the conservation of momentum in the scenario. While some argue that momentum can be considered conserved under certain conditions, others maintain that it is not conserved due to the nature of the forces involved. No consensus is reached on the validity of the assumptions made in the example.

Contextual Notes

The discussion highlights limitations in the explanation provided in the textbook, particularly regarding the treatment of forces and momentum. The assumptions made about the uniformity of tension and the nature of forces are points of contention that remain unresolved.

jessicaw
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I think the example is very weird.
Why we can use conservation of momentum? There is external force!

thx.
 

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The assumption is that the tension is the same throughout the string. So, in effect, the two masses are exerting equal and opposite forces on each other and thus momentum is conserved. Since the impulse is of short duration, any external forces on the masses can be ignored.
 
I think strictly speaking, jessicaw is being diligent. Momentum is clearly not conserved between the two masses in "normal" coordinates. The forces are not equal and opposite, they're just equal both in the up direction. What it is really assuming is that the two masses will have the same change of momentum; not that momentum is conserved. i.e pf - pi = (-mV) - (-mv) = (MV) - (0); because M has V and m has -V (-v initially).
 
kcdodd said:
I think strictly speaking, jessicaw is being diligent. Momentum is clearly not conserved between the two masses in "normal" coordinates. The forces are not equal and opposite, they're just equal both in the up direction. What it is really assuming is that they will have the same change of momentum; not that momentum is conserved. i.e pf - pi = (-mV) - (-mv) = (MV) - (0); because M has V and m has -V (-v initially).
I completely agree. It's not something 'obvious', but something that requires explanation. I think it was a good question that the textbook failed to properly address.

When I said the forces are in effect 'equal and opposite', I was of course taking my coordinates along the rope. (That too, should have been explained. :rolleyes:)
 
kcdodd said:
I think strictly speaking, jessicaw is being diligent. Momentum is clearly not conserved between the two masses in "normal" coordinates. The forces are not equal and opposite, they're just equal both in the up direction.
Correct. As you noted, the forces are not equal but opposite. They are equal and non-opposite. So there should be no expectation that momentum is conserved (and it is not conserved). One way to resolve this is to come up with an analog that simplifies and unfolds the system so that the forces are equal but opposite. The attached explanation did not do that, however.

Edit
Just to make things clear, the result obtained in the attachment to the original post is correct. The issue is the handwave regarding conservation of momentum needs a bit better explanation and justification.
 
Last edited:

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