What is the minimum PE gained by a string hanging over the edge of a table?

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Discussion Overview

The discussion centers around two main topics: the minimum potential energy gained by a string hanging over the edge of a table and a conceptual question regarding the momentum of a trolley colliding with a spring. The first part involves theoretical reasoning about potential energy, while the second part explores momentum conservation and energy transfer during a collision.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents a formula for the minimum potential energy gained by the hanging part of the string and expresses uncertainty about the reasoning behind it.
  • Another participant suggests focusing solely on the hanging part of the string and questions the location of its center of mass and the height it needs to be raised.
  • Several participants discuss a conceptual exam question about a trolley colliding with a spring, debating the fate of the trolley's momentum during the collision.
  • One participant dismisses the idea that momentum can be dissipated as sound and heat, while others express uncertainty about the correct interpretation of the options provided in the question.
  • There is a discussion about whether momentum can be "stored" and the relevance of friction in the context of the trolley's motion.
  • Participants question the conservation of momentum and where it goes during the collision, indicating a lack of consensus on these points.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the minimum potential energy gained by the string or the fate of the trolley's momentum during the collision. Multiple competing views remain regarding the interpretation of the exam question and the nature of momentum in this context.

Contextual Notes

Unresolved aspects include the assumptions made about the string's center of mass and the definitions of momentum storage and destruction. The discussion also highlights the lack of clarity regarding the role of friction in the trolley's motion.

Who May Find This Useful

Students preparing for exams in physics, particularly those interested in potential energy, momentum conservation, and conceptual problem-solving in mechanics.

abcd8989
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4/5 of a string of length L is placed on a smooth table while 1/5 of it hangs freely over the edge of the table, why the minimum PE gained by the string due to a force pulling it so that the whole string is placed on the table is (1/5 m) x g x (1/10 L) (This is the answer, but I don't know why)
(CG of the 1/5 string is considered)
 
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Forget about the 4/5 part, since it's already on the table. You only need to lift the hanging part. Where is the hanging part's center of mass? How high must its center of mass be raised to get it on the table?
 
Thanks.
Besides, while I am drilling for my exam, I find I don't know how to think of this conceptual past paper question:
A trolley travels with uniform velocity to the right on a horizontal ground and collides with a light helical spring attached to a wall fixed to the ground (earth). At the instant the trolley becomes momentarily at rest during collision, what has happened to the initial momentum of the trolley?
A. It has been transferred to the earth.
B. It has been stored in the spring.
C. It has been dissipated as sound and heat ( I guess this one is nonsence as only energy can be dissipated as sound and heat, right?)
D. It has been destroyed by the friction due to the ground.
 
abcd8989 said:
Besides, while I am drilling for my exam, I find I don't know how to think of this conceptual past paper question:
A trolley travels with uniform velocity to the right on a horizontal ground and collides with a light helical spring attached to a wall fixed to the ground (earth). At the instant the trolley becomes momentarily at rest during collision, what has happened to the initial momentum of the trolley?
A. It has been transferred to the earth.
B. It has been stored in the spring.
C. It has been dissipated as sound and heat ( I guess this one is nonsence as only energy can be dissipated as sound and heat, right?)
D. It has been destroyed by the friction due to the ground.
Well, what do you think? Yes, C is nonsense. What about the other choices?
 
Doc Al said:
Well, what do you think? Yes, C is nonsense. What about the other choices?
For A and B, I am not sure which is correct. Both seem to be reasonable. For D, I also don't know whether momentum can be "destroyed", but I think it is not the answer. As it seems to be quite irrelevant with the question. The trolley stopped because all the KE is converted to elastic PE which is temporarily stored in the spring, but not stopped by "the friction due to the ground". However, I don't know whether "a little part of the momentum" has really been destroyed.
 
abcd8989 said:
For A and B, I am not sure which is correct. Both seem to be reasonable.
How does one 'store' momentum?
For D, I also don't know whether momentum can be "destroyed", but I think it is not the answer. As it seems to be quite irrelevant with the question. The trolley stopped because all the KE is converted to elastic PE which is temporarily stored in the spring, but not stopped by "the friction due to the ground". However, I don't know whether "a little part of the momentum" has really been destroyed.
No, momentum cannot be 'destroyed'. And there's no friction mentioned in the problem anyway.

So what do you think happens to the momentum of the trolley? Is momentum conserved? (Momentum of what?) Where did it go?
 

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