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

[abcd8989]

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)

 

[Doc Al]

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?

 

[abcd8989]

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.

 

[Doc Al]

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?

 

[abcd8989]

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.

 

[Doc Al]

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?