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

In summary, the question is asking about the minimum potential energy gained by a string when pulled so that it is completely on a smooth table, with 4/5 of the string already on the table and the remaining 1/5 hanging off the edge. The center of mass of the hanging part needs to be lifted to get it on the table. For the conceptual question about the trolley colliding with a helical spring, the trolley's initial momentum is conserved and transferred to the earth or stored in the spring. It cannot be destroyed or dissipated as sound and heat.
  • #1
abcd8989
44
0
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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  • #2
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?
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 
  • #6
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?
 

1. What is Gravitational Potential Energy (PE)?

Gravitational Potential Energy is the energy an object possesses due to its position in a gravitational field. It is the energy that is stored in an object when it is raised above the surface of the earth or any other planet.

2. How is Gravitational Potential Energy calculated?

Gravitational Potential Energy is calculated using the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground.

3. What is the relationship between Gravitational Potential Energy and height?

The relationship between Gravitational Potential Energy and height is directly proportional. This means that as the height of an object increases, its Gravitational Potential Energy also increases.

4. How does Gravitational Potential Energy change when an object is moved to a different position?

If an object is moved to a higher position, its Gravitational Potential Energy will increase, and if it is moved to a lower position, its Gravitational Potential Energy will decrease. This is because the height of the object changes, affecting the value of h in the PE = mgh equation.

5. Can Gravitational Potential Energy be negative?

Yes, Gravitational Potential Energy can be negative. This occurs when an object is at a position below the reference point, and its height is negative. In this case, the value of PE will be negative, indicating that the object has less energy than it would have at the reference point.

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