A rope and a frictionless table

[davesface]

Homework Statement

A rope of mass M and length L lies on a frictionless table, with a short portion L₀ hanging through a hole. Initially the rope is at rest. Evaluate A and B so that the initial conditions are satisfied.

The Attempt at a Solution

Ok, so I understand the problem and have gotten the final 2 equations (according to my book):
yAe^yt-yBe^-yt=0
L₀=Ae^yt+Be^-yt

It looks like, according to the first equation, Be^-yt=Ae^yt. Plugging this into the second equation, L₀=2Ae^yt and L₀=2Be^-yt. This seems intuitively wrong, but I'm not sure exactly why. Any thoughts?

 

[davesface]

Bump. All I need is some confirmation, or a way to confirm, that I have the correct equations.

 

[baba89]

I would approach this problem by first reviewing the initial conditions and making sure that I understand them correctly. In this case, the rope is at rest and a short portion is hanging through a hole on a frictionless table. Next, I would review the equations given in the attempt at a solution and make sure they are correct. From my understanding, the second equation should be L0 = Aeyt - Be-yt, not L0 = Aeyt + Be-yt. This is because the rope is initially at rest, so the sum of the two forces acting on it (Aeyt and Be-yt) must be equal to zero.

Next, I would try to understand why the solution seems intuitively wrong. One possibility could be that the equation L0 = 2Aeyt and L0 = 2Be-yt implies that the mass of the rope is doubled, which is not consistent with the initial conditions given. Another possibility could be that the equations do not take into account the fact that the rope is hanging through a hole, which could affect the forces acting on it.

To address these concerns, I would suggest reevaluating the equations and incorporating the fact that the rope is hanging through a hole. This could potentially involve adding a third force (tension) to the equations. Additionally, I would double check the initial conditions and make sure that all assumptions are consistent with the given information.

Overall, as a scientist, I would approach this problem with a critical and analytical mindset, constantly reviewing and reassessing the given information and equations in order to find a solution that is consistent and accurate.