Inertia

[Nornh]

PROBLEM:

A weight of 15 lbs is suspended by a single rope. The weight is lifted 1 ft and dropped 1 ft.
What is the lb peak load on the rope?

[HallsofIvy]

There is not enough information to answer this question. One could do it in this way: Use "conservation of energy" to determine the velocity after the one foot drop. The velocity after the drop is 0 (or, if the rope is "springy" could be upward) so you calculate the change is speed. The force is the change in speed divided by the time in which that change took place.
You don't give a time so the last step can't be done. If you model the rope as a spring with given spring coefficient, then you could do this. A very "stiff" spring (high spring coefficient) will give a much greater force than a "soft" spring (low spring coefficient) so you definitely need to know the properties of the rope. Think of it as the difference between jumping off a cliff tie to a steel cable as opposed to a bunjee cord.

Is this the same problem as the one posted earlier with the "instantaneous" change (which would require an infinite force)?

[FZ+]

Depends on how fast the weight is lifted or dropped, and how it is done.