*SIGH* Did you guys even read what I wrote? If you want to research your incorrect answer some more, go to
www.google.com and type in "lewis carroll monkey on a rope".
This site gives a simple explanation.
http://rec-puzzles.org/new/sol.pl/physics/monkey
But here's some more about the problem also:
This problem was popularized by Lewis Carroll (1832-1898, né Charles Dodgson), who agonized over it [recall that the author of Alice in Wonderland was actually a professor of mathematics at Oxford from 1855 to 1881].
The answer is that the centers of inertia of the weight and the monkey will have the same vertical motion (we assume, of course, that the monkey only goes up or down but does not swing the rope). Thus, if the monkey and the weight are initially motionless at the same height, they will always face each other no matter what the monkey does. For example, they will both be in free fall if the monkey lets go of the rope, and both falls stop when the monkey grabs the rope again.
The reason for this is simply that all the forces that are acting on either the monkey or the balancing weight are always equal. There are only two such forces for each body, the weight and the tension of the rope. The weights are equal because the two bodies have the same mass and the rope also exerts the same force on either body because of the numerous "ideal" assumptions made here, including the absence of swinging on the monkey's side (so that the rope exerts only a vertical force in either case). It's also essential to assume not only the lack of any friction, but also the absence of mass for both pulley and rope (otherwise the rope's tension would not be the same on either side of an accelerating pulley and it would vary along the length of an accelerating rope).
[Note also that a "perfect" rope retains its length and transmits instantly its change of tension. This is clearly unrealistic, but it's logically consistent with the axioms of classical mechanics. Changes in tension propagate with infinite speed over the length of a "massless" rope. Such an assumption would be logically inconsistent in the context of relativistic mechanics.]
When the same forces act on bodies of the same mass their speeds change in the same way, so that the speeds remain equal if they are originally so (and we are told here of an original equilibrium where both speeds are zero). Both motions will therefore mirror each other.
From the monkey's perspective, pulling 2 feet of rope will get him only 1 foot higher from the ground, but will require as much effort (work) as would be necessary to climb 2 feet on a stationary rope. That's not surprising in view of the fact that 20 lb were lifted one foot in the process (the monkey and the weight went up one foot each), which is just as difficult a task for a 10 lb monkey as lifting his own weight up two feet...
It's deceptively simple; the monkey moves up, the rope moves up. The monkey moves down, the rope moves down.
If you have any questions, Private Message me and I will put you in touch with my physics professor.
~Crystal
Stay positive, keep studying and do your best. And again... good luck!