A Monkey's Tale of a Cat and a Bottle of Vodka?

Question

Two weeks ago a monkey faced the daunting task of retrieving a bottle of Vodka that Lewis Carroll had stashed on his roof. The monkey beat the challenge and shared the Vodka with his good friend the Cheshire Cat. See http://answers.yahoo.com/question/index;_ylt=AhvKefOetlVmVzowiKt64NLsy6IX;_ylv=3?qid=20071114125308AAbeCwb

But now, Carroll has a new bottle and he has also rigged the mechanism so the Monkey can't use his old trick.

A Cable hangs over frictionless pulley, next to roof on which is nice bottle of Vodka. The cable has uniform mass.

A weight hangs on one end of the cable, on the other side, the monkey has a knot he can sit on. The weight and the monkey balance exactly.

Additionally to prevent the monkey from climbing up the cable until the weight jams into the pulley, Carroll attached a latch. If the weight gets too high up the latch is triggered, the weight falls to the ground as so does the monkey.

Within minutes, the monkey had stolen the vodka.

What did he do?

And no, he can't reach the other cable, and no, he did not make himself lighter by defecating.

Ah, people are thinking. You are getting close, but that's not quite the answer I was thinking of.

The answer is in the title to this question.

The cable ends at the knot the monkey is sitting on and the cable is too slick for him to climb and he doesn't want to jump off (for reasons I don't understand -- but I'm no monkey psychologist). Does our little guy have any other options?

The Answer:

The monkey grabs the knot with his MONKEY'S TAIL and swings down below the knot. Since the whole system is in an unstable equilibrium, the weight starts to drop.

The impulse force of the monkey stopping his swing will not be enought to stop the drop. This is because there now is more chain on the far side of the pulley. The monkey than gets an elevator ride up to the roof.

After the Vodka is snatched, the Monkey slides down the cable on the far side. Or he can sit on the knot and with the additional weight of the Vodka, can cause the weight to start back up and he can take an elevator ride down to the ground.

Pretty cool.

Answer 1

The first answerer is right to an extent. All the monkey needs to do is jump down from the knot. The weight on the other sides will fall to the ground and stop there.

But more significantly, now there is more cable on the mass side of the pulley than on the monkey's side. Once the monkey jumps off, all the cable will want to go over the pulley to the other side, but the monkey can solve that problem by just holding on lightly to it.

With this set up, he can now climb very slowly to the top (ON HIS SIDE), since there is sufficient weight on the other side to support his ascent.

Let's say there is M1 mass of cable on the other side, and M2 < M1 on the monkey's side.
m = mass of monkey and the weight

The monkey climbs such that the tension satisfies
mg < T < (M1-M2)g + mg
This tension will be sufficient for the monkey to climb, but not high enough to disturb the cable and mass.
So the monkey slowly climbs while the mass remains on the floor.

The question rightly states that within minutes (not seconds), the monkey steals the vodka.

*EDIT*
You said the answer is in the title? It doesn't have anything to do with a cat, does it?

If all of this happens high above the ground so that the mass never touches the ground, then once you get a little cable over the pulley, the monkey can just sit still and the weight of the cable will take him up to the ceiling. The problem is to get this started.

Let's say the monkey is hanging on in equilibrium with the weight. Then he lets go momentarily and grabs back on. In the moment he lets go, some cable will go over to the mass side. Now there will be a greater cable mass on the other side, and the monkey will just be pulled up by the weight of the cable.

I'm not sure as yet about the impact force that occurs when the monkey grabs back on.

To get back down, he will have to swing so that he can generate a large tension than his weight. He'll need to do this in order to pull up the cable from the other side.

Answer 2

The monkey jumps down to the ground. The weight will fall and the monkey side of the cable with the knot will go up. The knot will get stuck at the pulley. Now the monkey just need to climb up the other side of the rope.