Monkey on a Rope

Factual Questions
21

I know there have been previous threads on this topic, but I don’t know if it is widely known that this riddle goes back to Lewis Carroll.

The real-world answer involves uneven acceleration (anthropoids climb ropes by a series of small yanks, jerks, and tugs, not by a smooth linear acceleration) and, of course, friction.

I just did a quick Youtube search, and didn’t see any actual experimental examples (using a human athlete rather than a monkey.) Has anyone ever actually gone out and performed this experiment? Seems to be one of the simplest possible physics lab-problems ever!

22

At the risk that this is a serious question, and the questioner is somehow assuming that the climbing monkey might affect the balance, the answer is, “nothing.” The equilibrium is not affected by the position of the objects (monkey, bucket) on the rope, but the weight on either side. If the weight is the same, the balance is the same.

Now if it’s a weasel and a bucket of shit, all bets are off.

23

It’s not additional mass, no - it is however mass that has changed from one side of the pulley to the other, thus changing the equilibrium.

Which is why when this kind of problem shows up in a physics book, the rope is always assumed to be massless (or, at least, of negligible mass) along with the frictionless pulley.

The traditional answer is that the monkey and the bucket should be raised at the same rate, while the amount of rope that the monkey “climbs” is equal to twice the actual height gained.

24

Figure the pulley is fifty feet up and there’s a hundred feet of rope (which we’re assuming effectively weighs nothing). So the monkey and the bucket are separated by one hundred feet of rope.

The monkey reaches up a foot and pulls himself up. There are now ninety-nine feet of rope separating the monkey and the bucket. Because they weight the same, they remain an equal distance from the pulley. So both the monkey and the bucket rise six inches.

Every time the monkey pulls another foot of rope, both he and the bucket rise six inches until they meet at the pulley.

25

Dear Sir,

I am writing in response to your request for additional information in Block 3 of the accident report form. I put “poor planning” as the cause of my accident. You asked for a fuller explanation and I trust the following details will be sufficient.

I am a bricklayer by trade. On the day of the accident, I was working alone on the roof of a new six story building. When I completed my work, I found that I had some bricks left over which, when weighed later were found to be slightly in excess of 500 lbs. Rather than carry the bricks down by hand, I decided to lower them in a barrel by using a pulley, which was attached to the side of the building on the sixth floor. Securing the rope at ground level, I went up to the roof, swung the barrel out and loaded the bricks into it. Then I went down and untied the rope, holding it tightly to ensure a slow descent of the bricks.

You will note in Block 11 of the accident report form that I weigh 135 lbs. Due to my surprise at being jerked off the ground so suddenly, I lost my presence of mind and forgot to let go of the rope. Needless to say, I proceeded at a rapid rate up the side of the building.

In the vicinity of the third floor, I met the barrel which was now proceeding downward at an equal, impressive speed. This explained the fractured skull, minor abrasions and the broken collar bone, as listed in section 3 of the accident report form. Slowed only slightly, I continued my rapid ascent, not stopping until the fingers of my right hand were two knuckles deep into the pulley.

Fortunately by this time I had regained my presence of mind and was able to hold tightly to the rope, in spite of beginning to experience a great deal of pain.

At approximately the same time, however, the barrel of bricks hit the ground and the bottom fell out of the barrel. Now devoid of the weight of the bricks, that barrel weighed approximately 50 lbs. I refer you again to my weight. As you can imagine, I began a rapid descent, down the side of the building.

In the vicinity of the third floor, I met the barrel coming up. This accounts for the two fractured ankles, broken tooth and several lacerations of my legs and lower body.

Here my luck began to change slightly. The encounter with the barrel seemed to slow me enough to lessen my injuries when I fell into the pile of bricks and fortunately only three vertebrae were cracked.

I am sorry to report, however, as I lay there on the pile of bricks, in pain, unable to move, I again lost my composure and presence of mind and let go of the rope and I lay there watching the empty barrel begin its journey back down onto me. This explains the two broken legs.

I hope this answers your inquiry.

26

[Moderating]

Note that this thread was originally posted in Great Debates, and was moved to GQ by Gaudere.

Colibri
General Questions Moderator

27

This link http://physicsdemos.cwru.edu/mechanics/mechdemos/M520_1m.MOV shows a practical demonstration of the puzzle, where the mass of the rope is negligible relative to the climber (or at least, relative to the frictional forces in the pulley). If the mass of the rope is not negligible, then that mass is moved to the monkey side of the pulley, and the monkey will start to sink, as the masses are now unbalanced.

28

What if the monkey is riding backwards on a pig?

29

This problem seems to be trivially obvious to me, so maybe I’m missing something.

First, what color is the monkey?

Just kidding. Moving forward…

As I see the premise, we have a single pulley at some high location and a rope threaded through it, hanging down toward the ground. The rope has two ends. One end has a bucket of sand tied to it. The other has a monkey (why a monkey, why not a duck?).

Both ends, with cargo, are off the ground. The weight of the bucket exactly equals the weight of the monkey. No bananas are in evidence, and we are in balance.

Am I right so far? Then…if the monkey climbs the rope, and there are no other factors like wind, jerking the rope, planets passing close by or whatever, the position of the rope vis-a-vis the pulley will not change since the weight on each side does not change, monkey high or monkey low. Therefore, the answer to “What will happen?” is “nothing.”

Am I missing something?

30

Check the video** si_blakely** posted. It does not agree with your analysis.

I think the issue is you’re viewing the problem statically, which it is not.

31

I can’t tell from that video what is happening, and there is no explanation. Is the box on the left side acting as a winch? What physical forces are causing the weights on the right to rise?

32

the box on the left is a rope climber - effectively a winch that pulls in the rope, analogous to the monkey climbing the rope and wrapping the free end round its waist as it goes.

The rope climber provides the force that pulls the weights up.

What is balanced at the start is not the weight on both sides, but the forces.

You cannot start with the weights at different heights, that (at least) should be a simple experiment to try.

33

Perhaps. I think a big question is, can an anthropoid climb a rope without jerking it? Would a monkey (or a man) be able to pull gradually and smoothly, in the course of climbing? In ordinary practice, when I climb a rope, I yank, rest, yank, rest, yank, rest. (My whole life is a series of jerks…)

A robot could be devised that smoothly accelerates up the rope, perhaps by gripping it between rollers. But a climbing animal?

The question can be seen as a contrast between mathematical ideals and the rough, dirty, awkward, and klutzy nature of “real life.” We can declare that the rope is weightless, and that the pulley is frictionless. These are ideas we can pretty much grasp intuitively. But climbing a rope “smoothly?” Is it possible for animals that use muscles attached to skeletal limbs?

34

This is what I thought, with the addition of oscillations if the monkey climbs in jerks.

35

In case it’s not been made clear, the force needed for the monkey to climb the rope is greater than the force needed for it to simply remain in place. So if the system starts out balanced, then when the monkey starts to climb there is additional force being applied to the bucket, which therefore rises at the same rate as the monkey.

36

It has nothing to do with being an anthropoid. It is simply F=ma. Anything that accelerates, no matter how slowly or gently, must exert an additional force. That force (alongside the force from the balanced weight) is transmitted through the rope to the bucket. The bucket weighs the same, so it must accelerate at the same rate as the monkey.

Of course, all this goes out the window if the pulley has friction, or the rope has mass, or whatever.

37

{SLAPS Czarcasm WITH A WET TROUT}

Go peddle that stuff on Newser. :smack::mad:

38

I guess I was thinking intuitively, as I don’t have a rope, pulley or a monkey handy to try out the experiment. If the video is valid, I’d like to know why this happens and what forces are involved. I can imagine climbing such a rope, but I wouldn’t expect my climbing action to pull it down.

39

To further clarify, the climbing itself does not require any additional force. What does require some extra force, though, is the transition from not-climbing to climbing, since that’s an acceleration. That’ll pull a little bit of rope over to the monkey’s side. Unfortunately, even that little bit of rope is a killer, as the original situation was unstable: If we’re in the real world and the rope isn’t massless, then there’s now a little bit more weight of rope on the monkey’s side, and a little bit less on the counterweight’s side, and so the system isn’t balanced any more: More rope pulls over, the imbalance gets even greater, and the whole thing goes out of control.

40

:smiley: