Subject:
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Re: Monkey and pulley test -what's the answer to this?
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Newsgroups:
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lugnet.off-topic.fun
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Date:
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Sat, 30 Jun 2001 14:51:45 GMT
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Viewed:
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263 times
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In lugnet.off-topic.fun, Geoffrey Hyde writes:
> Monkey and Pulley test:
>
> A piece of rope weighs four ounces per foot. It is passed over a pulley, and
> on one end is suspended a weight, and on the other end a monkey. The whole
> system is in equilibrium. The weight of the monkey in pounds is equal to the
> age of the monkey's mother in years. The age of the monkey's mother added to
> the age of the monkey is four years. The monkey's mother is twice as old as
> the monkey was when the monkey's mother was half as old as the monkey will
> be when the monkey is three times as old as the monkey's mother was when the
> monkey's mother was three times as old as the monkey. The weight of the rope
> or the weight at the end is half again as much as the difference between the
> weight of the weight and the weight of the weight plus the weight of the
> monkey. How long is the rope? Assuming the pulley to be negligibly small,
> what fractional part of the rope is on the same side of the pulley as the
> monkey when the system is at rest?
Okay, I came up with a rope 6 ft long. That was based on a monkey's
age of 1 yr, and a mom's age of 3 yrs.
For the second question, I have it that the monkey is standing on
top of the weight, making about 3 feet of the rope on the monkey's
side.
The problem I have are these two somewhat conflicting statements:
- "The whole system is in equilibrium."
- "...when the system is at rest".
Equilibrium can be moving at a constant speed (but not accelerating).
But if the system is ever at rest, then it must stay at rest. So
I'm having trouble reconciling these two statements.
The weight descriptions gave me these two relations:
Weight of rope = half of monkey weight
weight of weight = half of monkey weight
So weight of weight = weight of rope.
To have equilibrium at rest, I only came up with two possible cases:
- The monkey is standing on the pulley, or
- The monkey is standing on the weight.
Otherwise, if the monkey were freely suspended, he would begin to
fall and the weight would rise until it hit the pulley. Okay,
I guess that makes a 3rd possible case:
- All 6 ft of the rope is on the monkey's side, as the weight is fetched
up against the pulley. Actually, yes, this is my final answer.
No doubt it's all much simpler than this.
KDJ
_______________________________________
LUGNETer #203, Windsor, Ontario, Canada
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Message is in Reply To:
 | | Monkey and pulley test -what's the answer to this?
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| The following was posted to a non-LEGO message board, and I seem to recall that this is one of those problems that should be simpler than it looks - can anyone make heads or tails out of the heap of arguments thrown into that paragraph below my (...) (23 years ago, 30-Jun-01, to lugnet.off-topic.fun)
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