# Science Question - Two masses suspended from a pulley
**URL:** https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484
**Category:** Factual Questions
**Created:** [August 6, 2013, 10:38am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484 "2013-08-06T10:38:50Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [August 6, 2013, 10:38am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/1 "2013-08-06T10:38:50Z")
The eleven year old sat a nationwide science test recently (he did exceptionally well but you will be glad to hear that the parental boasting section of this post is now over). He was able to bring the paper home. One of the questions he got “wrong” - which sounds slightly familiar except it involves no monkeys - was as follows:
> [@](#):
>
> Ms Lee had two identical masses (A and B) joined by a light piece of string. She passed the string over a pulley so that the masses could be easily moved up and down. She held the two masses still in the poisition shown in diagram 1 [diagram shows masses at equal height below pulley]. When she let go of them, they stayed in that position.
>
> Then Ms Lee moved the masses to the position shown in diagram 2 [which shows mass A about half as far from the pulley as mass B] and held them still again.
>
> What will happen when Ms Lee lets go of the two masses?
>
> A/ The masses move back to where they were originally and stop. [diagram shows as for diagram 1 ie masses at equal heights]
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> B/ The masses stay where they are. [diagram shows masses as for diagram 2]
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> C/ The masses move back and past where they were originally. [diagram showing the opposite of diagram 2 ie mass A about twice as far from the pulley as mass B]
>
> D/ The masses move further past where they were moved to. [diagram shows Mass A all the way up and mass B all the way down]
What answer is correct or what answers could be correct, based on the question as asked? Needless to say I don’t agree with the “official” answer but I won’t bias you by telling what it was.
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### Author:  [@bob\_2](https://boards.straightdope.com/u/bob_2)
#### Post date: [August 6, 2013, 10:47am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/2 "2013-08-06T10:47:19Z")
Since the string is stated to be ‘light’, and friction low (easily moved up and down) I would say that ‘A’ is correct.
In reality, friction would stop the construct from regaining equilibrium but this is for eleven year olds.
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### Author:  [@aNewLeaf](https://boards.straightdope.com/u/aNewLeaf)
#### Post date: [August 6, 2013, 10:47am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/3 "2013-08-06T10:47:52Z")
D) is the answer I choose
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### Author:  [@Fear\_Itself](https://boards.straightdope.com/u/Fear_Itself)
#### Post date: [August 6, 2013, 10:48am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/4 "2013-08-06T10:48:07Z")
I say D), because the weight of the string makes B heavier than A, which pulls B down.
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### Author:  [@Patty\_O\_Furniture](https://boards.straightdope.com/u/Patty_O_Furniture)
#### Post date: [August 6, 2013, 10:54am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/5 "2013-08-06T10:54:09Z")
Aren’t their weights identical and therefore the pull of gravity equal on both sides, regardless of how the two weights are situated with respect to each other? Each acts as a counterweight to the other.
If one side gets heavier when the two weights are at different heights, then counter-weighted elevators wouldn’t work, would they?
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### Author:  [@Musicat](https://boards.straightdope.com/u/Musicat)
#### Post date: [August 6, 2013, 10:55am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/6 "2013-08-06T10:55:25Z")
This is a variation on the [Monkey on a rope](http://boards.straightdope.com/sdmb/showthread.php?t=696328) question.
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### Author:  [@ticker](https://boards.straightdope.com/u/ticker)
#### Post date: [August 6, 2013, 10:58am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/7 "2013-08-06T10:58:34Z")
I say B). The force acting on each mass is gravity - equal for each mass, and the effect of gravity on the other mass transferred through the string - again equal for each. This ignores the mass of the string and the reduction in gravity due to the upper mass being further from the Earth.
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [August 6, 2013, 11:00am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/8 "2013-08-06T11:00:31Z")
> [@Musicat](#):
>
> This is a variation on the [Monkey on a rope](http://boards.straightdope.com/sdmb/showthread.php?t=696328) question.
Not really because the question is carefully phrased to ensure that each phase starts with all items stationary, and what happens from there is a function purely of gravity and friction, where the monkey problem is dynamic.
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [August 6, 2013, 11:03am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/9 "2013-08-06T11:03:12Z")
> [@Patty\_O\_Furniture](#):
>
> If one side gets heavier when the two weights are at different heights, then counter-weighted elevators wouldn’t work, would they?
Counter-weighted elevators have motors to overcome any slight imbalances. This must be true as, for a start, consider that sometimes elevators have people in them and sometimes they don’t.
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### Author:  [@Musicat](https://boards.straightdope.com/u/Musicat)
#### Post date: [August 6, 2013, 11:25am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/10 "2013-08-06T11:25:05Z")
> [@Princhester](#):
>
> Not really because the question is carefully phrased to ensure that each phase starts with all items stationary, and what happens from there is a function purely of gravity and friction, where the monkey problem is dynamic.
The monkey problem starts with all items stationary, too. I think they are the same problem and share the same physics. I also think that friction is not intended to be a factor.
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [August 6, 2013, 11:29am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/11 "2013-08-06T11:29:02Z")
> [@Musicat](#):
>
> The monkey problem starts with all items stationary, too.
Yes but then the monkey moves. Anyway, this thread is about the precise question in the OP, not the monkey problem. Let’s keep this clean and not hijack off into another question.
What is the answer a person doing the test should give to this particular question?
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### Author:  [@Bozuit](https://boards.straightdope.com/u/Bozuit)
#### Post date: [August 6, 2013, 11:34am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/12 "2013-08-06T11:34:31Z")
I believe the answer should be B. It’s basically an[Atwood Machine](http://en.wikipedia.org/wiki/Atwood_machine), isn’t it?
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### Author:  [@njtt](https://boards.straightdope.com/u/njtt)
#### Post date: [August 6, 2013, 11:37am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/13 "2013-08-06T11:37:46Z")
B or D, depending on which is the more negligible, the friction in the pulley or the extra mass of the mass of the extra mass of the longer (but “light” string on one side. If the string is entirely weightless, then B.
I suppose with a perfectly frictionless pulley it might matter that the lower mass is slightly closer to the Earth’s center of mass, thus leading gravity to pull on it infinitesimally more strongly. So, in that case, D.
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### Author:  [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)
#### Post date: [August 6, 2013, 11:41am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/14 "2013-08-06T11:41:05Z")
> [@bob\_2](#):
>
> Since the string is stated to be ‘light’, and friction low (easily moved up and down) I would say that ‘A’ is correct.
The problem statement said nothing about friction.
The problem statement did say the string was light, the implication of which is that its mass can be safely disregarded. This means the mass on either side of the pulley is the same, regardless of what height the masses are at.
With negligible string mass, the correct answer is B.
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### Author:  [@YamatoTwinkie](https://boards.straightdope.com/u/YamatoTwinkie)
#### Post date: [August 6, 2013, 11:46am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/15 "2013-08-06T11:46:57Z")
Poorly worded question. Depending on what weight values of “light string” you assume, and how much pulley friction is input for “easily moved up and down”, the answer can be either B) or D). Although since this is test is geared at 5th grade level, and they specified “light” string the answer they were looking for is probably B).
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### Author:  [@Princhester](https://boards.straightdope.com/u/Princhester)
#### Post date: [August 6, 2013, 11:47am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/16 "2013-08-06T11:47:12Z")
> [@Machine\_Elf](#):
>
> The problem statement said nothing about friction.
Incorrect. The problem says the string goes “over a pulley so that the masses could be easily moved up and down”.
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### Author:  [@Mangetout](https://boards.straightdope.com/u/Mangetout)
#### Post date: [August 6, 2013, 11:47am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/17 "2013-08-06T11:47:20Z")
> [@njtt](#):
>
> B or D, depending on which is the more negligible, the friction in the pulley or the extra mass of the mass of the extra mass of the longer (but “light” string on one side. If the string is entirely weightless, then B.
Concur - the question is a little vague in that the specification of the string being ‘light’ _may_ be intended to mean “to be ignored”. I’d go for D, on the basis that ‘light string’ is not explicitly massless.
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### Author:  [@scr4](https://boards.straightdope.com/u/scr4)
#### Post date: [August 6, 2013, 11:47am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/18 "2013-08-06T11:47:33Z")
To me, “light piece of string” implies that the mass of the string is negligible compared to the mass of the, um, masses. And given the real-world description of the pulleys (rather than “frictionless”), I would assume the friction is non-zero. So my best guess would be that B is the intended answer.
Also, if the pulley were frictionless and the string had non-zero mass, none of these answers would be true. What would happen is, the masses would move past the original point, move twice as far and stop, then start moving back. It would oscillate forever, with the original point as the center of the oscillation. (Well, unless we factor in air resistance, in which case it would eventually come to a stop at the original point.)
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### Author:  [@Bozuit](https://boards.straightdope.com/u/Bozuit)
#### Post date: [August 6, 2013, 11:54am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/19 "2013-08-06T11:54:12Z")
Was this really in a science test for 11 year olds? Are they actually expected to calculate the answer or is it just taught? Is it one of those tests that just gets harder and harder, or do you have a particularly smart 11 year old?
I don’t remember any real calculation of mass, gravity, friction etc. at school until a few years after 11.
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### Author:  [@Malacandra](https://boards.straightdope.com/u/Malacandra)
#### Post date: [August 6, 2013, 11:57am UTC](https://boards.straightdope.com/t/science-question-two-masses-suspended-from-a-pulley/665484/20 "2013-08-06T11:57:49Z")
Given massless inextensible string and frictionless pulleys, available from all good mathematical axiom shops, and neglecting the difference in gravitational attraction due to height, the masses will stay right where they are. They don’t need to “return to equilibrium”; they are _in_ (neutral) equilibrium already. Option B. Next!
Enlarging: Object A with mass _m_ has force _mg_ acting on it vertically downwards. Also object B. They’re therefore both applying the same tension to the string and so each object is experiencing a force of -_mg_ exactly balancing the force of gravity. (I should be using vectors here, but eh.) Therefore each mass experiences a net force of zero, so it doesn’t move.
There is no particular reason why the two masses need to have equal potential energies, and there is no scope for the system as a whole to reach a lower-energy state.
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