I have a degree in Anthropology and choose B as well, although the question is obviously biased.
Either B or D, as others have explained. The only way to know for sure is to check out what material is covered in science class for eleven year olds (5th grade?) If they cover friction - the answer is probably B. Answer D requires someone to guess that the string has significant mass in relation the the large weights and that seems advanced for young kids.
So the correct answer is a big F for the testers, in red marker pen. They pulled this question from a text book somewhere and presented it out of context.
Er… Oh.
Right. Good point. F[sub]1[/sub] is actually zero, which is why it doesn’t move. :smack:
But we still get the non-moving original setup as F[sub]1[/sub] = m[sub]1/sub - m[sub]2[/sub](9.8 m/sec[sup]2[/sup]) = 0
And F[sub]2[/sub] = m[sub]2/sub - m[sub]1[/sub](9.8 m/sec[sup]2[/sup]) = 0
So when they’re moved, it’s still F[sub]1-new[/sub] = m[sub]1/sub - m[sub]2[/sub](9.8 m/sec[sup]2[/sup]) and F[sub]2-new[/sub] = m[sub]2/sub - m[sub]1[/sub](9.8 m/sec[sup]2[/sup]).
Yes?
So B is the book answer, and D is the real-world answer.
I’d like to think D is the correct answer for a science class, build it and see what happens.
But it’s not.
I very much doubt D is the real-world answer. For the masses to move, the “string” would have to be heavy enough to overcome the pulley’s friction. And not the weight of the entire length – just the weight of the extra portion of string that was on the long side.
I am absolutely confident that the gravity business can safely be disregarded even for a real world calculation, unless Ms. Lee is dangling this contraption from a tall mountain.
D is a possible real world answer, at best.
A real world application, one I am far too intimately familiar with, is old style double hung windows. It’s actually a 3 weight, 2 pulley system, but the concept is the same. Window in the middle, cast iron weights on either side, with the mass of the weights intended to be equal to the mass of the window.
If the weights are equal (enough) a small amount of friction in the window/pulley is enough to hold the window in place regardless of how high the window is raised.
For what it’s worth I chose B before reading the responses. I ignored the mass of the string and the friction of the pulley. I inferred that’s what the question was going for.
Y’all’s analisations are what’s confusing things. IMHO 
D&R
I agree with the general concensus that the answer is B. A lot of the analysis in this thread, though, is way past the level of what an 11yo is expected to think about this sort of question and the question is clear about the context they want the kid to think in. Before even asking the question, it gives a explicit example that when both masses are at the same height and start motionless, they don’t move. So it’s clear they just want the kids to think about whether them being at different heights will matter.
Remember, an 11yo probably doesn’t understand gravity as a function related to the the square of the distance from the center of mass of the Earth; hell, an 11yo is, at best, only vaguely familiar with quadratic equations in the first place. So expecting an 11yo to consider than an object a little higher or lower will affect gravity is silly.
Further, we have to expect that the kids will need to ignore the mass of the string and the friction of the pulley. They need to say light because I think an 11yo might intuitively realize that a chain connecting them would make one side heavier, but a thin piece of string wouldn’t. Besides, an 11yo isn’t going to know how to calculate the friction on the pulley or how the mass of the string relates to that friction.
It’s clear they just want the kid to realize that two equal masses will have equal downward force and will not move. A kid might choose A because he intuitively, but incorrectly, thinks they need to be at equal heights because they’re the same mass. Or he might choose C because he thinks a higher mass will have more energy and force its way down, or D because he thinks the lower mass will have more energy. But it’s only answer B that clearly demonstrates a basic understanding of Newton’s laws of motions, which is exactly what I’d expect an 11yo to be getting taught. Anything more than that, I think is incorrectly applying higher level understanding of physics to what is just supposed to be a basic conceptual question for a 5-6th grader.
All of that said, in the real world, or in more advanced question, B may not be what actually happens. However, we can’t know because we’re not given any values to do the calculations with. What’s the friction coefficient of the pulley? What’s the mass and lengths of the string? It could still be B if the friction on the pulley is greater than the small amount of mass the string adds to one side, or it could be D if it isn’t. But we have no way of knowing that without having some measurements and doing calculations.
Even better: What if mass A was a box of birds and Ms Lee whacked with a stick?
And that’s why the real answer to a multiple-choice question is the answer that the test-maker expects, which is typically dependent on the context in which the test was created. So a history test for 5th graders that asked what the cause of the US Civil War was would be answered “slavery”, even though there are legitimate arguments that slavery was only one element of a set of elements that created an overall environment that was conducive to setting off pent-up anger. The answer is not economic disparities, religion, or the nature of the State/Federal system because little children aren’t expected to understand that stuff.
I was reading a while back that the official test for US citizenship that the federal government gives to prospective citizens explicitly specifies in the answer key that claiming that the Statue of Liberty is in New Jersey should not be marked “wrong” because there is a legal argument that has not been fully adjudicated claiming that the statue is legally in NJ.
I agree with all of Cheesesteak’s answers. I’ll add that I suspect the students wouldn’t have taken this test in a vacuum, and would have been exposed to previous problems in class where “light string” meant ignore the string’s mass, and “could be easily moved up and down” meant ignore friction. They would have been working in a uniform gravitational field and ignoring gravity of one mass on the other as well, for these types of problems.
You can’t expect a test writer to explicitly put all these qualifications into every problem they wrote.
My HS physics class had pulleys that could be moved by the difference in weight of 2-3" of thread. They were plastic, and rotated on a polished metal shaft, and were damn near frictionless.
So, I think the problem needs to explicitly state whether the string is massless and the pulleys frictionless or not.
The question is unanswerable. A slightly different question would be answerable, and I suspect this is how the error in question writing was made.
If the masses were different and one were interested in calculating their accelerations, then the phrases “a light piece of string” and “easily moved up and down” are meaningful and actionable. They imply that “mass of string” is much smaller than “difference in the test masses” and that “static friction in pulley” is much smaller than “difference in gravitational force on the test masses”. These conditions let you calculate what happens regardless of the details of the small quantities.
The question writer mistakenly assumed that this holds for any values for the test masses. However, when the test masses are equal, the behavior of the system is governed by the relative sizes of “mass of string” and “static friction in pulley”. These are no longer small(*) quantities. They are the only relevant quantities. The behavior of the system is entirely driven by the comparison “mass of string” less than / greater than “static friction in pulley”.
To say it more directly: “light string” and “easily moved” cannot be taken here to imply “massless” and “frictionless”. That’s only valid if “difference in test masses” is non-zero and dominates the behavior.
I suspect the question writer wants “B”, and that is a possible outcome given a low-friction pulley and low-mass string. But “D” is also a possible outcome, and one cannot choose which happens without knowing more.(**)
(*) “Small” always implies “small in relation to something larger and more important”. Here, there is nothing larger or more important, so these quantities aren’t small. In fact, the small quantity here is the different in the test masses, which we are taking as zero.
(**) A rebuttal of “Oh, just assume its all frictionless and massless” suggests that the problem is just a riddle rather than a question about physics. If they wanted a mathematically idealized answer, they should have given a mathematically idealized statement of the problem. Otherwise, they should not design a problem where the bulk physical behavior is governed by aspects that are typically safe to approximate away.
There’s no such thing as “not enough force to overcome inertia”. Inertia isn’t something to be overcome. If you put a large force on a small mass, the mass will accelerate. If you put a small force on a large mass, the mass will still accelerate. The acceleration will be lower, but it will be nonzero, and even small accelerations tend to have large effects, given enough time.
What you need to be comparing, as others have said, is the weight of the string to the friction in the pulley. Which one is bigger? The problem doesn’t give us enough information to say. All it says about both is that they’re both “small”. If they had specified a typical string and a low-friction pulley, then the answer is D. If they had specified a lightweight string and a typical pulley, then the answer is B. If they specify both that the string is light and the pulley is low-friction, then we can’t tell.
Thanks for your answers. The official answer was B. As an experienced sitter of physics exams, that would have been my answer too. However…
To give some context, this is an optional voluntary national exam. The children taking it have not studied most of the material covered by the exam at all. The first time my 11 yr old had seen a problem of this nature was on the exam, and the same would have been true of the others. The children would not have known there was some particular principle that the examiner was seeking to demonstrate. They were answering based purely on their ability to figure stuff out.
My son answered D. I asked him why and he said obviously the two masses are the same so that won’t make either side go down, but the weight of the string is now greater on one side, so it will go down on that side. So he got punished for knowing the physics and being meticulous.
I struggle to see any reasonable basis upon which his answer was wrong*. It’s only wrong in one of two ways. One can take the **Malacandra **approach and conclude that probably light string isn’t going to provide enough mass to overcome pulley friction (which involves assumptions that the examinees shouldn’t have to make). Or one can take the “convention” approach and say that the “convention” in physics problems is to ignore minor variables. In which case the problem is in signficant part testing “exam convention” knowledge and not physics ability. Which I doubt was the examinor’s intent (and IMHO should certainly not have been the examinor’s intent).
It’s a piss poor problem. **Pasta’s **second last paragraph I agree with. It’s a riddle, not a question about physics. And the problem could have been rectified so easily by just saying “ignore the mass of the string”. I would be more forgiving if the question was one set by some local schoolteacher but this was set at a national level by people who I think one has a right to expect to have a frickin’ clue.
*It may not be right (because on one view B is right) but I struggle to see his answer as wrong.
FWIW, in every kinematics class I’ve ever taken, the words “light string” meant “massless”, however, we were explicitly told this (both by the book and the instructors). I think it’s a poor choice of words for somebody not already told that it’s magic-problem-speak. (We never used “easily moved up and down” though, they always just said “massless, frictionless pulley”)
I don’t think we can assume frictionless pulleys. If the pulleys were truly frictionless, then the system would be inherently unstable. Any imbalance, however small, would result in one of the weights falling. The fact that the weights balanced in the beginning necessitates some friction in the system.
Well said.
And ‘kudos’ to your kid for being smart enough to know that there could be another answer. 
Which actually didn’t even occur to yours truly. Shows you how much I know. :smack:
I also think that Blaster Masters last post was an excellent explanation of why the answer is B.
You guys should build it IRL and see what happens. :thumbup: