What if one mass was a KG of feathers and the other mass was a KG of depleted uranium?
And do they ever use “slugs” as a unit of mass anymore?
Ugh. I noticed my poor choice of wording (static friction rather than inertia) after I posted but figured it wasn’t worth correcting.
Anywho, the conundrum is: when you can answer in two different ways, which do you choose: book smarts or street smarts? Which answer is “more” correct, a practical one or a theoretical one?
I would answer B, but the question is ambiguous, and the OP’s son’s answer deserves credit.
Here’s why I’d answer B. The problem is, we can’t answer the question with the information provided, because we don’t know whether the weight of the extra string exceeds the static friction of the pulley. So, we have to make assumptions.
massless string, ideal pulley: Answer is B
massless string, pulley has resistance: Answer is B
massy string, ideal pulley: Answer is D
massy string, pulley has resistance: Depends on values that aren’t given.
Clearly, the 4th option above isn’t intended, because there’s not enough information. So the question is, which of the other three are intended?
IMHO, the first option is simplest. Furthermore, the clue “light string” tends to imply massless string (albeit weakly), meaning first or second options (or else 4th option, already ruled out).
I’d hate to ask an 11-year-old to make that kind of analysys, though. Given that, both B and D are reasonable answers.
Admittedly, it’s hard to ask the question well without using “massless” and “frictionless”. The best way would be to say “Ignore the weight of the string.” They tried to do this by saying “a light string” but IMHO that’s not quite good enough. (That was why I picked B first, though.)
I’m not impressed that they used “light” and “easily moved” to try to clarify that the mass of the string is negligible but the friction of the pulley is not. I also dislike questions where, as you add knowledge, you get different answers. Alas, life is like that, and so are tests (as someone mentioned above, regarding the civial war). I think they could have done better in this case, but there will always be borderline questions where a more thorough analysis can result in the answer that’s not intended.
Huh?
If you’re ignoring both string mass and pulley friction, and the weights are exactly identical, it’s in equilibrium. What’s wrong about that?
I have to say I’ve worked through plenty of mechanics problems which did indeed assume that the string had zero mass and the pulley was frictionless - the only areas of interest were the various moments and tensions exerted by the masses on the levers and strings they were attached to.
Ignoring the string mass means assuming that the weight of the string is small compared to the difference in weight of the masses or to the friction in the pulley, whichever is larger. Ignoring the friction in the pulley means that it’s small compared to either the weight of the string or to the difference in weight of the masses, whichever is larger. We’re explicitly told that the difference in weight of the masses is zero, so that can’t be the larger one. So ignoring both the weight of the string and the friction means each must be smaller than the other.
An important distinction in this thread, by the way: There’s a difference between “correct answer to a test question” and “answer which will (or is most likely to) get marked as full points on the test”. The latter probably is B, in this case, but that’s still not the correct answer. The correct answer is “Insufficient information”, even though that’s not a multiple-choice option and is thus guaranteed not to get you any points.
Are we to assume normal air pressure and gravity? Neither were specified in the question, and if we are assuming massless string and frictionless pulleys, why not imagine other non-reality based conditions like reduced gravity or a operation in a vacuum?
The point of the post wasn’t why B is the right answer in what would happen in the real world. It was why B was the correct answer for the question asked on the test as it was written. In the post, at the end, I agree that it’s indeterminable whether B or D is what would actually occur, but based on what an 11yo would be learning and the context of the question, it’s possible to determine what the question writer was looking for, even if he failed to write a good enough question to really make it clear.
That said, the explanation given the the kid in the OP is a good one and he deserves credit, especially given that he was taking the test without that. His intuition was reasonable and did grab the concept the question writer was after. It’s the question writer’s fault, but it is what it is.
I agree that the “What was the questioner thinking?” line of reasoning is appropriate vis a vis getting the highest score on the test. I just make the (admittedly semantic) argument that that doesn’t make B the correct answer to the question asked. There is no determinable correct answer to the question asked (by my semantics), even though there is a box the student can tick to get points on the test. My impression is that the OP was primarily interested in this factual correctness rather than correctness defined as “what gets me points on this broken exam question”. Begin able to suss out the latter is, of course, an important skill in an imperfect world, and one could even define that as finding the “correct” answer, but for this discussion I think such a definition hides the key issues in question.
I think it’s pretty cool that days later a group of highly educated adults are still discussing it- and still sort of think the kid was right, even though it was the wrong answer.
How do you imagine either a vacuum or reduced gravity would alter the results?
If they’re both zero, they’re both small. They don’t both have to smaller than the other.
Are you proposing to include air pressure? So now we have to consider whether the “light string” is more or less dense than the air, to know which way it will move if the pulleys are frictionless? Maybe the masses have some unstated charge, and will attract or repel each other, and that’s what determines which way they move.
Any problem is going to have unstated assumptions.
The more I read this thread, the more I say D is actually the answer I think is “more” right. To me, saying that the string is “light” is saying that it does in fact have some mass, that cannot or should not be ignored in all cases. Maybe in some cases you could argue that “light” means to ignore it, but you can’t make that argument for every case. Basically, the question explicitly defines that the string is not massless. Light means that it does have some mass (you do not describe a massless/weightless object as light, ever, light implies some mass), which makes D the best answer, unless you assume that the friction in the pulley is greater than the extra mass of the “light” string on the longer side, which is an extra assumption that is not explicitly stated in the question.
Basically my argument is thus:
- The string is stated explicitly to be light. This, by definition, implies some mass.
- The system is said to “move easily” which may or may not imply some friction. The pulley could be frictionless under this description.
- The masses are stated to be identical.
Therefore, the best answer is D, because it matches the information given in the problem best. The answer could be B but I think it’s “less” correct than D.
This demonstrates a lack of understanding of the way physics problems are set up. When we say “Assume a massless string”, we don’t mean a string that has a mass of literally zero, since that’s impossible, and does not correspond in any way to the real world (and physics, like any science, must always seek to describe the real world). What we actually mean is “Assume that the mass of the string is so small compared to other relevant quantities that its precise value doesn’t matter”.
So what’s being tested- knowledge of how physics problems are set up?
“Massless” means “has mass” is not intuitive in any way.
I would like to point out that Chronos, while a far more learned and adept physicist than me, does not speak for all of us.
To this physics guy, “assume a massless string” means exactly what it says. All models in physics are just models, some are better than others, and we often (always?) assume impossible things like massless strings, in order to get results. The less impossible stuff we assume, the better, but sometimes (always?) you have to work with assuming impossible stuff.
I would never read “assume a massless string” to mean “the string actually has mass that you might consider in certain situations” or whatever Chronos is implying.
I’ve taken physics courses, with physics problems. I’ve never seen it described this way.
On the moon, the answer would be the same.
When I was studying mechanics, just three or four years back, that’s exactly what it did mean: neglect the force exerted by gravity on the string and the force needed to accelerate it. In every case. 