Help me understand a misconception....

[asterroc]

An interesting situation came up in my Physics class today, where two of my students surprised me with a question they asked. To try and understand their thinking so I can teach the content better, I'd like to ask that everyone take a look at the below situation and tell me what you think will happen. I don't care if you know any physics or if you're a professional ear-wax taster, I want to know what you think and why.

In the picture below, Box 1 (m₁) is hanging from a string that passes over a pulley. There's no friction in the pulley, and the pulley has no mass, so it can spin freely. The string is then connected to Box 2 (m₂) sitting on a table. For simplicity, let's assume there's no friction on the table - there's some lubrication between the box and the table.



[Poll #1162218]

X-posted a couple places.

Comments

[dlakelan.livejournal.com]

what do the students think? please don't say they think the hanging one moves up...

[inahandbasket]

oops, failed to see your "assume no friction."
Change all my answers to A.

[calzephyr77.livejournal.com]

I'm scared to answer because I didn't take high school physics, but I'll give it a shot :-)

[xoder.livejournal.com]

You can fix your own answers, if you haven't already.

[littlez-star.livejournal.com]

I liked this questionnaire, and I'm very curious about the right answers. Will you post them up?

[chipuni.livejournal.com]

For a (hypothetical) fourth question...

May I fill box 1 with hydrogen gas? Pleeeeeease?

[ka3ytl.livejournal.com]

but you're the specific type of person that he wants to have answer :) Even better if you get the wrong answer and show your reasoning. *grins*

It doesn't really help that much for all of us to get the right answers with the right reasoning *grins*

[zandperl.livejournal.com]

Hah! The correct answer is A for all.

I only gave the third situation to my class, they were to find the value of the acceleration, and two students said to me either during class or after "shouldn't the system not move since m2>m1 ?" I was surprised in both cases considering the particular students, so I wanted to see how widespread the misconception was, as well as what caused it.

[zandperl.livejournal.com]

If there were friction, it would actually depend upon how strong the friction were compared to the masses, so you'd have to answer D for all.

[zandperl.livejournal.com]

Thanks for being a good sport! The other person is right, I'm looking for people without degrees in physics to help me figure out my students' reasoning. In case you didn't check what others, said your guess of C on the third situation is what many people say, including those two physics students, and it's exactly the misconception I am trying to understand.

You did a great job explaining your reasoning in that third one. In the real world where there is friction between Box 2 and the table, chances are you'd be right, that Box 1 wouldn't be heavy enough to drag Box 2 along with it. In the ideal frictionless world this problem assumed, this situation would be the same as if you put two boxes on an icy surface with a rope between them, and pulled on just the first box. If the surface is slippery enough, then the second box would get pulled along too.

(FWIW, this comparison was suggested by someone in physics.)

[zandperl.livejournal.com]

Exactly! Thanks for the encouragement. :)

[zandperl.livejournal.com]

A for all.

As explained by moosehead_beer here,

"What we really have here is two blocks which, for all we care, could be floating freely in space, and we have a force acting on one of them, resulting in a tension in the string."

A more detailed explanation would require a Free Body Diagram and further knowledge of Forces - want that too?

[rosefox]

and pulled on just the first box

I think people are missing the "pulled on" part. I don't get any sense, from the way that you phrased the question, that Box 1 is in motion.

[sethrates.livejournal.com]

I'll need to reserve judgment until I've run 50 billion monte carlo simulations on computers distributed throughout the world, and had all of them fail because of coding errors.

[rosefox]

I really, really hate "ideal world" puzzles, and this sort of thing is exactly why.

[gemini6ice.livejournal.com]

Ooh, good point. Well, the friction would depend (linearly?) on the weight of box 2, right, so if friction enters the picture, there would definitely be SOME ratio of heavy/light between the boxes that would ensure movement. So if we say "2 is heavy and 1 is light," we can assume that they are SUFFICIENTLY heavy and light to overcome the friction. So I claim we would get A for the first. But still D for the second and third.

[gemini6ice.livejournal.com]

gravity acts on it...? Without gravity, there's no sense of heavy/light

[zandperl.livejournal.com]

Depends on whether you're planning to set it on fire, and how far away you're standing when you do it. ;)

[zandperl.livejournal.com]

Heh. I think the actual situation I have my students *did* have friction, and Box 2 was more massive than Box 1, and it *still* moved. It depends on how much friction there is compared to how big m1 is.

[q10.livejournal.com]

i think they're probably overgeneralizing from the case where the pulley is right above the boxes, Box 2 is resting on a surface, and the Box 1 is dangling from a rope draped over the pulley. in this case (if i remember how these things work - which is a big if) Box 2 can't move down (because it's supported) and so long as Box 1 is lighter it won't pull enough to lift Box 2.

[zandperl.livejournal.com]

The "pulled on" is gravity. The question is whether they *should* be in motion or not.

[rosefox]

Right, I get that, but I don't think it's obvious because the puzzle is a mix of things that are stated very clearly ("there is no friction between the table and the second box") and things that are put in very vague terms ("heavy" and "light"), and it's really hard to tell what unstated things to assume unless you've seen lots of puzzles like this before. I might as well assume that box 2 and the table are both magnetized and strongly attracted to each other, or that gravitational attraction goes up rather than down, or... whatever I want, really.

[zandperl.livejournal.com]

Well, the friction would depend (linearly?) on the weight of box 2, right,

Right.

So I claim we would get A for the first.

Not necessarily, if there's a LOT of friction and m1 (hanging) is only a smidge heavier than m2 (table).

FWIW, the specific situation I gave my students had Box 2 (table) heavier than Box 1 (hanging), *with* friction, and yes they moved (at around 1/3 of g, even). I don't have the numbers on me right now.

[rosefox]

If it were going to be in motion, it would already be in motion; there would not exist this state where I could examine it while it was still. Therefore, if it's not moving, it won't move. I just assume that there's other information I don't have that would explain why it's not moving.

I can shift my brain around to think about this the way you're thinking about it, but it's not a way of thinking that comes naturally to me at all.

[ka3ytl.livejournal.com]

gotta love those field forces *grins*

but yeah, that is something that is non-obvious that the reader is expected/presumed to know,

And throwing the pulley in throws people off.

I mean if the question was, A force is applied to box 1 so that it accelerates at a rate of 9.81m/s^2, what happens to box 2 in the following scenarios: ex1 ex2 ex3

most people wouldn't get it wrong.