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...

[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.

[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.

[inahandbasket]

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

[xoder.livejournal.com]

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

[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.

[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.

[inahandbasket]

I did. hah!

[calzephyr77.livejournal.com]

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

[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]

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.)

[littlez-star.livejournal.com]

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

[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?

[chipuni.livejournal.com]

For a (hypothetical) fourth question...

May I fill box 1 with hydrogen gas? Pleeeeeease?

[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. ;)

[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.

[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.

[sirroxton.livejournal.com]

Teaching is hard.

Most textbooks are terrible. Authors accumulate a lot of knowledge over a lifetime, and then think, "Oh, if only it had been broken down for me *this* way, it would have been easy to understand." But the way people learn doesn't map well to these after-the-fact hierarchical breakdowns.

So it's always heartening to see examples like this, with teachers really digging at those fundamental, hard-to-articulate questions of how people think and how to convey new ways of making meaning to those who haven't internalized those ways. (It's easy to teach students who already know a lot of the critical ways of learning things; that's the teaching equivalent of grunt work.) Keep digging, and cheers. :)

[zandperl.livejournal.com]

Thank you. I swear teaching is as much sociology/psychology as whatever subject you're teaching.

Edit:
Regarding how authors choose to present material to students, for me personally the issue is that I've always had an easy time of learning physics, while I watched my classmates struggle with it, so I've spent much of my physics career trying to figure out how what's going on in my head differs from what's going on in their heads. My default is to present material how I learned it, but I know that it won't work for the majority of students, so I have to keep trying to figure out other things to attempt.

[kelsin.livejournal.com]

Having taken physics I think the problem was stated fine. I understood it perfectly. It did take me a second to think of the answers but I got them all right after about 10 seconds of thought on each. I just made myself think of the forces, and in all cases you have a downward force on box 1 and nothing on box two (since gravity on it doesn't do anything since it's perpendicular to the box and there is no friction.

Obviously like you're saying above, even if there was friction the answer would still likely be A for all situations, but when you simplify it (as in the problem) you don't even have to worry about the weights.

So free body diagram ftw?

[zandperl.livejournal.com]

The students in question were capable to doing FBDs, but couldn't get past their intuition that the objects shouldn't move. When your intuition says something so strongly, you make bad assumptions and can't get any further - they probably wrote things like σF=0 when attempting to do the math, for example.

[catalyst37.livejournal.com]

Well it is an easy question. You would think that on a frictionless surface you would have any force cause box two to move. You should let your students think of it in realistic terms instead of abstract or mathematical if they can not fully grasp them. You should also try and get them to break down the whole question into a couple smaller ones then try to connect them. I am a firm believer that most students who do poorly in any subject is merely laziness in thought. If they can not figure out the question immediately or at least have the logical path of figuring it out they do not try to THINK it through, instead they cut the loss of marks and move on to the next. I know this because I once thought like this, so hopefully this gives you some insight into how your weaker students think. They need to know that this is in most cases the reason for not completing a question and once they know or realize that subconscious process they can correct it.

I hope this helps
Alexzander

[sirroxton.livejournal.com]

I think part of the problem might be that this setup just doesn't make sense in a physical context to someone who doesn't understand friction.

We look at this diagram, and we have an intuition about it. But our intuition has everything to do with friction, and we don't understand anything about friction in mathematical terms -- it's a frustrating bit of voodoo. Personally, I remember having a serious eureka moment when I learned about the distinction between static and kinetic friction.

Usually when teachers present something intuitive, it's supposed to be a springboard to understanding a general concept. In this case, the intuition is just confusing.

embarrassing

[michimusic.livejournal.com]

I wasn't thinking about friction, and I answered "C" on the last one. Even more embarrassing - I have a minor in physics. Intuition sucks. Guess it's good I have a day job.