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

[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.)

[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.

[gemini6ice.livejournal.com]

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

[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]

The specific situation I gave my students had numbers. I didn't want to confuse readers by making them think that they needed to do math here. If it would help, I think I had around 4.5kg for hanging Box 1, and 8.3kg for Box 2 on the table.

Magnetism is a different course so would not be discussed here.

[rosefox]

Unless you give us the phrasing you gave your students, I can't see how our feedback can possibly be useful to you.

[zandperl.livejournal.com]

What I gave to my students was the picture with numbers on it, and words said aloud that I cannot recall verbatim but were similar to what I said. Since this is a text medium, I am not capable of giving the exact format I gave to my students.

What I am expecting from my readers here is that they internalized the situation from the text and picture, much like my students internalized the situation from the audio and picture, and then applied their own preconceived notions in the process of analyzing it, and spit out an answer. I'm trying to understand the process by which people internalize the situation, and the preconceived notions in their heads. You've already shown me that the exact format (wording, sequence, etc.) in which I present the material can make a difference for some people, which I wasn't consciously aware of.

[zandperl.livejournal.com]

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

[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.

[zandperl.livejournal.com]

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.

I'm not saying it is still at the instant this picture was drawn - think of it as stop-motion photography. Or if you do want to call it still, say that I just set up the boxes and just this instant let go of them and snapped the photo.

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.

Yeah, I know my students have issues with that too. How do you make that shift in your brain, and what can I, as a prof, do to encourage it? By now my brain is just stuck in that mode so I'm not clear how it got there or if it was always that way.

[rosefox]

How do you make that shift in your brain, and what can I, as a prof, do to encourage it?

I don't go for "What's most likely to be right?"; I go for "Which answer that looks wrong is most likely to be the one the teacher thinks is right?". In other words, my way of solving this has very little to do with physics, and much more to do with having taken a great many exams in various subjects.

The big problem with teaching to the test, or teaching with tests, is that it mostly teaches people how to take tests. I don't think that's actually something to encourage, except insofar as it seems to be necessary for academic success these days. I think that rather than asking "How can I get my students to understand situations that are not real-world situations?" or "How can I get my students to anticipate my meaning when I give them instructions that are presented in the way that makes the most sense to me?", you should be asking "How can I create real-world problems for my students?" and "How can I create problems that don't rely on either presenting instructions a certain way or my students getting used to me presenting them my way?".

[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.

[meleah.livejournal.com]

..and FWIW, as someone with degrees in science who has nonetheless never taken any physics at all (not even high school), I think I got the right answer for 3 with the wrong reasoning - I misread the question, as is obvious when you view my response. Had I read the question right, I would have answered 'stationary', which is incorrect.

I didn't understand that 'frictionless' made the difference.