I’ve been producing a series of video story problems for a few weeks now, and up until recently I’ve been sticking mostly to math problems. I suppose it could be that there just happens to be a plethora of really awesome math problems that I encounter everyday, but more likely it’s that my brain can’t seem to shut off the spigot of curiosity every time I see a bunch of numbers. I’ve been reluctant to post science videos though, due to my conceptual nature of scientific understanding (graduated with a science minor for elementary education). The big bad secondary teachers give me dirty looks whenever I try to talk physics without the calculus or chat about chemistry and mention how I managed to destroy no fewer than 3 crucibles during a particularly potent lab activity.
Regardless of how secure I feel in my scientific understanding and knowledge, what’s really important as an educator is to be able to help facilitate honest discussion surrounding a difficult concept, and admit when you may or may not be wrong. The worst thing that could happen is some lost instructional time while you figure out what went wrong. I know that I could be vilified by many for saying such a thing, but highly intelligent engineers and scientists make mistakes all the time, all over the world, and it costs their employers a pretty penny (or bodily harm) to figure those problems and mistakes out.
What is it then, that I’m beating around the bush about? It’s my latest video story problem, involving friction and momentum, and I really think it needs a lot of work with the aid of some brains much bigger than mine (I’m putting out an SOS to @falconphysics). Give it a look, and please, tell me what’s wrong, and what’s right from a conceptual standpoint, because the numbers on this one aren’t so much important for the time being.
P.S. My daughter was really excited to help make this video!
OK, I’ll bite, and I’ll try not be gentle, but I am a big bad secondary teacher. First off, before I get all nit picky, I want to say this is a great question and it gave exactly the opposite result I was expecting!
I think this one may be more about Inertia than momentum (often confused with each other). Newton defined momentum as the “quantity of motion” an object has. It can be calculated by multiplying velocity by mass. Inertia is the property of matter that tells us how difficult it is to change the velocity of an object. More mass means more inertia. (i.e. objects at rest tend to remain at rest and objects in motion tend to stay in motion…). I think this is a better inertia idea than a momentum idea as inertia deals with how forces can cause an object to slow down (or speed up for that matter)
This is a bit of a complicated problem. In a perfect world (no friction) velocity down the hill would actually be the same. I’m not sure if it is in your problem, but velocity for each run are probably pretty close. The more massive car has more inertia and so seems like it should go further (which is actually what I expected to happen). However, heavier objects have greater frictional forces (slight simplification here). So it looks like the friction was a more important factor in this experiment than inertia.
Now, where is the friction acting? We use wheels to minimize friction with the track. So the friction is probably all in the rubbing of the axles.
One last bit, please do me the favor of not asking, “Which one wins, Inertia or Friction?” As this would seem to imply that inertia is a force that opposes friction. Inertia is not actually a force. Students always want it to be as they think there must be a force that keeps the object moving. Inertia tells us we don’t need a force to keep something moving. the force is what makes it speed up or slow down.
OK, I’ve rambled enough. Feel free to let me know if my explanation wasn’t clear enough.
First of all Steve, a HUGE thank you for responding to my SOS. It’s a very vulnerable and nail-biting position I put myself in when I post things like this, especially outside of my professionally trained area of expertise. To be fair, I do have a pretty good grasp on Newton’s laws, and scored pretty well on my certification tests for science at the elementary and middle school level, but you totally nailed everything that I thought was wrong with this.
And that’s totally awesome! Because if I want my instructional practice to get better, I have to walk the walk, and put myself out there for possible failure. Thankfully, I’ve got a great network of people like yourself that are there to help me readjust, rather then just make me feel stupid (which isn’t difficult to do).
Now enough fluff, and to your actual critique. I had a feeling that momentum was wrong, and I’m glad you pointed out that inertia is really what I wanted. I’ve already adjusted the title on the post, and will render the movie again with an updated title.
I was just as surprised about the outcome as you were, which is why I made the video. My daughter and I were playing with the trains when I noticed what was happening; I was compelled to capture it and take the moment of curiosity back into someone’s classroom. My best guess was that the extra weight on the poorly lubricated axles is what caused the extra friction, but I wouldn’t have had the expertise to be able to escape framing the problem as friction versus inertia, so I’m glad that you pointed that out.
And I’ll certainly take your advice on not asking the wrong question; I’ve been pointedly trying to stay away from the more simplistic questions for two reasons; one that I don’t trap myself in asking a fundamentally flawed question as you pointed out, also to get some more open ended responses.
As a former “big bad” physics teacher myself, I too appreciate you putting this question out there to wrestle w/. Always fun to see a difference between what you expect & what happens!
I’m in agreement w/everything in the comments above- now, I’m most curious about one thing: what’s the investigation that helps to explore the relationship further? Personally, I’m interested in “systematically” adding mass to the lighter car (maybe taping quarters to it or something) and seeing the stopping distance changes. Or perhaps changing the starting height on the hill with the same car? Lots of interesting next steps to explore…
Finally, while I did ID myself as a former secondary teacher, I personally think the concepts are more important than the math/calculus of it. And to talk about it “with” the calculus of it doesn’t mean throwing numbers into some equation- the more important part of calculus are the concepts themselves. Thanks for putting the focus where it belongs.
PS- Good blog about conceptual calculus here from the NYTimes- http://opinionator.blogs.nytimes.com/2010/04/11/change-we-can-believe-in/
I thought about doing some sort of systematic testing with progressively heavier weights, but unfortunately I was limited to the one egg container they had at the toy store 🙂
More seriously, after thinking about it, I really wanted these videos to be a conversation starter, an investigative prompt if you will. I thought that doing a series of trials would start moving it towards the realm of a full on demo or video lab, and I don’t think that would serve anyone as well as if they were to do it live in their classroom. If I were to use this in my classroom, I would definitely have a bunch of track and a few cars and weights for the students to experiment with after watching this puzzler.
I’m really glad to hear that you’re a big fan of the conceptual understanding. I think that gets underplayed as we try to focus so much attention of those honors and AP kids (I was one of those), that may very well end up never using the advanced math once graduating from high school (again, me).
And thanks for the blog suggestion, I’m definitely going to be digesting it!
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