» What is that, a hup? ConvergeDiverge

What is that, a hup?

Today in non-major, algebra-based physics we went over the fairly classic problem of determining which will win a race down a hill, a sliding block or a hoop, cylinder, or solid sphere? I like working through this problem because it’s a great way to show students the value of not plugging in numbers too early, but rather let the equations play out so that you whittle the problem down into what really affects the difference in answers between all the options. It’s also a nice example of thinking about a distribution of initial energy; in this case, the object will go slower when some of its potential energy gets converted into rotational kinetic energy. The object that has the least amount of energy going into rotation (or none, in the case of the sliding block) will have the most available to go into its translational kinetic energy. And that will be determined by the objects’ moments of inertia.

Everything was proceeding like it has in years past when I’ve taught this section, but then a question came up: should we account for friction? One student in particular noted that he thought that there had to be friction present in the rolling objects’ case, even if you said the sliding part was frictionless. And for the conservation of energy equation to play out, you really did need to include it.

I’ve got some ideas, but I want to ask you all – what do you think? Part of me feels that this is connected to an oddity I see in a lot of my non-majors, in that they are always wanting to think about friction, air resistance, etc. (Compare that to my physics majors, who in today’s Matlab class were very pleased to not account for air resistance in a model we coded for hitting a baseball a certain distance.) I’ve been thinking a lot about why my non-major students are so attached to the ideas of friction and drag. In class we talk a lot about setting up models, adding in additional factors as we get more and more specific with the model. But this year’s class especially isn’t happy with the discussion. They ask, “if we live in a world with friction, why would we even bother to ignore it?” I was talking with a colleague in the health sciences, and he said that the students (many of them the same ones I have in my class) ask essentially the same thing for some models he talks about. So at the very least, their questions like this aren’t limited to physics.

But to get back to the original question, do we need to include rolling friction in the analysis of which rotating object will go down the ramp the fastest?

*”hup” is how my college physics professor pronounced “hoop” when we covered this. He said, memorably, “what is that, a hup?” and I almost always dissolve into giggles thinking about it even now. I guess you had to be there.

[Image Creative Commons licensed / Flickr user phonogalerie.com]

http://dawes.wordpress.com/ Andrew Dawes

Great question… maybe the best approach is to follow that tangent: ask them what would cause the friction to increase and then make two hoops with different surfaces. Wrap sandpaper around one for instance. Then do the experiment again with new predictions. Sure friction plays a part but they need to isolate that variable and show that it isn’t as large an effect as the moment of inertia is.

For every question there is an experiment
Rob Knop

The answer is : if you want to just think about energy, then no. Friction would be a dissipative force, but static friction is dissipating no energy. If you want to think about the dynamics and do F=ma, then, yeah, you have to include friction. The static friction force on the rolling thingies is what gives you a net force lower than the sliding net force, so it’s gotta be there. It’s also friction that gives you the torque that gets the rolling thingies rotating.

The scary thing is when you think about the work (or, rather, the k-work, as Thomas Moore in his “Six Ideas” would call it, which I think is a good idea) done by static friction. At first blush, it seems obvious that static friction is doing negative k-work on the object… but that would then seem to make it have *less* energy at the bottom than it really does. The answer is what you had in twitter: static friction doesn’t do work because there’s no relative motion between the two surfaces for which there is static friction. It’s kind of annoying, as it breaks down a bit the model we use of “consider extended objects as particles”, and it makes things more subtle, but that is ultimately what’s going on. Kinetic friction would dissipate energy, but again to figure out the amount of k-work done, you’d have to use the dr or dr/dt of the surface that was moving relative to the other surface.
Allen Newton

I think that concepts like friction and air resistance come up so frequently because they are tangible concepts. Students can feel them, and they intuitively understand what sort of effect they will have (or at least they think that they do). They work from that which they understand.
drmagoo

It depends – static friction, I wouldn’t include (I talk to my students about how the static friction is what turns the U_g into K_rot, not just K_trans), but rolling friction (which is another beast entirely) can matter. Maybe roll a heavy ball down a board and a board lined with foam as an example.