air resistance, again

I should stop complaining about air resistance, but I can't help myself! I am teaching this semester from Kibble & Berkshire, and in Chapter 3 there are problems about air resistance that use speeds of around 100 meters per second and an atmospheric drag law that is proportional to velocity to the first power. I don't think there is any physical system that could have these properties: If you are small enough to have viscosity matter, you can never go 100 meters per second. Well, I guess molecules can go that fast, but (a) that isn't what the authors have in mind, and (b) molecules aren't really well described by continuum mechanics!

sheep–sheep collisions

A very nice paper appeared on the arXiv today on sheep–sheep collisions. It makes the point, which I stressed here, that collisions involve immense forces. It also makes some realistic estimates of the physical properties of the horns and skulls of bighorn sheep. But perhaps my favorite thing about the paper is that it begins by deconstructing a laughably wrong analysis in one of the many bad textbooks.

Hooke's Law

Hooke's Law is usually described as F=−kx, and thought only to apply to idealized springs, but really Hooke's Law is that stress is proportional to strain, and it applies not just to idealized springs but to every object in the entire universe (for small distortions), for extremely fundamental reasons. What an observation Hooke made! I tried to impress this upon my class today.

blocks on planes

In class yesterday I compared two problems: the block on an inclined plane (sliding without friction) and the car sliding around an icy (frictionless), banked curve. In the latter, the challenge is to enter the banked turn at exactly the right speed that you make it out the other side without either sliding uphill or down. The nice thing about doing both these in one lecture is that they have nearly identical free-body diagrams, both of which have a massive particle acted upon by gravity and a normal force (at the same angle to the vertical if you set it all up correctly), and yet the physical situations are so different and the accelerations point in different directions. The comparison brings out a lot of conceptual material about contact forces and kinematic constraints.

The banked turn example is also hilarious, and has many nice details, such as that in general if you enter a conical banked curve and slide around to the other side without friction, you will come out with the car pointing in a strange (and non-trivial to calculate) direction.

forces and formality

Yesterday in class I worked through the problem of a bouncing ball, concentrating on estimating the magnitude of the force from the floor at bounce. Not a single student was even close to getting the magnitude of that force correct, even after many minutes of discussion, a few minutes of working in small groups, and more discussion. Eventually two students got it and understood after my demonstration in which I prepare to drop a book on a student's hands (comparing with the case in which the student is just holding the book).

Before, during, and after the class, students asked me if the class is going to be more formal soon or ever. I said yes. But what disturbs me is that if we go and do formal problems with vectors and calculus before the class can see even roughly the magnitude of the normal force on a bouncing ball, we are teaching math, not physics. I understand where the students are coming from: They like physics in part because it is formal. But there is no point in calculating forces when you don't understand what forces are.