LHC energy and momentum

Problem: The LHC delivers 8 TeV per particle in bunches of 10¹¹ particles. What is the kinetic energy and momentum of a bunch, in SI units and then as compared to (a) a small-caliber bullet and (b) a Major-League baseball pitch?

I get that the bunch has far more kinetic energy than either a bullet or a baseball pitch, but far less momentum. A LHC particle bunch would burn you badly, but it wouldn't knock you down! Of course there are some 10⁹ bunches per second, so you don't want to be hanging out in the beam line when it's running.

Stokes vs ram pressure

Macroscopically, air resistance is ram pressure (proportional to cross-sectional area times velocity squared). Microscopically, drag is Stokes-like (proportional to radius times velocity). Where does the cross-over happen? I didn't have the guts to put that on problem set one of my course for pre-health students, but it will be in around problem set eight. It could be on problem set one, because the transition can be obtained purely by dimensional analysis.

In transport processes, there are often qualitatively different effects working at small scales than at large. Another good example is diffusion vs convection.

dimensions and symmetry

In class, I spend a lot of time on the dimensions of physical quantities. If the left-hand side of an equation is an energy, then the right-hand side must be also. Or if the left-hand side is a quantity measured in J, then the right-hand side must be also. Is it right to call this property a symmetry of physical law? It acts very much like a symmetry, because it selects out of all the things you might write down a very small fraction that could conceivably be physical laws or physical results. On the other hand, these issues are so fundamental, they almost transcend that.

teaching physics teachers

I took a break from my no-teaching, all-research sabbatical to make a guest appearance this week in Jhumki Basu's course Recent Advances in Physics in NYU's education program. Her students are building new science units with help and ideas from current researchers. I presented not really my research, but some of my research techniques: estimation and approximation. No surprise there!

I showed on dimensional grounds that cars like the ones we currently drive will never do far better than 30 miles per gallon. 100 maybe. But never 1000. A nice result, with important implications, using only techniques that a high schooler could easily muster.

After I spoke, we discussed, and it was noted by one and all that despite the simplicity of the techniques, in fact estimation and approximation techniques are non-trivial and sophisticated. It is hard to incorporate them incrementally into the existing New York State middle- and high-school curricula. On the other hand, it is my (perhaps optimistic and/or utopian) view that if these things were the focus of quantitative education from day one, they would be easy to have mastered by the end of high school. Of course the teachers I was talking to are going into the system that exists; they can't start from scratch!

Many other interesting things came up, which I hope to blog about at some pont in the future, including students' lack of contact with machinery and hardware and electronics, and the idea (that I hold, but others don't) that education ought to give students skills and tools, rather than knowledge.

cars and energy

I worked out a page of dimensional analysis and order-of-magnitude estimation to compare automobile energy expenditure in the form of acceleration with energy expenditure in the form of battling air resistance (ram pressure). After putting it together I realized the obvious: The air resistance losses exceed the acceleration/braking losses when the journey is long enough that the car has swept up its own mass of air! This means that for typical US cars, acceleration/braking dominates for journeys much less than 1 km (or city journeys in which there are stops much more frequently than once every km), and battling air resistance dominates for journeys that are uninterrupted by stops for distances much longer than 1 km.