Handwritten decay chain of U-238

It’s interesting and illuminating to get the data and make one’s own sketch.  I annotated each link with the half-life and the nature and energy of the particles emitted (yes, let’s be quantum-mechanical and call gamma ray photons as particles). The end of the chain wouldn’t fit on one page, so there’s a second page, on which I scribbled information on a number of radionuclides. The featured image has, of course, nothing to do with radioactivity other than showing something in the natural world, but it’s interesting. Hippos are a real hazard to people who live near them!


Second page:

Rapid electrical discharge experiment

17 November 2020.  We ran an experiment in the middle-school science lab today.  We discharged a big electrical capacitor through a tiny wire.  The energy deposited in the wire obliterated it.  We went way beyond the “Gee! Wow!” aspect of the experiment.  We use lots of physics and math in analyzing the results.  We use equipment uncommon in school labs for setting up the experiment and measuring the voltages.  We also used a high-speed video camera to catch the demise of the wire in action.  This revealed interesting details, including the huge power and huge current coming out the capacitor.

The write-up with lots of images is here:

Learning from a demonstration of an electrical spark vaporizing a bit of copper wire

Fun learning chemical kinetics

Our students in grades 4-7 at the Las Cruces Academy, our non-profit private school, enjoyed tracking the decolorization of phenolphtalein by hydroxide ion.  Phenolphthalein is that beautiful rose-pink indicator dye used in acid-base titrations.  It changes structure a bit in base but then slowly undergoes a permanent decolorization.  The kinetics (rate and order of reaction) are interesting and fun to follow.  A write-up from the 2018-19 school year is here.

Falling skydiver

A skydiver jumps from a plane. How fast is he or she going at any time? There is a fairly simple expression for the drag on a body falling in air (“body” as a generic in the physics sense, not meaning “dead body!”). One can insert it into a simple differential equation that is “straightforward” to solve by separation of variables; along the way, I prove some useful relations. I also show how far off is the prediction of a simpler form often given for its simpler math.

Model rocketry – equations and tests

Sort of a one-stop-shop for model rocketry theory, experiments, and data analysis for a high-school class, or an advanced middle-school class such as we have at the Las Cruces Academy:

Tsiolkovsky derived the equation for the final speed of a rocket in free space (no air drag) in 1903!  I have a derivation here, plus an elaboration that goes on to consider air drag and gravity for a surface launch, and another one that looks at how a rocket has to be designed with propellant, payload, and basic infrastructure (the shell, we may say).

Our students at the Las Cruces Academy did rocket launches in the desert, measuring the altitude achieved with geometric measurements.

Some pictures are useful.  Check out the link on the LCA News and Events page.

The results for altitude vs. rocket motor impulse are summarized in a spreadsheet.  Altitude looks to be linear in impulse, in line with numerical simulations I performed.  We had to be very careful with our measurements, btw, since small errors lead to big errors in altitude.

A sideline: where does the kinetic energy go, partitioned between exhaust gases and the rocket?  At burnout for a serious rocket, there’s more in the gases than in the payload that’s left.