Copasetic Flow

Lab Book 2014_05_16     Hamilton Carter Summary There's a minor setback.  The fiberglass Dewar has a leak.  On the theory side of things, the relativistic range equation is shown to be proper x velocity times the rapidity of the y component of velocity divided by the acceleration due to gravity which is about what you'd expect it to look like if you first looked at the classical result and then squinted.  Work is being done to determine what, if anything, to make of the result.  Notes and a brief Mathematica file are included. Leak testing the fiberglass Dewar today.  I’m also looking through the second Tehran paper . There is a leak at the Teflon joint that is away from the Dewar.  It’s a rather small leak that can’t be detected using the roughing pump gauge. I've very slightly opened the Dewar valve and begun pumping on the large volume.  After about five minutes, the vacuum was back down to 3 * 10^-1. ...

Lab Book 2014_05_15     Hamilton Carter Summary Almost the entire day was spent finally actually using the leak detector!  The new stopcock was attached to the glass helium Dewar early this morning.  After that, I attended a theory meeting.  After cleaning and vacuum greasing a few fittings we found out that the glass liquid helium Dewar is leak tight!!!  The next step, glass Dewar-wise, will be to modify the table that it sits in so that it can be placed between the poles of the electromagnet.   I did some more thinking about the relativistic trajectory problem and found some possilbe symmetries in Shahin's expression for the y vs. x.  Both the expressions for hang time and the maximum range equations are interesting. Hang time is interesting because it's actually the same for the relativistic and classical cases.  Range is interesting because the expression involves the vertical component of the projectiles rapidity. ...

Think everything that's publishable for say an old classical topic like projectile motions has already been published?  Turns out the old 'lob the projectile at a constant velocity in a constant gravitational field' problem is still producing.  Check out this paper from J. L. Fernandez-Chapou, A. L. Salas-Brito, and C. A. Vargas published in 2004.  It eventually made its way into the American Journal of Physics.  In the paper, the authors show that if you write down the trajectory of a projectile in terms of its launch angle and then solve for the x and y position when the projectile has reached it's maximum height, the solutions will trace out a nice little ellipse like the figure below excerpted from the arxiv version. References: 1.  Elliptic envelope of parabolic trajectories paper http://arxiv.org/abs/physics/0402020v1 1.a.  AJP version of the paper http://scitation.aip.org/content/aapt/journal/ajp/72/8/10.1119/1.1688786