Copasetic Flow

The factor of kinetic energy over force in the focus equations got me thinking about work integrals. The work integral also led me to think about the vertex height as a projection back on the y axis. Why? Because work is only done in the direction tangent to the force, which in this case is in the y direction. The calculation of the projection angle was a bit messy, but wound up with a clean if rather obscure result. The following is neither here nor there, and I suspect will waste more time than it's worth at the moment, so I'm just including it as extra notes to go back to later. I already know there's a Gudermannian lurking in all of this. The function for the arc length of the parabola contains one. The projection angle consisted of a tanget half angle formula which also leads back to Gudermannians, (see https://en.wikipedia.org/wiki/Tangent_half-angle_formula#The_Gudermannian_function ).

I had  lot of ups and downs in the lab yesterday.  The kids, (Jr. aged 3, and Sam aged 1), and I went out ot Bryan Hose and Gasket and picked up our new vacuum hose yesterday.  They had the hose ready and waiting for us and they had the free popcorn machine up and running, so the kids got popcorn.  So, that was cool.  The hose looked a bit small though. After taking the kids out to visit Blinn College for lunch with their physics professor mom and then returning them to daycare after their mini-adventure, I made it back into the lab.  Sure enough, the hose was too small to fit over our vacuum fitting.  It had seemed like a good idea to cut the old hose behind the fitting to get a better measurement, but I hadn't really thought about the pipe that someone had jammed into one end to permanently expand it so it would fit over the fitting.  The 'jam a pipe in' expansion technique worded fine for red rubber vacuum hosing I'm replacing because its str...

I've had an undeniable urge to write about well... nothing... this week.  I'm finally giving in.  Indulge me and in a bit, we'll get back to the normally scheduled physics programming.  This all started when I went for a brief walk around campus. First, I hit our local Wells Fargo where they serve free coffee.  As a point of reference, if you open up an account with these guys you can just walk over every morning deposit what you would have spent on coffee and walk out with a cup of coffee.  It's like Starbuck's, but you come out ahead. Next, I headed back across campus towards the library.  Someone recalled one of my books so I had to hustle and get it back before the end of the week when the overdue fines begin to accumulate.  Walking past the engineering technology building, I noticed that PAID was getting ready for their weekly luncheon.  PAID is the professional association for industrial distribution.  What's industrial distribution...

From [1] I'm reading up on a recent expeirment that used a neutron/gravity spectrometer to look for evidence of dark matter and dark energy.  I haven't got to review enough material to say something truly pithy here yet, but I thought I'd point you towards the stuff that's available.  First, here's a discussion of the experiment [1] from Texas A&M's own Dr. Schleich.  He's talked about this kind of thing before, (using neutrons for experiments involving gravity).  In fact, a little more than a year ago he gave a talk here on the KC interferometer  and how it measured the acceleration due to gravity as opposed to the gravitational redshift as claimed by the authors[2].  His summary of the current set of experiments comes with the added bonus of a pointer to the open access version of the Physics Review Letters article on the experiment [3].  If you'd like to know how exactly you reflect a neutron from a wall without using coulombic forces which ...

We're still working on figuring out a way to geometrically, or verbally, explain the fact that an ellipse is formed by by tracing through the apexes of a family of parabolas that describe the trajectories of a projectile launched with the same initial velocity but different launch angles.  Try saying that three times fast, and in the meantime, see picture 1, and refer to the excellent open access article that derives the ellipse mathematically [1]. After I wrote about the elliptical envelope a few days ago  +rocktoasted  asked if there was a way to describe the construction of the ellipse without using equations or algebra.  Hence, the search for a geometrical explanation was born.   +Bruce Elliott  joined in on the work, and now we have a new collaborator, the only already PhD'ed physicist in the house, my wife Elaine.  If you'd like to get in on the collaboration by contributing observations that lead to explaining how to construct the ellipse in...

In addition to the Meissner effect pictured to the left, superconductors have other odd properties.  One of them is something known as the London moment.  It's named after the London brothers who did some of the earliest work on the properties of superconductors.  If I had to take a guess, I'd say it was specifically named after  Fritz London who authored the two volume set of books, "Superfluids" [1].  So much for the naming of the thing, here's what happens.  When a superconductor is rotated, it produces a magnetic field aligned with the axis of rotation.  The magnetic field is linearly related to the angular velocity of the superconductor by the following equation, (picture 2)[2]. where m_e is the mass of the electron, c is the speed of light, and e is the charge of an electron. London theorized that the  magnetic field which bears his name was a result of the superconducting cooper pairs lagging behind the initial rotation of the sup...

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

We're trying a new type of roughing pump vacuum hosing.  We're moving away from the traditional classic, red rubber tubing and trying out Kuritech K7130 Polywire Hose!  The kids and I went on an adventure a week and a half ago to check the hosing out at Bryan Hose and Gasket!  Everyone was super nice, and it looked like if you turned up later in the day you could have free popcorn.  It was Sam's first science trip.  Jr. used to go on these all the time when were at Brookhaven National Laboratory.  The best part, besides the obvious of getting to hang out in a hose and gasket store?  On the way out, Sam and Jr. saw their first real bulldozer, (see the right hand side of the building in the picture).  After weeks of seeing them in Mater cartoons, they thought it was awesome! View Larger Map

Dr. David Hestenes, (pictured to the left [2]), the original author of geometric algebra, (it was his PhD dissertation work at UCLA), will be speaking at A&M today [1]. We're learning how to do literature review matrices in our writing class, so I thought I'd try out the technique while reading Dr. Hestene's bio [2] last night.  Here are the key points I came away with 1.  Hestenes was inspired by Marcel Riesz's book " Clifford Numbers and Spinors "[3] One day in the mathematics– engineering library I looked at a shelf of incoming new books and pulled down and some lecture notes entitled “Clifford Numbers and Spinors” by Marcel Riesz. It was about Clifford algebra as a mathematical system. I read, I think, for about 15 minutes and all of a sudden I had an epiphany. I exclaimed “Gee, differential forms and the Dirac algebra have a common algebraic structure!”… 2.  Dr. Hestenes received the Oersted medal for his work on the force concept...

I presented yesterday at the APS april meeting and it was lots of fun!  The room was fairly packed and there were a number of other interesting talks in the session that was on the history of physics.  One of the most interesting presentations discussed how Tesla viewed theories of the luminiferous ether. During my talk, I discussed how the special relativistic addition of velocities, in one dimension at least, is very simple if you first express the velocities in terms of rapidities. As it turns out, the addition of velocities in two dimensions is much more difficult until you understand what's going on.  It seems mysterious at first, but it's not.  Simply put, the problem is that if you add a velocity in the east direction with a velocity in the north direction, you'll get a different answer than you will if you add a velocity in the north direction followed by one in the east direction. That's right, change the order that you add velocities in and you get ...

I'm reading an excellent article[3] by one of my all-time favorite authors, Wolfgang Rindler[1][2].  In the article, Rindler and Perlick show how to use a generalized form of the line element to derive the circular geodesics and the associated gyroscopic precessions of a number of different metrics including everyone's standby, the Schwarzschild metric. Using the Schwarzschild metric and his newly defined method for calculating circular geodesics, Rindler first derives the Thomas precession which was originally a special relativistic result having to do with the precession of the spin of an electron around an atomic nucleus.  He then goes on to show how the Fokker-De Sitter precession of a gyroscope orbiting a massive body, (like the sun), can be calculated. See reference [7] I'd never heard of the Fokker-De Sitter precession before, so I read on.  It turns out that this precession contains a component due to the geometry of the Schwarzschild metric as well as a...