Kamis, 19 September 2013

Foucault Pendulum -- Latitude of a Google Doodle

On Wednesday, the Google Doodle showed a working Foucault Pendulum simulation.  As it happens, my research students are in the opening stages of a deep investigation of the Foucault in preparation for the US Invitational Young Physicists Tournament.    We are tasked with building a Foucault, using it to determine our latitude, and then conducting the error analysis to define the precision of the measurement.

What a useful coincidence... I added the question to my research students' quiz: "Determine the latitude portrayed by the Google Doodle."

The equation for the precession per day of a Foucault pendulum is 360 degrees times the sine of the latitude.  Solving, then, the latitude is the inverse sine of the precession per day divided by 360 degrees.*  We need to find the precession rate from the simulation.

*Explaining the geometry and conceptual physics behind this equation will be part of each research team's presentation at the tournament, of course.

One of my students sent a rather tetchy response, complaining that he'd have to sit there for most of an hour just to watch how long it takes for a peg to be knocked down.  Some cursory exploration finds a cheat:  look in the lower right corner at the clock face.  Click on the clock.  A slider appears, allowing you to fast-forward time.*

*A second slider allows you to adjust latitude.  I'm doing everything here for the default latitude when I just click on the doodle link.

I set the slider to 12:00, and fast-forwarded until all pegs were knocked down.  At 6:25 PM by the clock, the last peg was still standing; at 6:40 PM, the last peg had fallen.  This means that the pendulum rotates 180 degrees in somewhere between 18.42 hours and 18.67 hours.  Pro-rating this rotation rate, this works out to between 276 and 280 degrees per day.

Now plug into the relevant equation: the latitude of this pendulum is between 40.0 and 40.7 degrees.

Reader help, please:  I anticipated that the simulation either (a) used the geo-located latitude of the computer accessing the doodle, or (b) used a default latitude with some special meaning, such as Google's Mountain View, CA headquarters.  Oops.  I am located at Woodberry Forest, VA, 37 degrees north latitude; Mountain View is also 37 degrees north latitude.  Any clue where this Foucault is supposed to be?  (Or, alternately, any corrections to my calculations?)

And, if you'd like to participate in our tournament, solve three of these four problems and come to San Jose, CA on Jan. 31, 2014.  I'll be happy to help you out with both the physics and the attendance logistics.

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