NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Air Hockey Pucks and Gravity
From: Lu Abel
Date: 2008 Feb 01, 09:31 -0800
From: Lu Abel
Date: 2008 Feb 01, 09:31 -0800
frankreed@HistoricalAtlas.net wrote: > **Above I mentioned the tidal period. So there's no confusion, I'm not > talking about ocean tides due to the variation in the gravitational forces > of the Sun and the Moon over the surface of the Earth, but rather the local > "tidal" acceleration in the vicinity of any point on Earth due to the > variation in the gravitational force of the Earth itself. For an example, > imagine an air table with a disc on it ("air hockey" with a floating puck). > If I level the table perfectly at its center, and if the table is perfectly > flat, then the floating disc, if released near one edge, will "fall" towards > the center because that's the only place where the gravity vector is exactly > perpendicular to the table --everywhere else, the vector is slightly tilted, > pointing towards the center of the Earth, so a small component of the > gravity vector is pointing towards the center of the table. The amount is > directly proportional to the distance from the center of the table. The disc > will execute simple harmonic motion [natural frequency > omega=sqrt(g/R)=sqrt(GM/R^3)], as if it's attached to the center of the > table by a perfect spring, gliding back and forth across the table with a > period of 84 minutes (ignoring air resistance). Give it a slight sideways > motion and the disc will travel in a circular or elliptical path around the > center of the table with that same 84 minute period (no matter how big the > circle). That's the "tidal field" of the Earth. > I challenged several of my smart friends with this problem. After they found the solution, one of them asked if the axis of the puck's back-and-forth motion will rotate because it is in fact a Foucault pendulum. I suspect it would. But another asked about Coriolis forces on the back-and-forth motion and I didn't have an answer. Would the Coriolis force just be another manifestation of the Foucault effect? Lu Abel --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---