Re: weight of a bird in a cage

[Timothy Folkerts <tfolkert@TIGER.FHSU.EDU>]

FYI

> A long hour glass when turned, has sand particles accelerating to
> some maximal speed. We can be quite certain that this speed is well
> less than 120 mph. But we ( or rather I) am unaware of this speed,
> for the grain size commonly used in hour glasses.

 From the CRC Handbook

Terminal velocity for 0.1 mm, density = 2 g/cm^3, sphere:   ~ 50 cm/s
Terminal velocity for 1.0 mm, density = 2 g/cm^3, sphere:  ~ 600 cm/s

These are typical sizes for fine and coarse sand, respectively, although
the densities are a little low for typical rock.

Anyway, the time to reach 600 cm/s = 6 m/s in a vacuum would be,

     t = v/a = (6 m/s) / (10 m/s^2)  = 0.6 s
so
     x = 1/2 at^2 = (0.5) (10 m/s^2) (0.6s)^2 = 0.018 m ~ 2 m

But the time to reach 50 cm/s = 0.5 m/s in a vacuum would be,
     t = v/a = (0.5 m/s) / (10 m/s^2)  = 0.05 s
so
     x = 1/2 at^2 = (0.5) (10 m/s^2) (0.05 s)^2 = 0.0125 m ~ 1 cm


In these distances the sand, falling through the air, should be at least
approaching the terminal speed.  Obviously the size of the sand will make a
huge difference in whether or not terminal speed is achieved in a typical
hourglass.



Tim Folkerts