Re: cavendish expt

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

The sensitivity of the Cavendish apparatus is, directly proportional
to the square of its oscillation period T due to its inverse
dependence on the torsion constant of the suspending thread.
Unfortunately, this means that a sensitive Cavendish apparatus will
both take a long time to settle down AND be highly sensitive to
drafts as Wolfgang has mentioned.

It's not hard to show that the expected angle of deviation is something like

          G*M*T^2
  theta = -------
          2*L*d^2

where M is the mass of one of the fixed masses, L is the length of
the bar, and d is the effective separation between the fixed and bar
mounted masses.

Assuming (off the top of my head) T = 100 s, M = 100 kg, L = 1 m, and
d = 40 cm I get a few tenths of a milliradian.  Using a 5 m optical
lever, this would give you a spot motion of a couple of mm which
*might* be detectable.  I think, however, that the standard Leybold
apparatus (which easily sits on a small desk) produces several to ten
times this much deflection and it also provides thorough isolation
from drafts by completely enclosing the pendulum itself.

I did have a student who wanted to try building a Cavendish apparatus
once.  He didn't put in much effort, however, and had a concomitant
level of success.  He eventually settled for using the Leybold
apparatus which still requires a lot of time primarily to coax the
pendulum into an equilibrium position in which it does NOT make
contact with the sides of the enclosure.  He came to me at the end of
an apparently grueling four hour stint in the lab and remarked, "Boy,
Professor Mallinckrodt, that Cavendish must have been ONE PATIENT
DUDE!"

> Greetings phys-eders:
>
> I am attempting to set up an experiment similar to
> what Cavendish did when he "weighed the earth".
>
> I'm using two joint compound buckets filled with sand
> as the larger masses. I have a meterstick horizontally
> oriented with bottles of sand on each end. This is
> suspended from the ceiling with video tape.
>              |
>              |
>             /\
>            /  \
>           /    \
>          ________
>          0      0
>
>         OO      OO
>    (In front)  (In back)
>
> I'm finding that it takes an incredibly long time for
> the suspended meterstick to find its equilibrium
> position. Once it does, I'll move the buckets in
> closer to the bottles of sand and see if I can detect
> any torque on the meterstick.
>
> My questions are:
>
> 1)Do you think the incredibly small Fg would produce
> any effect?
>
> 2)Have any of you tried this before? If you did, how
> did it work?
>
> 3) Any suggestions?


--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.