From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 10 Sep 1999 15:31:58 -0500
Hi Thomas-
Not so quick, my friend:
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In Serway's 4th ed. of Physics for Scientists and Engineers, problem 57 of
Chapter23 (Electric Fields) states:
Two small spheres of mass m are suspended from strings of length l that are
connected at a common point. One sphere has charge Q; the other has charge
2Q. Assume the angles theta1 and theta2 that the strings make with the
vertical are small. (a) How are theta1 and theta2 related? (b).......
The solutions manual then shows these angles to be equal - but only by
making an assumption that FORCES this situation; i.e. by assuming the
electrical force on either to be horizontal. This should have nothing to
do with the original assumption that the angles are small, and I feel sorry
for anyone who tries to learn physics from such presentations. If you simply
allow yourself to think beyond translational equilibrium, the solution becomes
trivial.
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Unless I have made a trigonometric error, there is, formally,
a large angle solution to the equations of static equilibrium.
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography