I seem to have seen a way of dealing with connected masses in Resnick and
Halliday. Here you look at the tangential forces acting on the system of
strings and blocks. Forces perpendicular to motion direction balance out for
each block. You could then include the connected blocks and the strings in
the system and look at the tangential forces alone. The problem of Atwood's
machine would reduce to saying that force on one block is along a positive
tangent and on the other along a negative tangent. The rope as it passes
around the pulley experiences normal forces due to the pulley, so they do
not count.
To which I reply:
I think you're still likely to confuse a careful student: If the system of
rope + blocks experiences purely normal forces from the pulley, why doesn't
the system accelerate radially outward away from the pulley?
It seems to me that the pulley force of 2T vertically upward is equivalent
to two forces of T upward *tangentially* at the points where the string
first makes contact with the pulley. (One way to see this is to let the
system consist of the two masses plus that part of the string which is not
in contact with the pulley.) But in a "bent" coordinate system which goes
around the pulley, one of these (now external) tension forces is in the
positive tangential direction and one in the negative tangential direction,
and hence the net external force is only the difference of weights to which
neither the tension forces nor the pulley reaction force contribute.
But see how complicated this all is! I agree with those who say not to try
combine masses into one system when a pulley is involved!
Dr. Carl E. Mungan, Assistant Professor http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL 32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu