What do you mean by "two legs through the pulley?"
It's difficult for us to show pictures through this list, so we have to
describe the situation with words. I have found pulley problems are
frequently terribly worded because it isn't made clear how many times a
cable passes over the pulley and/or it isn't clear where the ends of the
cable are attached. If we do not know these things we cannot respond to the
question. We need to know how many tensions are supporting the weight.
Also, I frequently have seen pulley problems in which the number of cables
is properly figured, but the cables are not vertically oriented... they have
various slants. But the slanted cables are not handled with vector
resolution. This probably results from the instructor realizing the tension
is the same throughout, but not realizing the direction of the tension is
important in terms of supporting the weight.
Indeed, pulley pictures are often drawn incorrectly. For example, a cable
is attached to the ceiling. It runs vertically down to a pulley that has a
weight attached. The cable goes through the pulley and the second cable end
is held by a person standing off to the side. So the cable goes vertically
down from ceiling, goes through the pulley, then goes upward and sideways at
an angle of something like 45 degrees and is held by a person's hand. That
situation is not in equilibrium. The pulley and mass will move toward the
person until the cable angles become equal.
It is interesting that "simple machines" are probably stressed in
middle-school science classes more than at any other academic level... but
the treatment of pulleys is almost always botched by middle-school science
teachers who have not had a good college physics course... and that includes
a lot of teachers.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817
While surfing I stumbled on a children's quiz show -- ~~Smartest Kid in
America -- just as they were asking a pulley question -- it went by too
fast to sink in but I think that a 120lb weight is held by a pulley which
is supported by cable with two legs through the pulley.