There are a couple of unique aspects to your question. It will be
easier if you temporarily forget your question and look at question C
here, about Bob the Window Washer. Once this example makes sense,
your chain question should clear itself up:
http://www.cord.edu/dept/physics/p128/lecture99_13.html
The example on the left represents your version with the chain looped
over a hook (not a single chain link hooked). The example on the
right is the same as your single-strand of chain--you could also
connect the rope directly to an overhanging structure with no pulley
and have no effect (ignoring the weight of the rope).
Attaching the rope/chain to a fixed object simulates an identical
force in the opposite direction. In order to match the force of a
weight hanging from a single strand from a fixed point (roof or hook),
you would have to add another weight of equal amount to the other end
of the rope/chain hung over a pulley. By adding the pulley and
looping the chain through, you are now holding twice as much weight
from the same chain.
This is one of those things that never sound right at first, but the
logic works itself out. You can also see the Levi's question on the
same page above.
This is also similar to the question of which is worse, your car
crashing into an identical car coming at you at the same speed, or
crashing into a fixed wall. For your individual car it is the same,
although the second car might have something to say about it. But
translated to the chain scenario, you end up with twice as much
hanging capacity, just as the car scenario ends up with twice as much
car crushing done.
In your question, there are two differences worth noting:
1. It sounds like you might have two of the pulley-like arrangements
back-to-back (or rather top-to-bottom). This is fine, just examine
one end at a time.
2. In theory the looped rope over the pulley (or in your case a looped
chain over a hook) would double the weight capacity. But it doesn't
work 100% for a rope because bending the rope weakens it by placing
more stress on the outer part of the curve. A pulley should be as
large as possible to minimize this. With a chain looped over a hook,
you will end up with one or two loops hanging over the hook with a
good bending force on them. Despite the pulley logic, flexibility
issues migh break your chain at a lower force than either hanging
method would calculate. So don't actually do this! |
