YES NOPE9 wrote:
> I looked at this on intergoogle and while there were some example
> diagrams, I did not get a sense of what a rule of thumb for
> determining the mechanical advantage of pulleys.

Count number of rope segments going back and forth.  Yes it really is that
simple.

One way to prove this to yourself is to consider that the tension in the
rope is equal everywhere.  When the rope goes from one end to the other, the
tension is the force it's pulling the two ends together with.  Each rope
segment does this.  The total force is the total tension, which is the
tension in the rope times the number of rope segments going end to end.

> Assume that I weigh 100 grams.

Then I'd have to assume a bunch of other things you probably wouldn't like
(although rather amusing on this end).  100 pounds would be in the plausible
range, but 100 grams!!?  I'm trying hard to picture what you look like
weighing less than half a cup of water.

> I attach myself to the floor and pull on a rope that goes over a
> pulley ( attached to the ceiling ) and has has an object attached to
> it.  The object is gravitationally attracted to the ground with a
> force of one newton.
>             I have to pull with a force of 1 newton to lift the
> weight .... correct ?

Yes.

> Now I detach myself from the floor and move the rope to a hook at the
> top of my head.

LOL.  Is that like one of those propeller caps?

> Now I have to pull with a force of .5 newtons to lift
> myself.  .... correct ?

You're making a mess of the units.  You said you "weigh" 100 grams, which is
actually a mass.  On earth, 100 grams weighs about .98 Newtons.  Therefore
when you try to pull the rope down, a force exceeding .98N will then lift
you up instead.  If you weighed just a little more than 1N, then as your
pulling force got to 1N the weight on the other end of the rope would start
to lift.  Even at you weighing .98N and the weight on the other end 1N, both
are going to lift temporarily as you pull hard enough because the force to
cause accelleration will exceed the weight of both ends.

> Next I attach a rope to my head , run it up through side A of a double
> pulley ( attached to the ceiling ) , back down to a pulley attached to
> my head , back up through side B of the double pulley and back down to
> my hands.   I have to pull with a force of .25 newtons to raise
> myself ........  correct ?

Roughly right since you weigh about 1N, *if* you you are only counting on
the pulling force of the rope segment in your hand.  There are three rope
segments pulling on your head, which together pull with the remaining .75N
required to lift you.  Note also that you will have to pull the rope in your
hands 4 times as far as the distance you go up (all relative to the ground).


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