Re: using pulleys to lift oneself

Hey, James:
Your explanations were quite clear.  See attached sketches.  I'm assuming 
that the question is, "Can a person lift himself with one of these?"
The first device you describe is called a "Bosun's Chair"  They're pretty 
common. http://www.alaska.net/~mzeiger/bosunschair.html
 http://www.plastimousa.com/images/bosuns_10470.jpg
 http://www.lalizas.gr/products/Bosuns%2010210%20General.jpg

As for the second:  To analyze a system like this, Engineers use what is 
called a "Free Body Diagram"  This reduces the system to a lump of mass 
and the forces acting on it.  The rules are that the sum of forces in the 
X-X direction have to add up to zero, and all forces in the Y-Y direction 
also equal zero.

So, we have a platform with a pulley attached, a line from overhead going 
through the pulley, and a guy ("Jim") holding the bitter end of the line 
while standing on the platform.  Now, just looking at the sum of forces in 
the Y-Y direction, we see that gravity is pulling down at (say) 100 pounds 
weight (which is different from mass, doncha know)  That means that the 
tension in the line has to be 100 pounds, to balance the weight (sum of 
forces equals zero, +100 +(-100) = 0.)  Now we can make a free body of 
just the pulley.  The line supporting the system is under 100 pounds 
tension.  The rule with a pulley is that the tension in a line running 
around a pulley is the same on both sides (assume no friction), so the 
bitter end also has to be at 100 pounds of tension.  That gives us two 
upward forces of 100 pounds each.  To balance those two, the pulley must 
be pulled down at 200 pounds!
Now, Jim weighs 100 pounds, and he is pulling up on the line at 100 
pounds; so the free body diagram of Jim must have 200 pounds downward 
(+100 + 100 - 200 = 0 pounds) -- perfectly balancing the forces on the 
pulley! 
 
Now.  Jim gets ambitious and pulls up on his end of the line an additional 
five pounds worth.  So his free body diagram has now got 205 pounds 
pushing down.  The free body of the pulley, though, now has 210 pounds -- 
105 pounds of tension in each piece of line.  So the whole system. 
platform pulley and Jim, will acclerate upwards, at least until Jim stops 
pulling and the forces in the system balance out again.  (whew)
I don't mind admitting that this took me some head-scratching to figure 
out.  Thanks for the exercise!