Force Volume/ volume of force was something i showed some time ago, trying to simplify a quantity of work force by compairing to more familiar and tangible volume of water. Each a finite value, each could be spread far (distance) or high (power), and could not just magically make more from it's own self on top of this volume (only the either/or of power/distance). Also, neither would be 100% efficient on transfer; some water would evaporate, be stuck to the sides of previous vessel, spill etc.
And yes, if anything is taught of pulleys, it is generally, that a pulley on anchor is 1:1 redirect (no force increase, 1st class lever-that only changes direction between effort input and work output, pulley as pivot is between input and output just like a non-flexible lever). Also, if the pulley is on the load, it increases power (2nd class lever, effort and work move in same direction, power increase but more distance required in trade off, here the work load/output is between the pivot of anchored end, and the input effort just like a non-flexible lever).
But, what isn't shown normally(nor is shown in pics here): Is a 3rd position of the pulley in between the anchor of 1 end AND WORK OUTPUT end, with the input effort on the pulley (yielding 1/2 power at 2x speed, a 3rd class lever just like a non-flexible lever). Several times we had very steep 120' hill to pull loads of tree lumber up to 60' drive way, so i made this setup, with 1 end anchored high on hill, 1 end low to load at base of hill, and pulley in between to be pulled by truck up hill. Worked very well, but had to move truck slow, as load was moving at 2x speed, and either side of hill was full of tropical (some rare) plants at this fancy place. Over the years, any job we did there was known as 'Hell Hill' to the guys, and we always made this setup (No of course we didn't tell new guys they didn't have to drag it all manually, and perpetuated legend of 'Hell Hill' for 1 week prior to job...).
But also, not shown is this concept presented were the pulley can be on anchor / not moving as reverse/ load movement as work was in opposite direction of effort input (1st class lever) and could be used to input effort + it's equal opposite on to load (curiously, we can do this too with see-saw type lever).
this is a closed system, compaired to the normally shown 'open' systems, so more of the forces are conserved to target (bodyweight input not needed for this closed system, but why not use, and need to show that effort pulls/pushes do not pull against bodyweight, but rather each other). Taking a step further, if climber is load, and is being pulled up, that is 1:1, but if climber needs to go up, and pulls himself up in scenario 1, things change. Climber has to shorten both legs of rope 1' (total of 2') to lift her/himself 1'; so forces more distance input, than output, for more return of force. In the end, 1 100# climber in swing with own hand holding up on other side of pulley, only has 50# tension on each leg of rope from pulley (to support their 100# weight). So, has 2:1 mechanical advantage over his own body in trade for extra distance pulled. You might even see this in some old movies unknowingly, when man jumps inside of 'dumb waiter' and pulls themselves and dinner up to top floor (there would also be ballast weights, that about make empty dumb waiter 'float' no effort to fight 'car' or cable's weight, but friction inefficiencies keep in place).
i think there are new things to find all around as Derek states, they say we know less about inner spaces of sea and mind, than we do of outer space! But, then too; i think there are lost things that were known, perhaps even somewhat innately known/accepted by all , but unknown now, like this, pyramid making etc. working in background of daily lives.. But, it would be best to look at all things in wonder, even if thought know; for then eyes are opened more, to perhaps even see deeper into it's depths to see if really known, or even lessons to carry to other things (leverage in learning?). Some theories say, that everything is so interrelated, that one can know all/many things, just by knowing 1 thing so very well, and seeing the connections to to other things, including other knots, mechanical systems etc..
1 Pyramid theory of 'mind over matter':
(There are some subtleties here at changeover point of direction reverse and moving up to same step, then higher step; that are extra well thought out; and easy to miss)
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
