Is the effort greater?

[KC]

Continued from: Our Guild Mission Thread

where i posted this pic:



My point in drawing this pic, this way is that the effort is not greater; because in either scenario you only express 50# pull from each hand.   The reason the 2nd scenario builds more force, is that the pull from the '2nd hand' as equal and opposite to the primary hand pulling on the load; is redirected to pull on the load, rather than running away (in equal force/ opposite direction) from the load/work!

If it did take more effort, and you could only pull 50#, then ya couldn't get 100#?  The point is in each case you exert 100#/ 50 in each hand.  Actually i think what is more correct, is that we aren't pulling against an anchor (that can't move by definition)with the '2nd hand'; we are now pulling on the load that can move, so can gain distance with each hand??  Whereby power is distance x force still; but here we increase the distance multiplier in the 2nd hand, not the force multiplier.

Same as with the replacing the 2 hand pull with the pulley system scenario in the Flash animation and the ship's rig link.  IN the pulley systems inset rather than tagged on the primary systems, we are using both of the Equal/Opposites to target, rather than jsut 1 side of their forces, and terminating the other side at anchor.

If there is a theoretical Zer0 friction pulley overhead with line reeved thru, and i way 100#.  You lift me 20'; that is a 1:1; you lift 100# for 20'; there is 200# load on pulley and support.  Hand me line, to hold/lift self; support/pulley load drops to 100#/ system is more 'closed'.  But, i also now have a 2:1 over lifting self, as it only takes 50# of force, but for 40'.

There are many more uses i think of folding force against itself in this pattern.   A T-handled valve that you place 1 had on each side; allows the equal and opposite force to be placed to work on load too in this imagery; also guarantees always perpendicualr effort/tourque on target center.  This can save a weak back; in that the force routes across chest arms to find equal /opposite, and not down thru back to legs, that also gives only half as much power (when focusing on 1 side of the T handle).  But also, you can 2 hand the T handle, and preserve leg power / bodyweight for balance or to add more power!

Back to rope rigs-
i think that these elusive concepts are present inside of knot forces; only a rig enlarges them to be visible.

[squarerigger]

Hi KC,

Thanks for the new entry - WOW!! OK, my mistake - I should have said that energy is conserved and that the amount of energy is the same and I was wrong to say effort.  Let's look at the distance moved by the object being pulled and the distance being moved by the hands.  In case #1 and #2 the object still moves only 1 foot.  You doubled the mass moved, so you feel good about that.  However, you forgot about your shoes, as I will explain later.  For a moment though, look at the right hand in situation #2 - the hand is pulling on the loop at 50# and the standing part to which the loop is attached is also being pulled with 50#.  Attached to the base of that loop is a second standing part, which is attached around the anchor and then to the left hand.  Therefore, if the second SPart (short for Standing Part) is moving the same distance east as the first SPart is moving west, they are moving together at twice the rate the anchor and the SPart of situation #1 is showing.  That's because anchors don't move.  Therefore the total distance moved by both the hands is twice as much but each hand still pulled 50#, the energy just got transmitted into the loop in case #2 instead of being burnt up on the anchor and the feet on the floor in case #1, and the energy is the same - it is just lost as heat in the muscles and the feet and the anchor (OK it's small, but its still there) so the energy is no different.  That is what I should have said when talking about the effort - my bad!

Your point was not however, to talk about energy and its conservation but to talk about effort expended in the right direction!  I got that.  You definitely get a better result when you pull on two pieces of the same falls, but you better expend the energy together or you'll end up dragging one hand into the set of blocks!

Now, then you said that we could gain distance with each hand?  No, the distance each hand moves in #2 is the same as each other.  In case #1, only the right hand moves.  So in #1 you move your right hand 1 foot and you expend 50ft-lb with your right hand.  To balance your body, which you are assuming is standing still (the position of the power applied does not move) you have to apply 50 ft-lb to the anchor with your left hand in order for you to stay still, otherwise you'll drag yourself towards the load.  Therefore the energy expended is equal to 50 ft-lb (RH) plus 50 ft-lb (LH) or 100 ft-lb total.  In case #2, you stay still and could be standing on ice because your hands move towards each other by one foot each, thereby making the energy imparted the same (50 ft-lb with each hand) but now moving a 100 lb load by one foot, a total of 100 ft-lb.  This comprises 50 ft-lb with each hand usefully expended instead of being lost with friction between your feet and the floor as in case #1.  Try case #1 while you are standing on ice!

Ok, now where do you think this applies inside a knot?  I want to hear more from you!  This stuff is fascinating!

Lindsey

[KC]

Side Note: That analysis was for horizontal applications; without leg or bodyweight help that would add more to one of the hand pulls than the other.  In a vertical application; we could add A) bodyweight pull to one hand B) leg lift to one hand or even C) hang upside down and push legs on above anchor to add body weight and leg force both to one hand!  In these cases, would concentrate on the opposite hand, to get as much as possible into it, letting body weight and leg forces work autonomousely; also keep hands far enough apart (this can't be a too much of a shorty system) to be able to have the hands operating as equal and opposite forces of each other, then any bodyweight or leg force as added extra to one hand.

Depending on what you are doing, and what ya call a knot vs. rig; we could for instance take the above scenario off load and loop tail/bitters thru eye and bend back again to bind some type of bundle etc. and have both sides compressing in with leveraged force together on the center load...  

Of course operating the above rig; with tail/bitters thru eye and pulling on the load would give 3x pull on load and 2x on anchor; but could '2Hand' to get 4x on either; then inset that properly insdie a 5x rig runs into math like The Ship's Tackle i linked earlier.

i've had Bob, our 11 year old in yard easily pulling 1500# with 1 hand through pulley multiplier sets, measured on a used crane dynometer off ebay; showing him these differances.

Warning eye candy colors and animations in Flash that mihgt not be suitable for all viewers, enter at own risk