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