Originally Posted by 2Hulls
I really hate to belabor this, but no, you're wrong. The angle the "tail" makes exiting the final block has no bearing on the MA for moving the load directly to the fixed block, no matter which block the rope exits.
If this is not intuitive to you, visit any authoritative source on block and tackles and notice the absence of any mention of the exit angle. Please let me know if you find any scholarly support as I stand ready to learn.
That said, if you pull a rope to the side at 90* angle at the mid point of the rope suspending a weight, you have a tremendous MA to lift the weight small distances even without any tackle. This is due to trigonometry at small angles.
No, it certainly isn't intuitive to me, but I am thirsty for knowledge, so I glad of any input that corrects any false impressions I have.
I haven't found any "authoritative sources" on the internet
(anyone have anything to recommend that I can read?). I find these concepts interesting.
If I give you my reasoning regarding the angle of exist of the tail from the moveable object's end influencing the force required to move the object, could you please let me know where it is flawed?
Take these two situations:
1. The tail exists parallel to the direction of movement of the object at the object's end (rove to advantage) along with the other lines.
If you pull the tail x units, all the lines applying acting directly on the object effectively shorten by x divided by the number of these lines (this includes the tail - it lengthens by x less the movement of the object) and the object moves by this amount.
2. The tail exits perpendicularly to the direction of movement of the object at the object's end (rove to advantage).
The tail is is no longer exerting any force in the direction the object is moving. If you pull the tail x units, the object now moves x divided by the number of lines less
than the tail ie it moves a greater amount.
So, you have pulled the tail the same amount in both cases, but the object has moved different amounts. No physicist here, but surely if the object moves different amounts in the two cases, the force applied has been different?
If not, could you please explain why not?
PS If the tackle is rigged so that it emerges at the fixed end (rove to disadvantage) then it doesn't matter which direction you pull the tail - the tail is not acting directly on the object. These two situations are very different.