I am seeking a simple, clear and concise explanation of how the block and tackle works. How can a system of such pulleys increase the amount of weight lifted by a given amount of energy, or reduce the amount of energy needed to lift a given amount of weight?
I would very much appreciate it if you could help me out. Thank you.
Your question then needs to be restated in terms of these definitions:
"How can a system of such pulleys increase the amount of weight lifted by a given amount of force, or reduce the amount of force needed to lift a given amount of weight?"
A block and tackle multiplies the force applied to an object because the tension in a non-stretching rope is the same in every part of it. This is easy to see if you imagine the rope by itself without pulleys. When I pull on it, every inch of the rope pulls on the next inch with exactly the same force as I am applying to the inch I hold. If it were not so then the force at the far end would be reduced or increased, which would make no sense.
Imagine a block of iron weighing 100 pounds with a ring in the top of it, for lifting. If I attach a rope directly to the ring and pull upward, when the force I exert exceeds 100 pounds the block starts to raise. Now suppose we attach a single pulley to the ring in the block and pass the rope through it to fasten the far end to a beam overhead. When I pull upward on the free end of the rope, again when the total force on the block exceeds 100 pounds it will again start to raise. The difference now is that there are two parts of the rope exerting force on the block. Since the tension in the rope is everywhere equal, if each part has a tension of 50 pounds the total force on the block will be 100 pounds and it will start to raise.
Since the rope in the previous example slips through the pulley, I have to collect more of it to raise the block a certain distance. In fact to raise the block 5 feet I will need to gather in 10 feet of rope. That makes the work done or energy expended the same with or without the pulley. In the first instance it was 100 pounds times 5 feet. In the second instance it was 50 pounds times 10 feet. Energy is conserved. Of course we have taken no account of any friction in the pulley. Some work may be required to overcome the friction so the second instance requires a bit of excess force.
The mechanical advantage of the single movable pulley example is 2 since the force required to move the iron block is 1/2 its weight. We could increase the mechanical advantage by adding additional pulleys to the block and using other pulleys attached to the overhead beam just to reverse the direction of the rope for the next pass through the working end pulleys. The total mechanical advantage will be the number of parts of rope passing through the moving pulleys.