TACKLE
One rope, one tension, n strands — pull n× farther, n× lighter.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A load too heavy to lift, a ceiling, some pulleys, and one long rope. Sailors and riggers have known for three thousand years that the rope can be talked into carrying most of the weight — the only question is what it demands in exchange.
One tension
The whole trick in one sentence: it is a single rope, so the tension is the same everywhere along it — including at your hand. The moving block hangs from n strands of that rope, each carrying T, so nT holds the load and your hand holds one share.
Solve
F = W/n — the mechanical advantage is simply the strand count. But the rope keeps books: raising the block one meter shortens every strand by one meter, and all that rope comes out at your end. Pull n times farther; pull n times lighter.
Hoist
The hoist, quasi-static, with two distances racing: the hand line runs out exactly n times faster than the load rises — not roughly, exactly — because rope, like the press’s fluid, does not compress. Same law, new costume.
Audit
The books: F times d_pull equals W times d_load to machine precision — the third member of the virtual-work family, after the lever’s arms and the press’s pistons. Machines never create work. They only re-price it, and the tackle’s price is distance.