Geometry Everywhere
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Tower crane

Tangents, Pulleys and Moment Balance

The moment a tower crane picks up a load it has to pass two tests at once. The first is tipping: the load out on the long arm wants to pull the crane over, the concrete blocks on the tail pull it back, and the winner isn't the heavier one but the one with the bigger force-times-distance. The second is contact: whichever direction the rope arrives from, the pull stays exactly the same distance from the sheave's axle. Neither is a choice — geometry and physics impose both.

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