Friction of weights drawn along inclined paths
How a suspended weight loads its support, and how friction grows with the steepness of the slope
A page of mechanics crowded with diagrams: graduated quarter-circles used as protractors, a hanging weight on a support, and figures lettered a, c, m, o. Leonardo first argues that a body hung from a single support transfers its whole weight into that support, present in every part of its length. He then works a numerical example on the incline m c, claiming that a 12-pound body drawn along that obliquity meets a friction that has risen to a third of its power, so that a force exceeding 7 is needed; friction reaches only a quarter of the dragged weight when the pull is along the horizontal.
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A suspended body transfers its whole weight into its support
A heavy body held by a single support transfers all its weight into that support. The weight of any suspended body is wholly in the whole of its support and also wholly in every part of its length. Where supports meet the load at right angles, the one that bore more of the weight is the more burdened.
Worked example of friction on the incline m c
When by its position the weight reaches half its heaviness, its friction has gained a third of its power. Drawn to point m, beneath the middle of the horizontal a c, the line m c cuts the curve a o at its third. So a 12-pound body, whose friction on the flat would be a quarter (3), meets on this third-degree slope only a third of that power, and to drag it needs a force just past 7.
Friction is a quarter of the weight only on the horizontal
This figure shows the degrees of frictional power for weights drawn along different obliquities. Friction equals a quarter of the dragged weight's power only when the pull is horizontal, because the increments of weight are equal only at the beginning and the end. He concludes that the weight m presses on line m c by only half its heaviness, so its friction has reached half its power.