Forces in pulleys and cords bearing a weight
How a cord over a pulley bears twice the load, the effect of moving weights, and a weight wavering on a balance arm
This mechanics sheet analyses the forces in cords running over pulleys (carrucole). An immobile cord of uniform weight hangs equally from both sides, while the cord supporting a pulley through which a load's cord passes bears twice the load. When the two hung weights move against one another the pulley feels more than their natural weight, the faster their contrary up-and-down motions, and the cord in the mover's hand feels more weight than the one joined to the rising load. A final note treats the wavering (titubazione) of a weight hung from an arm of a balance. Below the text, drawings of spoked wheels carrying weights at their rims are set out but are not covered by the transcription.
On this page
Pulley figure with numbered loads
The first figure is a pulley marked 8, b a, 4, 4, setting up the numerical loads for the analysis of cords that follows.
A cord over a pulley bears twice its load
A cord hanging from the opposite sides of a fixed pulley, being immobile and of uniform weight and thickness, is of equal weight on both sides; but the cord supporting a pulley through which passes the cord holding a weight in the air bears upon itself twice that weight.
Moving weights make the pulley feel extra load
If the two weights at the cord's ends move one another, the pulley feels more than their natural heaviness in proportion as their contrary motions up and down are faster; and the cord in the mover's hand feels more heaviness than the one joined to the rising weight, otherwise the weight would be immobile.
Wavering of a weight on a balance arm
Labelled b - d a - c - f e, the figure concerns the wavering (titubation) of the weight joined to the hanger of one of the arms of the balance.
Wheels with peripheral weights
The lower part of the sheet is filled with drawings of spoked wheels carrying weights or pivoted arms at their rims, of the kind used to study rotation and moment; these figures are not covered by the transcription.