Statics: levers, inclined planes, pulleys and balances

The three angles of a lever

For a lever with a cord, the notes name c the angle of the lever and the cord, b the angle of the power and the cord, and n the angle of the power and the lever.

A weight on an inclined plane and its centre of gravity

Every heavy body is said to weigh along the line of its motion and to set its centre below the centre of the cord that sustains it. The further the centre of gravity moves outside its central line, the more it presses on the second support that removes it from that position.

Pulley train with halving loads

A vertical column of numbers beside a pulley system halves at each stage — 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4 — against a load figure of 400000, illustrating the mechanical advantage of the compound pulley.

Weight S distributed among many cords

For the figure m - a b c d e f g h - n - S, the note asks what share of the weight S is carried by each cord when acting alone, and then by all of them together, in holding the weight away from its central line.

Weighing in air and water to compare resistances

A balance with equal weights in air is used to test proportions of resistance: one weight is placed in water and the added weight needed to restore balance is noted. This measures how much greater the resistance of water is than that of air, and the same method is proposed for comparing one water or air with another.

The central line and a beam on two cords

The 'central line' is defined as the line imagined from the centre of the world to the centre of a suspended weight. A uniform beam can hang level from its two ends only if the two cords are equally oblique, in which case they are equally loaded.

Metà inferiore, colonna sinistra. Due figurine di peso oscillante:

Leva, con:

Corpo sollevato su piano inclinato, con:

A destra, sistema di carrucole, con:

Foglio capovolto.

Due figure, coi pesi:

Metà superiore, foglio capovolto.

Figura analoga, con:

Bilancia con un peso entro vasca:

Colonna centrale.

Trave sospeso a due corde:

Corpo sferico su piano inclinato, con:

Colonna sinistra. Peso oscillante:

Margine inferiore.

Lower half, left column. Two small figures of an oscillating weight:

Lever, with:

Body raised on an inclined plane, with:

On the right, a system of pulleys, with:

Sheet turned upside down.

Two figures, with the weights:

Upper half, sheet upside down.

Analogous figure, with:

Balance with a weight inside a basin:

Central column.

Beam suspended by two cords:

Spherical body on an inclined plane, with:

Left column. Oscillating weight:

Lower margin.