(1) Leverage principle: Archimedes’ principle. Formula: power × power arm = resistance × resistance arm.

Leverage is also called effortful lever, effortless lever and equal-arm lever. The lever principle is also called "lever balance condition". For a lever to be balanced, the two moments (the product of the force and the moment arm) acting on the lever must be equal in magnitude. That is: power × power arm = resistance × resistance arm, expressed in algebra as F1·L1=F2·L2. In the formula, F1 represents power, L1 represents power arm, F2 represents resistance, and L2 represents resistance arm.

Mozi in the Warring States Period was the first to propose the principle of leverage. In "Mozi·Jingxia" he said that "a balance must be correct, and it must be gained"; "A balance must be weighed on one side, and the weight must be beaten If they are not similar, but if they are balanced, then the short mark will be long and the two will be added together. If the weights are similar, then the mark will be lowered and the mark will be right." These two articles speak comprehensively about the balance of leverage.

There are those with equal arms and those with unequal arms; there are those that change the weight of the two ends to make it deviate, and there are also those that change the length of the two arms to make it deviate. It should also be mentioned here by the way that the ancient Greek scientist Archimedes has a famous saying that has been around for a long time: "Give me a fulcrum and I can lift the entire earth!" This sentence refers to the principle of leverage.

(2) Law of buoyancy: Archimedes’ law. Formula: F float = G drain = ρ liquid gV drain.

Buoyancy is caused by the difference between the upward and downward pressure of liquid (or gas) on an object. An object immersed in a liquid experiences an upward buoyant force equal to the gravity of the liquid it displaces. F float = G row =ρ liquid V row g. It can be seen from the formula that the buoyancy of a liquid on an object is related to the density of the liquid and the volume of the liquid displaced by the object, but has nothing to do with the object's mass, volume, gravity, shape, immersion depth, etc.

Applicable conditions: liquid (or gas).

(3) Principle of quadrature: "Exhaustion method". Another outstanding discovery of Archimedes is that the volume and surface area of ??a sphere are both 2/3 of the volume and surface area of ??a cylinder circumscribing the sphere.

Extended information:

The discovery of the ancient Greek scholar Archimedes' law has been widely used in various fields of human social production, and its influence is huge. According to the principle of buoyancy, the force exerted on an object partially or completely submerged in liquid is equal to the weight of the liquid displaced by the internal volume of the object. This is useful for calculating the density of the object and then designing and constructing submarines, ocean-going ships, and ships. , is of critical significance, so people use Archimedes' law more widely.

Archimedes' law: The net force exerted on an object immersed in a stationary fluid by the fluid is equal to the gravity of the fluid displaced by the object, and the direction is vertically upward. The formula is F buoyancy = G displaced fluid, and the formula can be further transformed into F buoyancy = ρ fluid × g × V displaced fluid. This law applies not only to liquids, but also to gases.