How to Prove Lever Theorem by Mathematical Method
I think it can be understood as follows: we know that any machine is labor-saving, so it is impossible for a lever to save labor. According to the functional relationship, how much work has been done and how much energy has been transformed. For example, if we lift a stone with a lever, it is no different from lifting it with our hands. Suppose that in an ideal situation, no extra work is done by using the lever. In order to save effort, you should use a lever with a power arm longer than a resistance arm; If you want to save distance, you should use a lever with a force arm shorter than a resistance arm. Therefore, the use of levers can save manpower and distance. However, if you want to save energy, you must move more distance; If you want to move a shorter distance, you must work harder. It is impossible to save energy and move the distance. It is from these axioms that Archimedes discovered the lever principle on the basis of the "center of gravity" theory, that is, "when two heavy objects are in equilibrium, their distance from the fulcrum is inversely proportional to their weight. This also conforms to W=FS and conservation of energy.