Chinese name
lever principle
Foreign name
lever principle
Another name
Lever balance condition
express
F 1 L 1=F2 L2。
presenter
Archimedes
Show time
About 245 BC
Applied discipline
natural science
area of application
Lever mechanics
area of application
Architecture, physics, machinery
Proposal in principle
Archimedes, an ancient Greek scientist, has a long-standing famous saying: "Give me a fulcrum and I can pry up the whole earth!" This sentence means the principle of leverage.
Archimedes first put forward the lever principle in the book On the Balance of Plane Figures. He first regarded some empirical knowledge in the practical application of leverage as "self-evident axioms", and then proceeded from these axioms, applied geometry, and obtained the principle of leverage through strict logical argumentation.
Archimedes
These axioms are:
(1) Hang equal weights at both ends of the weightless bar at the same distance from the fulcrum, and they will be balanced;
(2) Hang unequal weights at the same distance from the fulcrum at both ends of the weightless bar, and the heavy end will fall;
(3) Hang an equal weight at both ends of the weightless bar with different distances from the fulcrum, and the far end will incline downward;
(4) The function of one weight can be replaced by the function of several evenly distributed weights, as long as the position of the center of gravity remains unchanged. On the contrary, several evenly distributed weights can be replaced by a weight hanging from their center of gravity.
(5) The centers of gravity of similar figures are distributed in a similar way. ...
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." Archimedes' research on lever not only stays in theory, but also makes a series of inventions according to this principle. It is said that he once used levers and pulley blocks to let ships parked on the beach enter the water smoothly. In the battle to defend Syracuse from the Roman navy, Archimedes used the lever principle to make long-range and short-range catapults, and used them to launch various missiles and boulders to attack the enemy, which once made the Romans stay outside Syracuse for three years.
Incidentally, there are also records about leverage in the history of China. Mozi in the Warring States period once summed up this law, and there are two special records about the principle of leverage in the Book of Mohism. These two articles elaborated the balance of leverage very comprehensively. There are equal arms and unequal arms inside; Some change the weight of both ends to make it biased, and some change the length of the two arms to make it biased. Such a record is also very valuable in the history of world physics.
Conceptual analysis
edit
When using a lever, in order to save labor, a lever with a power arm longer than a resistance arm should be used; 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.
The fulcrum of the lever does not have to be in the middle. A system that satisfies the following three points is basically a lever: fulcrum, force point and force point.
The formula is written as follows: power× power arm = resistance× resistance arm, that is, F 1×L 1=F2×L2, which is a lever.
Power arm extension
Levers also have labor-saving levers and labor-saving levers, which have different functions. For example, there is an air pump that is pedaled by feet or a juicer that is pressed by hands, that is, a labor-saving lever (power arm >; Resistance arm); But we have to press it down for a distance, and the stressed end only moves a little. There is also a laborious lever. For example, the crane on the roadside, the fishing hook is at the tip of the whole pole, the fulcrum is at the end, and the hydraulic press is in the middle (torque >; Arm of force), this is a laborious lever, but it is hard to get that the middle point of force will move a considerable distance as long as it moves a short distance.
Both levers are useful, but it is necessary to evaluate whether it is necessary to save labor or range of motion. There is another thing called shaft, which can also be used as a lever, but the performance may sometimes be added with the calculation of rotation.
Archimedes, an ancient Greek scientist, famously said, "If you give me a fulcrum, I can pry up the earth", which is not only an inspiring aphorism, but also has a strict scientific basis.