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Leverage principle

Introduction to levers

If an object can rotate around a fixed point under the action of force, it is called a lever. In life, the lever can be made straight or curved according to needs, but it must be an object. Archimedes first proposed the lever principle in his book "On the Balance of Plane Figures". He first regarded some empirical knowledge in the practical application of levers as "self-evident axioms", and then based on these axioms, he used geometry to derive the lever principle through rigorous logical argumentation. These axioms are: (1) Hang equal weights on both ends of a weightless rod at equal distances from the fulcrum, and they will balance; (2) Hang both ends of a weightless rod at equal distances from the fulcrum. If there are unequal weights, the heavier end will tilt downward; (3) If equal weights are hung on both ends of a weightless rod at unequal distances from the fulcrum, the far end will tilt downward; (4) The effect of a heavy object This can be replaced by the action of several evenly distributed weights, as long as the position of the center of gravity remains unchanged. On the contrary, several uniformly distributed weights can be replaced by one weight suspended at their center of gravity; the center of gravity of the figure is distributed in a similar way... It is from these axioms that on the basis of the "center of gravity" theory , Archimedes also discovered the lever principle, that is, "When two heavy objects are balanced, their distance from the fulcrum is inversely proportional to their weight." Archimedes' research on levers not only stayed in theory, but also based on this principle. Made a series of inventions. It is said that he once used levers and pulleys to successfully launch a mast ship parked on the beach. In the battle to defend Syracuse from the Roman navy, Archimedes used the lever principle to create long and short slings, and used it to shoot various missiles and boulders to attack the enemy. He once blocked the Romans in Syracuse. It lasted for 3 years outside the ancient city. It should also be mentioned here by the way that there are long records of leverage in the history of our country. The Mohists of the Warring States Period once summarized the laws in this area, and there are two articles specifically recording the principle of leverage in the "Mo Jing". 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. Such records are also very valuable in the history of world physics.

Lever definition

A lever is a simple machine. An object that can rotate around a fixed point under the action of force is a lever. The lever does not have to be straight, it can also be curved, but it must be ensured. The lever in the physics book

is an object. Seesaws, scissors, wrenches, pry bars, etc. are all levers. The pulley is a deformed lever. The essence of the fixed pulley is an equal-arm lever, and the essence of the movable pulley is a lever whose power arm is twice the resistance arm.

Lever composition

People usually call an object that rotates around a fixed point under the action of force a lever. Composition: fulcrum, an object Fulcrum: The fixed point around which the lever rotates is called the fulcrum.

The fixed point around which the lever rotates is called the fulcrum. The force that causes the lever to rotate is called power (the point where the force is applied is called the power point). The force that prevents the lever from rotating is called resistance (the point where the force is applied is called the resistance effect). point) When the effects of power and resistance on the lever's rotation cancel each other out, the lever will be in a state of equilibrium. This state is called lever balance, but lever balance is not a balance of force. Note: When analyzing the problem of lever balance, you cannot just judge based on the size of the force. You must consider basic knowledge to solve the problem in a well-founded way. Do not solve the problem based on subjective feelings. Whether the lever is stationary or rotating at a constant speed is called lever balance. Fixed pulley and movable pulley

The straight line passing through the action point of the force in the direction of the force is called the line of action of the force. The vertical distance L1 from the fulcrum O to the line of action of the power F1 is called the distance of the power arm from the fulcrum O to the resistance F2. The vertical distance L2 of the line of action is called the condition of the resistance arm lever balance (text expression): Power × Power Arm = Resistance × Resistance Arm Formula: F1 × L1 = F2 × L2 To be a lever, a hard rod must not only have a strong effect , and must be able to rotate around a fixed point. Without any of these conditions, a hard rod cannot become a lever. For example, a wine bottle screwdriver cannot be called a lever when it is not in use. Power and resistance are relative. Whether it is power or resistance, the force-receiving object is a lever, and the object acting on the lever is a force-exerting object. The key concepts of the moment arm: 1: The vertical distance must not be understood as the fulcrum to the force The length of the action point. 2: The moment arm is not necessarily on the lever.

The three elements of the moment arm: braces (or represented by |→←|), letters, and vertical symbols

Equilibrium conditions

When using a lever, if the lever is stationary or moves at a constant speed around the fulcrum Turn, then the lever is in equilibrium. Power arm x power = resistance arm x resistance, that is, L1 Dependent on the direction of action. If the power arm is n times the resistance arm, the power is 1/n of the resistance. Leverage principle

"Big head sinking" The longer the power arm, the more effort it takes, and the longer the resistance arm, the more effort it takes. Effort-saving lever distance ;Effortless lever saves distance. The equal-arm lever is neither labor-saving nor labor-intensive. You can use it for weighing. For example: balance. In many cases, the lever is tilted and stationary because the lever is acted upon by several balancing forces.

Classification of levers

Category 1: The fulcrum is between the power point and the resistance point. It is called the first type of leverage. It may be labor-saving or labor-intensive, mainly determined by the position of the fulcrum, or the length of the arm. The power arm and the resistance arm are the same length, so this type of lever is an equal-arm lever. Examples: seesaw, balance, etc. Category 2: The resistance point is between the power point and the fulcrum. It is called the second type of leverage. Since the power arm is always larger than the resistance arm, it is a labor-saving lever pulley block

lever. Examples: nutcrackers, doors, staplers, diving boards, wrenches, (beer) bottle openers, (carrying cement, bricks) trolleys. Category 3: The power point is between the fulcrum and the resistance point. It is called the third type of leverage. The characteristic is that the power arm is shorter than the resistance arm, so this type of lever is a laborious lever, but it can save distance. Examples: tweezers, arms, fishing rods, kayak paddles, jaws, shovels, brooms, clubs, hairdressing scissors, and other instruments that use one hand as the fulcrum and the other hand as the power. In addition, tools such as axles are also deformed levers. Let’s take the simplest fixed pulley, which is similar to the first type of lever. The axis of the pulley is like the fulcrum, and the pulling force of the objects at both ends is like the force exerted by the two ends of the lever. If the pulley is a perfect circle, the force arm and resistance The arms will both be the radius of the circle.

Compound lever

A compound lever is a set of levers coupled together. The resistance of the previous lever will immediately become the power of the following lever. Almost all scales use some kind of compound lever mechanism. Other common examples include nail clippers and piano keyboards. In 1743, the inventor John Wheat of Birmingham, England, contributed the idea of ??a compound lever when designing a weighing scale. The weighing scale he designed first used four levers to transfer loads.

Lever in life

A lever is a simple machine; a hard rod (preferably not bendable and very light) can be used as a lever. In the picture above, the square represents the weight, the circle represents the support point, and the arrow represents the use. So, can you see it? In the right lever experiment

the downward lever is an equal-arm lever; the second is that the focus is in the middle, the power arm is larger than the resistance arm, and it is a labor-saving lever; the third is that the force point is in the middle, and the power arm is smaller than The resistance arm is the effort lever. Effortless levers such as: hair scissors, tweezers, fishing rods...levers may be labor-saving, labor-intensive, or neither labor-saving nor labor-intensive. This depends on the distance between the force point and the fulcrum: the farther the force point is from the fulcrum, the less effort it takes, and the closer it is, the more effort it takes; it also depends on the distance between the key point (resistance point) and the fulcrum: the closer the key point is to the fulcrum, the less effort it takes, and the farther it is, the more effort it takes. Effortless; if the key point and the force point are the same distance from the fulcrum, such as a fixed pulley and a balance, there will be no effort or effort, but the direction of the force will be changed. Labor-saving levers such as bottle openers, juicers, nutcrackers... This kind of lever must have a force point closer to the fulcrum than the key point, so it is always labor-saving. If we use flower scissors (the blade is shorter) and foreign scissors (the blade is longer) to cut cardboard, the flower scissors are more labor-saving but time-consuming; while the foreign cutting scissors are labor-intensive but time-saving. There is no lever that saves both effort and distance. Application of lever 1. Cutting hard objects requires greater force to cut hard objects, which means the resistance is greater. Use scissors with a longer power arm and a shorter resistance arm. 2. Cutting paper or cloth: You can cut soft objects such as paper or cloth with less force, which means the resistance is smaller. At the same time, in order to speed up the shearing speed, the knife edge should be longer. Use scissors with a shorter power arm and a longer resistance arm.

3. Cut branches When pruning branches, on the one hand, the branches are hard, which requires the power arm of the scissors to be long and the resistance arm to be short; on the other hand, in order to speed up the pruning speed and make neat cuts, the scissors blades must be long. Use scissors with longer power arms, shorter resistance arms, and longer blades.