As shown below, it is an equal arm rod. If a semicircular plate is added above and below it, and a shaft is installed at the fulcrum to make it rotate, this is a pulley.
Rod model of pulley
So the pulley is essentially a rotatable lever. The balance condition of lever also applies to pulley.
There are three kinds of pulleys: crown block: its shaft is fixed or its position remains unchanged during rotation. Moving pulley: in the process of rotation, its shaft can move with the object, or the position of the shaft changes constantly. Pulley: A combination of two or more pulleys.
Characteristics of the crown block: According to the lever principle analysis, excluding friction, F 1l 1=F2l2, because L 1=L2, therefore, F 1=F2, the essence of the crown block is an equal-arm lever, which can change the direction of power without effort.
Rod model of crown block
Features of the moving pulley: As shown in the following figure, regardless of the weight and friction of the moving pulley, it is analyzed according to the lever principle: F 1l 1=F2l2, because L 1=2L2, the essence of the moving pulley is that the power arm is twice as labor-saving as the resistance arm. Using a moving pulley can save half the force, but it can't change the direction of the force. The fulcrum of the moving pulley is variable. If only the friction between shafts is ignored, the pulling force F= (G +G) /2.
Rod model of moving pulley
Features of pulley block: Using pulley block can save labor and sometimes change the direction of power. Excluding the friction between shafts and the gravity of the moving pulley, the pulling force f = g/n. If only the friction between shafts is ignored, the pulling force f = (g+g)/n..
The pulley block is composed of several crown blocks and moving pulleys, which can save labor and change the direction of force. In use, the degree of labor saving determines the winding mode of the rope.
Representative pulley block
The principle is that when n is odd, the rope is driven by pulley. When using a moving pulley, you have to bear three sections of rope, and then you add two sections of rope for each additional moving pulley. If n=5, two movable pulleys (3+2) are needed. When n is an even number, the wire rope starts from the crown block. At this time, all the moving pulleys are only borne by two ropes. If n=4, two movable pulleys (2+2) are needed.
Determine the number of crown blocks as required. The principle is: generally, two ropes are equipped with a moving pulley, and a moving pulley is generally equipped with a crown block. When there is no need to change the direction of force, even-numbered ropes can reduce one crown block; To change the direction of force, you need to add a crown block.
The design principles of pulley block can be summarized as follows: odd motion and even determination; Move a certain number, even number MINUS a certain number, change direction plus a certain number.
On the basis of the above knowledge, we can discuss the physical principle of pulley labor saving. For the crown block, what is discussed above is an ideal machine. When the crown block is actually used, the friction between the rotating shaft and the wire rope and pulley should be considered. Therefore, using the crown block cannot save labor, which is not discussed in this article.
The labor-saving principle of pulley block is the same as that of moving pulley, but the number of moving pulleys is different. Therefore, this paper does not discuss the pulley block, but only the typical pulley-moving pulley.
Firstly, the principle of lever can be used to analyze the labor-saving principle of moving pulley.
If it is an ideal moving pulley, regardless of the weight and friction of the moving pulley, according to the lever principle analysis, the power arm is twice as large as the resistance arm, and using the moving pulley can save half the force. Using a moving pulley, the distance of power movement is greater than that of heavy objects.
Secondly, the labor-saving principle of moving pulley is analyzed from the perspective of static balance.
Without considering the friction, when the moving pulley is stationary or moving in a straight line at a constant speed in the vertical direction, the moving pulley is balanced by four static forces, namely, the self-weight of the moving pulley (G motion), the pulling force of the heavy object on the moving pulley (equal to the weight of the object G) and the pulling force f of the two ropes on the moving pulley. Because the pulling force f of two ropes on the moving pulley is equal regardless of friction, there is an equilibrium equation: 2 F= G object +G motion, and the pulling force F= (G object +G motion) /2.
G motion is small relative to G object, so F is smaller than G, that is, moving pulley saves effort.
Thirdly, the labor-saving principle of moving pulley is discussed from the perspective of mechanical working principle.
Principle of mechanical work: no work can be saved by using any machinery. Understand its meaning in the following situations:
1. When you finish something, the work you do is a constant value, no matter what method you adopt. Labor-saving will inevitably cost distance; Hard work is bound to save distance.
2, regardless of friction and mechanical self-weight: the work done by lifting things with manpower F is equal to the work done by lifting things mechanically.
3, regardless of friction and mechanical self-weight: the work done by power F is equal to the work done by resistance.
4. If friction and mechanical self-weight are considered, G motion (actual machinery): the work done by power F is equal to the work done by machinery to overcome all resistance.
5. If we consider the friction and the self-weight of machinery (that is, the actual machinery), using machinery can not only save labor, but also do more extra work.
So for an ideal machine, W=FS=Gh, and since S=2h and F=G/2, this is the principle that the moving pulley saves half the effort.
If only the self-weight of the machine is considered without considering the friction force, then FS=Gh+G moves H. Since S=2h, F= (G object +G moves) /2. G moving is very small compared with G object, and moving pulley is relatively labor-saving.
If friction and mechanical self-weight are considered, G-motion: The work done by power is equal to the work done by machinery to overcome all resistance. At this time, η= Gh/FS, because S=2h, so F=G/2η, η is the mechanical efficiency, which is always less than 1, that is, the moving pulley still saves effort.
Special reminder: not all moving pulleys can save labor. Below, the moving pulley on the right is laborious.
Pulley is a kind of deformed lever, which belongs to a simple lever machine and has a wide range of uses. In China, as early as the Warring States Period, there were records about pulleys in the book Mo Jing. Pulley blocks are widely used in cranes, winches, elevators and other machinery. The differential pulley (commonly known as chain block) commonly used in factories is also a kind of pulley block.
Archimedes explained the kinematics theory of pulley in detail. It is said that Archimedes once pulled a seagoing ship full of goods and passengers with a composite pulley alone. In the 1st century A.D., Hong analyzed and wrote the theory about compound pulleys, and proved that the ratio of load to acting force is equal to the number of rope segments bearing load, that is, the pulley principle.