Force is a part of the total weight of the object and the moving pulley.
Number, the principle is: 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.
Secondly, the number of crown blocks is determined according to the needs. The principle is: generally, two ropes are equipped with a moving pulley, and generally, a moving pulley is 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.
To sum up, the design principles of pulley blocks can be summarized as follows: (1) odd motion and even determination; Move a certain number, even number MINUS a certain number, change direction plus a certain number.
[Edit this paragraph] pulley
A simple machine that can rotate around the central axis consists of a grooved disc that can rotate around the central axis and a flexible cable (rope, adhesive tape, steel cable, chain, etc.). ) across the disk. Pulley is the deformation of lever, which belongs to lever simple machinery. In China, as early as the Warring States Period, there was a record about pulleys in the book Mo Jing. The pulley with the fixed central shaft is called the crown block, which is a deformed equal arm lever, and can change the direction of force without any effort. The pulley whose central axis moves with the weight is called the movable pulley, which is a deformed unequal arm lever, and can save half the force without changing the direction of the force. In practice, a certain number of moving pulleys and crown block are often combined into various pulley blocks. The pulley block can save labor and change the direction of force.
The differential pulley (commonly known as chain block) commonly used in factories is also a kind of pulley block. Pulley blocks are widely used in cranes, winches, elevators and other machinery.
There are two kinds of pulleys: crown block and moving pulley, which are combined to form a pulley block.
(1) crown block
The crown block is essentially an equal arm lever, which is labor-saving and effortless, but it can change the direction of force.
Characteristics of crown block
It is not labor-saving to pull the hook code through the crown block. Whether there is a crown block or not, the reading of the spring scale is the same. It can be seen that the direction of force can be changed easily by using the crown block. Many times, changing the direction of force will bring convenience to work.
Crown block principle
The crown block is essentially an equal arm lever, and the power L 1 and the resistance L2 arm are equal to the pulley radius. According to the lever balance condition, it can also be concluded that the crown block is not labor-saving.
(2) Move the pulley
The moving pulley is essentially a lever with a force arm twice as large as the resistance arm, which saves 1/2 force and spends 1 times more distance.
Characteristics of moving pulley
Using a moving pulley can save half the force and waste the distance. This is because when using the moving pulley, the hook code is hung by two ropes, and each rope only bears half the weight of the hook code. Although the use of moving pulley saves power, the distance of power moving is greater than the distance of hook code rising, that is, the distance is wasted.
Moving pulley principle
The moving pulley is essentially a lever, and its arm of force (L 1) is twice as big as the arm of resistance (L2).
(3) Pulley block
Pulley block: Pulley block consisting of crown block and driven pulley, which can save labor and change the direction of force.
The pulley block uses several lengths of rope to lift the object, and the force used to lift the object is a fraction of the total weight. The free end of the rope bypasses the moving pulley, but not the crown block.
Although using pulley block saves labor, it consumes distance, and the distance of power movement is greater than that of heavy objects.
Purpose of pulley block:
In order to save energy and change the direction of power, the crown block and the moving pulley can be combined into a pulley block.
Labor-saving size
When using the pulley block, the pulley block uses several pieces of rope to lift the object, and the force used to lift the object is a fraction of the weight of the object.
Characteristics of pulley block
It is easy to see that the pulley block is labor-saving, but it consumes distance-the distance of power moving is greater than the distance of goods rising.
[Edit this paragraph] pulley block principle
Some middle school physics textbooks think that using pulley blocks to transport or lift goods can only save labor, but not labor. The conclusions in the above physics textbooks for middle schools are very important for engaging in machinery.
Engineers who design mechanical transmission have great influence. Because vehicles such as cars, trains and ships and various mechanical devices will frequently start, accelerate, decelerate and stop in the process of use, and a lot of energy will be consumed in the process of starting, accelerating, decelerating and stopping, it is absolutely necessary to explain theoretically how to design or use the transmission system of vehicles such as cars, trains and ships to make them in the best energy-saving state. However, the above conclusions in middle school physics textbooks make mechanical engineers often ignore the relationship between the number of pulley blocks or the transmission ratio of reducers and energy saving when they are engaged in mechanical transmission design and guiding people to use transport vehicles and mechanical devices, resulting in high energy consumption and small amount of goods transported by many existing transport vehicles and mechanical transmission devices.
Through the analysis of two physical exercises, it is shown that pulling objects with pulley blocks can not only save labor, but also transport more objects to their destinations, saving energy.
The pulley block used to move in the horizontal direction pulls the object.
The analysis is as follows:
Put the object M with the mass of m on a horizontal plane and connect it with the object M by a pulley block through a rope. The number of knots of the rope pulling the object M is k, and the traction force of the rope is f. By using the power device, the object M accelerates along the horizontal plane from the static state, which is known from Newton's law of motion:
KF=ma2 ( 1)
Where a2 is the acceleration of the object m, and
a2=a 1/K (2)
Where a 1 is the rope acceleration at the input end of the pulley block, the solutions of (1) and (2) can be obtained:
a 1=K2F/m (3)
The purpose of using pulley blocks is to transport or lift a certain amount of goods to their destinations. Everyone engaged in a particular job wants Dora to run fast, that is, to finish the work quickly and easily. In order to compare the difference between using pulley block and not using pulley block, the rope acceleration at the input end of pulley block is a 1. In this state, the output power of the power plant is equal. Assuming that the mass m of the object conveyed by the power plant is m when the pulley block (k = 1) is used, there are
f/m′= K2F/m(4)
After simplification, you can get:
m = K2m′(5)
However, when the pulley block is used, when the pulley block is not used, the distance that the power device conveys the object M is L/K.. For the convenience of comparison, the power plants in two states are operated for k times respectively, so that the power plant with pulley block transports the goods with the mass of K2m'' to the distance L, and the power plant without pulley block transports all the goods with the mass of km' to the distance L. At this time, it can be seen from the comparison that the mass m transported by the power plant with pulley block is.
When there is frictional resistance F in the motion of the object M, the equation (1) becomes
KF-f=ma2 (6)
Where f = μ mg, μ is the friction coefficient.
Solve equations (2) and (6) and bring f = μ g into the available:
a 1=(K2F-Kμmg)/m (7)
Similarly, when the pulley block is used or not, the rope acceleration at the input end of the pulley block is a 1. In this state, the power consumed by the power device is equal. Assuming that the mass of the object M conveyed by the power device is m'(k = 1) when the pulley block is used and the mass of the object M conveyed by the power device is m, then:
(F- μ m ′ g)/m ′ = (K2F-kμ mg)/m (8)
After simplification, you can get:
M = K2FM ′/(f+kμ m ′ g-μ m ′ g) (9)
Similarly, when the pulley block is used, the distance that the power device transports the object M is L/K. For the convenience of comparison, the power devices in two states are operated k times respectively, so that the power device with pulley block can transport the goods with the mass of K2FM ′/(f+kμ m ′ g-μ m ′ g) to the L distance, and the power device without pulley block will have the mass of km ′. When the pulley block is used, the mass m of the object M conveyed by the power device is KF/(f+kμ m ′ g-μ m ′ g) multiplied by the mass of the object M ′ lifted by the power device when the pulley block is not used. That is to say, under certain conditions, transport vehicles and mechanical transmission devices can not only save labor, but also save energy by transporting more objects to their destinations.
Because cars, trains, ships and other vehicles will frequently start, accelerate, decelerate and stop in the process of use, and a lot of energy will be consumed in the process of starting, accelerating, decelerating and stopping, the above conclusions can be used to guide and explain the design or use of transmission systems of cars, trains, ships and other vehicles in theory, so as to make them in the best energy-saving state. For example, cars, trains, ships and other means of transportation can use a transmission system with a large transmission ratio at the start and acceleration stages and sprint at full speed, instead of using a transmission system with a small transmission ratio.
For the pulley block or reducer moving in the vertical direction, the analysis is as follows:
An object M with a mass of m is suspended in the air, and the output end of the pulley block is connected with the object M through a rope. The number of knots of the rope pulling the object M is k, and the traction force of the rope is f. By using the power device, the object M accelerates upward in the air from the static state, which is known from Newton's law of motion:
KF-mg=ma2 ( 10)
Where a2 is the acceleration of the object m, and
a2=a 1/K ( 1 1)
Where a 1 is the rope acceleration at the input end of the pulley block, and the solutions of (1 1) and (12) can be obtained:
a 1=(K2F-Kmg)/m ( 12)
The purpose of using pulley blocks is to transport or lift a certain amount of goods to their destinations. Everyone engaged in a particular job wants Dora to run fast, that is, to finish the work quickly and easily. In order to compare the difference between using pulley block and not using pulley block, the rope acceleration at the input end of pulley block is a 1. In this state, the output power of the power plant is equal. Assuming that the object mass m conveyed by the power plant is m' and the object mass m conveyed by the power plant is m when the pulley block is used, there are:
(F-m′g)/m′=(K2F-Kmg)/m( 13)
After simplification, you can get:
m = K2m′/〔 1+(K- 1)m′g/F〕( 14)
However, when the pulley block is used, the height of the object M lifted by the power device is h/K when the pulley block is not used. For comparison, the power devices of the two states are operated for k times respectively, so that the goods with the mass of K2m ′/[1+(k-1) m ′ g/f] can be lifted to the height of h by the power devices of the pulley block. At this time, by comparison, it can be seen that the mass m of the object M lifted by the power device when the pulley block is used is k/[1+(k-1) M' g/f] times that of the object M' lifted by the power device when the pulley block is not used.
When there is frictional resistance F in the motion of the object M, the formula (1 1) becomes
KF-mg-f=ma2 ( 15)
Where f = μ mg, μ is the friction coefficient.
Solve equations (12) and (16) to bring f = μ g into the available:
a 1 =(K2F-Kmg-kμmg)/m( 16)
Similarly, the acceleration of the rope at the input end of the pulley block is a 1 when the pulley block is used or not. In this state, the output power of the power plant is equal, assuming that the object mass m lifted by the power plant is m' when the pulley block is not used, and the object mass m lifted by the power plant is m when the pulley block is used, there are:
(f-m ′ g-micron ′ g)/m ′ = (k2f-kmg-kμ mg)/m (17)
After simplification, you can get:
M = k2fm ′/(f+km ′ g+kμ m ′ g-m ′ g-micron ′ g) (18)
Similarly, when the pulley block is used, the height of the object M lifted by the power device is h/K when the pulley block is not used. For the convenience of comparison, the power devices in the two states are operated for k times respectively, so that the goods with the mass of K2Fm'/(F+Km'g+Kμm'g-m'g- micron' g) can be lifted to the h distance by using the power devices of the pulley block. At this time, by comparison, it can be seen that the mass m of the object M lifted by the power device when the pulley block is used is KF/(f+km ′ g+kμ m ′ g-m ′ g-micron ′ g) times that of the object M ′ lifted by the power device when the pulley block is not used. That is to say, using pulleys or reducers to lift objects can not only save manpower for transport vehicles and mechanical transmission devices under certain conditions, but also save energy by lifting more objects to their destinations.
From the above analysis, it can be seen that for all kinds of longitudinal transportation equipment such as elevators and cranes, the transmission system with large transmission ratio can be used in the start-up and acceleration stages, rather than the transmission system with small transmission ratio.
From the above analysis, it can be seen that the power plant can transport objects through pulleys or reducers in both horizontal and vertical directions, and can transport more goods to the destination with certain energy consumption.
Assembly of pulley block: pulley block
The pulley block is composed of several crown blocks and moving pulleys, which can save labor and change the direction of force. In use, how much labor is saved and how the rope is wound depends on the use effect of the pulley block. The moving pulley is carried by two ropes, that is, each rope carries the object and the moving pulley.
Force is a part of the total weight of the object and the moving pulley.
Number, the principle is: 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.
Secondly, the number of crown blocks is determined according to the needs, and the principle is: 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.
To sum up, the design principles of pulley blocks can be summarized as follows: (1) odd motion and even determination; Move a certain number, even number MINUS a certain number, change direction plus a certain number.
As for the rope laying method, one thing to remember is that the ropes can't intersect. In fact, the pulley block is the most difficult to pull the rope. As long as you master the key, it is not difficult to pull it up. If there are several pulleys in the pulley block, pull them out of the crown block first. On the contrary, if you want fewer crown blocks, start with moving pulleys; If it's the same, you still have to go around the pulley first.