What Is a Pulley Block?

The pulley unit is a simple machine assembled by multiple moving pulleys and fixed pulleys, which can save effort or change the direction of force. The amount of effort of the pulley group is determined by the number of rope strands. The total weight of the weight and the moving pulley is borne by the n strands of rope. The force used to lift the weight is 1 / n of the total weight. Its mechanical efficiency is determined by the gravity of the object being pulled, the gravity of the moving pulley, and friction. A pulley is a small wheel with grooves around it, which can rotate around an axis. A simple machine ^[1] consisting of a disc with grooves that can rotate around the central axis and a flexible cable (rope, tape, steel cable, chain, etc.) that crosses the disc and can rotate around the central axis is called a pulley.

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Formula: s = nh. v rope = n * v F = (1 / n) * G total

s: the distance the free end of the rope moves. v rope: the speed at which the free end of the rope moves (rising / falling)

h: The height at which the weight is lifted. v: the speed at which the object moves (rises / falls)

n: the number of load-bearing rope segments (the rope connected to the moving pulley). Total G: weight + pulley weight (G object + G slide).

Secondly, the number of fixed pulleys is determined according to requirements. The principle is: general: two strands of rope are equipped with a moving pulley.

There are two types of pulleys: a fixed pulley and a movable pulley, which are combined into a pulley group, which can save effort and change the direction of the force.

Some middle school physics textbooks believe that using pulley units to transport or lift goods can only save effort, but not energy. The above conclusions of middle school physics textbooks have a great impact on engineers engaged in mechanical transmission design work. And various mechanical devices will frequently start, accelerate, decelerate, stop and other movements during use, and consume a lot of energy during various movements such as start, acceleration, deceleration, and stop. The above explains how to design or use the transmission system of transportation devices such as cars, trains, ships, etc. to make it the best energy-saving state. When vehicles and mechanical devices are used, the relationship between the number of segments of the pulley set or the transmission ratio of the reducer in various states is often related to energy saving. The quantity of goods is small.

The following analysis of two physical exercises shows that using a pulley set to tow objects can not only save effort, but also save energy by delivering more objects to their destination.

For a pulley set for moving objects in a horizontal direction

analyse as below:

An object M of mass m is placed on a horizontal plane, and the pulley M is connected to the object M through a rope. The number of segments of the rope to pull the object M is K, and the traction force of the rope is F. The power device is used to accelerate the object M along the horizontal plane from a static state. Movement, according to Newton's law of motion:

KF = ma2 (1)

Where a2 is the acceleration of the object M, and

a2 = a1 / K (2)

Where a1 is the acceleration of the rope at the input end of the pulley block. Solving the formulas (1) and (2) gives:

a1 = K2F / m (3)

The purpose of using the pulley set is to transport or lift a certain amount of goods to the destination. Everyone who is engaged in specific labor wants Dora to run quickly, that is, to save labor and quickly complete the work. In order to compare the difference between using the pulley group and not using the pulley group, the acceleration of the rope at the input end of the pulley group is a1 value when using the pulley group and without the pulley group. In this state, the power output by the power unit is equal. When the pulley group is not used (K = 1) The mass of the object M transported by the power unit is m , and the mass of the object M transported by the power unit when the pulley set is used is:

F / m = K2F / m (4)

After simplification, we can get:

m = K2m (5)

However, the distance that the power unit transports the object M when using the pulley unit is L / K when the pulley unit is not used. For comparison, the power unit in the two states is made to work K times respectively. In this way, the power unit using the pulley unit can Goods with a mass of K2m are transported to a distance of L, and power units without a pulley set are used to transport goods with a mass of Km by a distance of L. At this time, it can be seen by comparison that the mass M of the object transported by the power unit when the pulley is used The mass M of the object transported by the power unit is K times the pulley set.

When the frictional resistance f exists in the motion of the object M, then equation (1) becomes

KF-f = ma2 (6)

Where f = mg, is the coefficient of friction.

Solving equations (2) and (6), and bringing f = mg into:

a1 = K2F-Kmg / m (7)

Similarly, the acceleration of the rope at the input end of the pulley unit is a1 value when the pulley unit is used and when the pulley unit is not used. In this state, the power consumed by the power unit is equal. Let the mass of the object M transported by the power unit when the pulley unit is not used (K = 1) be m , the mass of the object M transported by the power unit when using the pulley set is m, then:

(F-mg) / m = (K2F-Kmg) / m (8)

After simplification, we can get:

m = K2Fm / (F + Kmg -mg) (9)

Similarly, the distance that the power unit transports the object M when the pulley unit is used is L / K when the pulley unit is not used. For convenience of comparison, the power unit in the two states is operated K times. In this way, the power unit of the pulley unit is used. A mass of K2Fm / (F + Kmg -mg) can be transported to a distance of L. The mass M of the object transported by the power unit when the pulley unit is used is the mass M of the object lifted by the power unit when the pulley unit is not used. KF / (F + Kmg-mg) times. That is to say, using a pulley set to tow objects, under certain conditions, not only saves energy on transport vehicles and mechanical transmissions, but also saves energy by delivering more objects to their destination.

Because transportation devices such as cars, trains, ships, etc., frequently start, accelerate, decelerate, and stop various movements during use, and consume a lot of energy during various movements such as start, acceleration, deceleration, and stop, The above conclusions can be theoretically used to guide and explain the design or use of transmission systems for transportation devices such as cars, trains, ships, etc. to make them in the best energy-saving state. For example, transportation devices such as cars, trains, ships, etc. can use a transmission system with a large transmission ratio during the start-up and acceleration phases, and sprint with full horsepower instead of using a transmission system with a small transmission ratio.

The analysis of the pulley unit or reducer that moves the traction object in the vertical direction is as follows:

An object M of mass m is suspended in the air, and the output end of the pulley set is connected to the object M through a rope. The number of segments to which the rope pulls the object M is K, and the traction force of the rope is F. The power device is used to make the object M start in a static state in the air. For upward acceleration motion, we can know from Newton's law of motion:

KF-mg = ma2 (10)

Where a2 is the acceleration of the object M, and

a2 = a1 / K (11)

Where a1 is the acceleration of the rope at the input end of the pulley block. Solving the formulas (11) and (12) gives:

a1 = K2F-Kmg / m (12)

In this state, the power output of the power unit is equal. If the mass of the object M transported by the power unit when the pulley unit is not used is m , and the mass of the object M transported by the power unit when the pulley unit is used is m, then:

(Fmg) / m = (K2F-Kmg) / m (13)

After simplification, we can get:

m = K2m / [1+ (K-1) mg / F] (14)

However, when using a pulley unit, the height of the object M is h / K when the pulley unit is not used. For comparison, the power unit in the two states is operated K times. In this way, the power unit using the pulley unit can Goods with a mass of K2m / [1+ (K-1) mg / F] are lifted to the height h. Without the power unit of the pulley set, the goods with the mass Km are lifted to the height h. It can be seen that the mass m of the object M lifted by the power unit when the pulley unit is used is K / [1+ (K-1) mg / F] times the mass M of the object M lifted by the power unit when the pulley unit is not used.

When the frictional resistance f exists in the motion of the object M, then equation (11) becomes

KF-mg-f = ma2 (15)

Where f = mg, is the coefficient of friction.

Solving equations (12) and (16), and bringing f = mg into:

a1 = K2F-Kmg-Kmg / m (16)

Similarly, the acceleration of the rope at the input end of the pulley group is a1 value when the pulley group is used and when the pulley group is not used. In this state, the power output by the power unit is equal. Let the mass of the object M that the power unit lift when the pulley group is not used is m When the mass M of the object lifted by the power unit is m, there are:

(Fmg-mg) / m = (K2F-Kmg-Kmg) / m (17)

After simplification, we can get:

m = K2Fm / (F + Kmg + Kmgmg-mg) (18)

Similarly, the height of the power unit M when using the pulley unit is h / K when the pulley unit is not used. For comparison, the power unit in the two states is operated K times. In this way, the power unit of the pulley unit is used. Goods with a mass of K2Fm / (F + Kmg + Kmgmg-mg) can be lifted to a distance of h, without using the power unit of the pulley unit, all cargo with a mass of Km can be lifted to h At this time, through comparison, it can be seen that the mass m of the object M lifted by the power unit when the pulley unit is used is KF / (F + Kmg + Kmgmg-mg) ) Times. That is to say, using a pulley set or a reducer to lift objects, under certain conditions, not only can save transportation vehicles and mechanical transmissions, but also save energy by lifting more objects to their destination.

As can be seen from the above analysis, for various longitudinal transport devices such as elevators and cranes, a transmission system with a large transmission ratio can be used during the start-up and acceleration phases, rather than a transmission system with a small transmission ratio.

According to the above analysis, it can be seen that the power unit can transport objects through pulley units or reducers, whether in the horizontal direction or the vertical direction, and can transport more goods to the destination under the condition of consuming certain energy.

Assembly of pulley blocks: pulley blocks

The pulley unit is made up of several fixed pulleys and movable pulleys, which can achieve the purpose of saving labor and changing the direction of force application. In use, how much effort is saved and how the rope is wound depends on the use of the pulley set. The moving pulley is borne by several ropes, and the force is a fraction of the total weight of the object and the moving pulley. The principle is: when n is an odd number, the rope driven pulley is the starting point. When using a moving pulley, there are three sections of rope to bear, and after each additional moving pulley, two sections of rope are added. For example: n = 5, two moving pulleys (3 + 2) are required. When n is an even number, the rope starts from the fixed pulley. At this time, all the moving pulleys only bear two ropes. For example: n = 4, two moving pulleys (2 + 2) are required.

Secondly, the number of fixed pulleys is determined according to the requirements. The principle is that one movable pulley is generally equipped with one fixed pulley. When the direction of force action is not required to be changed, the even-numbered rope can reduce one fixed pulley; to change the direction of force action, an additional fixed pulley needs to be added.

In summary, the design principles of the pulley unit can be summarized as: odd and even motion; once the motion is fixed, the even number decreases and the change direction increases.

One thing to keep in mind about the rope winding method is that the ropes cannot intersect. In fact, it is difficult to pull the rope by the pulley set. As long as you master the key, then it is not difficult to pull. Wrap around; on the other hand, if there are fewer pulleys, then you must follow the pulleys first; if there are as many as possible, you still have to rotate the pulleys first.

The fixed pulley can change the direction of the force, but cannot pull the animal with less effort. The moving pulley cannot change the direction of the force, but can pull the animal body with half the force. The pulley unit combines a fixed pulley and a movable pulley, which can change the direction of the force and pull the animal body with less effort. If you do not consider the extra work done in the use of the pulley block, the more you use the pulley, the more effort you save.