Movable and fixed blocks. Simple mechanisms. Block Fixed block
Blocks are used to lift loads. The block is a wheel with a groove, mounted in a holder. A rope, cable or chain is passed through the block chute. motionless they call such a block, the axis of which is fixed and when lifting loads it does not rise or fall (Fig. 1, a, b).
A fixed block can be considered as an equal-arm lever, in which the arms of the applied forces are equal to the radius of the wheel. Consequently, it follows from the rule of moments that a stationary block does not provide any gain in force. It allows you to change the direction of the force.
Figure 2, a, b shows moving block(the axis of the block rises and falls along with the load). Such a block rotates about the instantaneous axis O. The moment rule for it will have the form
Thus, the movable block gives a double gain in strength.
Usually in practice a combination of a fixed block and a movable one is used (Fig. 3). The fixed block is used for convenience only. By changing the direction of the force, it allows, for example, to lift a load while standing on the ground.
Block is a device shaped like a wheel with a groove through which a rope, cable or chain is passed. There are two main types of blocks - movable and fixed. For a fixed block, the axis is fixed and does not rise or fall when lifting loads (Fig. 54), while for a movable block the axis moves along with the load (Fig. 55).
A stationary block does not provide a gain in strength. It is used to change the direction of a force. So, for example, by applying a downward force to a rope thrown over such a block, we force the load to rise upward (see Fig. 54). The situation is different with a moving block. This block allows a small force to balance a force that is 2 times greater. To prove this, let's look at Figure 56. By applying force F, we strive to rotate the block around an axis passing through point O. The moment of this force is equal to the product Fl, where l is the arm of force F, equal to the diameter of the OB block. At the same time, the load attached to the block with its weight P creates a moment equal to where is the arm of the force P equal to the radius of the block OA. According to the moment rule (21.2)
Q.E.D.
From formula (22.2) it follows that P/F = 2. This means that the gain in power obtained using the moving block is equal to 2. The experiment depicted in Figure 57 confirms this conclusion.
In practice, a combination of a moving block and a fixed one is often used (Fig. 58). This allows you to change the direction of the force impact with a simultaneous double gain in strength. 
To obtain a greater gain in strength, a lifting mechanism called chain hoist. The Greek word “pulley” is formed from two roots: “poly” - a lot and “spao” - pull, so in general it turns out to be “many pull”.
The pulley is a combination of two clips, one of which consists of three fixed blocks, and the other of three movable blocks (Fig. 59). Since each of the moving blocks doubles the traction force, in general the pulley gives a six-fold gain in strength. 
1. What two types of blocks do you know? 2. What is the difference between a movable block and a fixed one? 3. For what purpose is a fixed block used? 4. What is the movable block used for? 5. What is a chain hoist? What gain in strength does it provide?
Bibliographic description: Shumeiko A.V., Vetashenko O.G. Modern look on a simple “block” mechanism, studied in physics textbooks for grade 7 // Young scientist. 2016. No. 2. P. 106-113..07.2019).
Physics textbooks for grade 7, when studying a simple block mechanism, interpret winning in different ways force when lifting a load from using this mechanism, for example: in Peryshkin's textbook A. B. winnings in strength is achieved with using the wheel of the block, on which the forces of the lever act, and in Gendenstein's textbook L. E. the same winnings are obtained with using a cable, which is subject to the tension force of the cable. Various textbooks, various items And different forces - to receive winnings in force when lifting a load. Therefore, the purpose of this article is to search for objects and strength, with through which the winnings are obtained force, when lifting a load with a simple block mechanism.
First, let’s take a look and compare how gains in strength are obtained when lifting a load with a simple block mechanism, in physics textbooks for the 7th grade. For this purpose, we will place excerpts from textbook texts with the same concepts in a table for clarity.
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Peryshkin A.V. Physics. 7th grade. § 61. Application of the lever equilibrium rule to the block, pp. 180–183. |
Gendenshtein L. E. Physics. 7th grade. § 24. Simple mechanisms, pp. 188–196. |
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"Block It is a wheel with a groove, mounted in a holder. A rope, cable or chain is passed through the block gutter. "Fixed block they call such a block the axis of which is fixed and does not rise or fall when lifting loads (Fig. 177). A fixed block can be considered as an equal-armed lever, in which the arms of forces are equal to the radius of the wheel (Fig. 178): OA=OB=r. Such a block does not provide a gain in strength (F1 = F2), but allows you to change the direction of the force." |
“Does a stationary block give you a gain in strength? ...in Fig. 24.1a the cable is tensioned by a force applied by the fisherman to the free end of the cable. The tension force of the cable remains constant along the cable, so from the side of the cable to the load (fish ) a force of the same magnitude acts. Therefore, a stationary block does not provide a gain in strength. 6.How can you gain strength using a fixed block? If a person lifts yourself, as shown in Fig. 24.6, then the person’s weight is distributed equally into two parts of the cable (on opposite sides of the block). Therefore, a person lifts himself by applying a force that is half his weight." |
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« Movable block- this is a block whose axis rises and falls along with the load (Fig. 179).
Figure 180 shows the lever corresponding to it: O is the fulcrum of the lever, AO - arm of force P and OB - arm of force F. Since the OB arm is 2 times larger than the OA arm, then the force F is 2 times less than the force P: F=P/2. Thus, the movable block gives a gain offorce 2 times". |
"5. Why does a moving block give a win inin forcetwice? When the load is lifted uniformly, the moving block also moves uniformly. This means that the resultant of all forces applied to it is zero. If the mass of the block and the friction in it can be neglected, then we can assume that three forces are applied to the block: the weight of the load P, directed downwards, and two identical tension forces of the cable F, directed upwards. Since the resultant of these forces is zero, then P = 2F, that is the weight of the load is 2 times the tension force of the cable. But the tension force of the cable is precisely the force that is applied when lifting the load with the help of a moving block. Thus we have proven that the movable block gives a gain in force 2 times". |
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“Usually in practice they use a combination of a fixed block and a movable one (Fig. 181). The fixed block is used for convenience only. It does not give a gain in strength, but it changes the direction of the force, for example, it allows you to lift a load while standing on the ground.
Fig. 181. A combination of movable and fixed blocks - a chain hoist." |
“12.Figure 24.7 shows the system blocks. How many movable blocks does it have and how many fixed ones? What gain in strength does such a system of blocks give if friction and can the mass of the blocks be neglected? .
Fig.24.7. Answer on page 240: “12. Three moving blocks and one fixed; 8 times." |
Let’s summarize the review and comparison of texts and pictures in textbooks:
The proof of obtaining a gain in strength in the textbook by A. V. Peryshkin is carried out on the wheel of the block and the acting force is the force of the lever; when lifting a load, a stationary block does not provide a gain in strength, but a movable block provides a 2-fold gain in force. There is no mention of a cable on which a load hangs on a fixed block and a movable block with a load.
On the other hand, in the textbook by Gendenstein L.E., the proof of the gain in force is carried out on a cable on which a load or a movable block with a load hangs and the acting force is the tension force of the cable; when lifting a load, a stationary block can give a 2-fold increase in strength, but there is no mention in the text of the lever on the block wheel.
A search for literature describing the gain in force using a block and a cable led to the “Elementary Textbook of Physics”, edited by Academician G. S. Landsberg, in §84. Simple machines on pp. 168–175 are given descriptions of: “simple block, double block, gate, pulley and differential block.” Indeed, by its design, “a double block gives a gain in strength when lifting a load, due to the difference in the length of the radii of the blocks” with the help of which the load is lifted, and “a pulley block gives a gain in strength when lifting a load, due to the rope , on several parts of which a load hangs.” Thus, it was possible to find out why a block and a cable (rope) give a gain in strength when lifting a load, but it was not possible to find out how the block and cable interact with each other and transfer the weight of the load to each other, since the load can be suspended on a cable , and the cable is thrown over the block or the load can hang on the block, and the block hangs on the cable. It turned out that the tension force of the cable is constant and acts along the entire length of the cable, so the transfer of the weight of the load by the cable to the block will be at each point of contact between the cable and the block, as well as the transfer of the weight of the load suspended on the block to the cable. To clarify the interaction of the block with the cable, we will conduct experiments to obtain a gain in force with a moving block when lifting a load, using the equipment of a school physics classroom: dynamometers, laboratory blocks and a set of weights in 1H (102 g). Let's start the experiments with a moving block, because we have three different versions of obtaining a gain in strength with this block. The first version is “Fig.180. A moving block as a lever with unequal arms" - textbook by A. V. Peryshkin, the second "Fig. 24.5... two equal tension forces of the cable F" - according to the textbook by L. E. Gendenstein and finally the third "Fig. 145. Pull Block" . Lifting a load with a movable clip of a pulley on several parts of one rope - according to the textbook by G. S. Landsberg.
Experience No. 1. "Fig. 183"
To carry out experiment No. 1, obtaining a gain in strength on the movable block “with a lever with unequal shoulders OAB Fig. 180” according to the textbook by A. V. Peryshkin, on the movable block “Fig. 183” position 1, draw a lever with unequal shoulders OAB, as in “Fig. 180”, and begin lifting the load from position 1 to position 2. At the same instant, the block begins to rotate, counterclockwise, around its axis at point A, and point B, the end of the lever behind which the lift occurs, comes out beyond the semicircle along which the cable goes around the moving block from below. Point O - the fulcrum of the lever, which should be stationary, goes down, see “Fig. 183” - position 2, i.e. a lever with unequal shoulders OAB changes like a lever with equal shoulders (points O and B pass through the same paths).
Based on the data obtained in experiment No. 1 on changes in the position of the OAB lever on the moving block when lifting a load from position 1 to position 2, we can conclude that the representation of the moving block as a lever with unequal arms in “Fig. 180”, when lifting load, with rotation of the block around its axis, corresponds to a lever with equal arms, which does not provide a gain in strength when lifting the load.
We will begin experiment No. 2 by attaching dynamometers to the ends of the cable, on which we will hang a moving block with a load weighing 102 g, which corresponds to a gravity force of 1 N. We will fix one of the ends of the cable on a suspension, and using the other end of the cable we will lift the load on the moving block. Before the ascent, the readings of both dynamometers were 0.5 N each; at the beginning of the ascent, the readings of the dynamometer for which the ascent occurred changed to 0.6 N, and remained so during the ascent; at the end of the ascent, the readings returned to 0.5 N. The readings of the dynamometer, fixed for a fixed suspension did not change during the rise and remained equal to 0.5 N. Let us analyze the results of the experiment:
- Before lifting, when a load of 1 N (102 g) hangs on a movable block, the weight of the load is distributed over the entire wheel and transferred to the cable, which goes around the block from below, using the entire semicircle of the wheel.
- Before lifting, the readings of both dynamometers are 0.5 N, which indicates the distribution of the weight of a load of 1 N (102 g) into two parts of the cable (before and after the block) or that the tension force of the cable is 0.5 N, and is the same along the entire length of the cable (the same at the beginning, the same at the end of the cable) - both of these statements are true.
Let's compare the analysis of experiment No. 2 with the textbook versions about obtaining a 2-fold gain in strength using a moving block. Let's start with the statement in the textbook by Gendenstein L.E. “... that three forces are applied to the block: the weight of the load P, directed downward, and two identical tension forces of the cable, directed upward (Fig. 24.5).” It would be more accurate to say that the weight of the load in “Fig. 14.5" was distributed into two parts of the cable, before and after the block, since the tension force of the cable is one. It remains to analyze the signature under “Fig. 181” from the textbook by A. V. Peryshkin “Combination of movable and fixed blocks - pulley block.” A description of the device and the gain in strength when lifting a load with a pulley is given in the Elementary Textbook of Physics, ed. Lansberg G.S. where it is said: “Each piece of rope between the blocks will act on a moving load with a force T, and all pieces of rope will act with a force nT, where n is the number of separate sections of rope connecting both parts of the block.” It turns out that if we apply to “Fig. 181” the gain in force with a “rope connecting both parts” of the pulley from the Elementary Textbook of Physics by G. S. Landsberg, then the description of the gain in force with a moving block in “Fig. 179” and, accordingly, Fig. 180" would be an error.
Having analyzed four physics textbooks, we can conclude that the existing description of how a simple block mechanism produces gains in force does not correspond to the real state of affairs and therefore requires a new description of the operation of a simple block mechanism.
Simple lifting mechanism consists of a block and a cable (rope or chain).
The blocks of this lifting mechanism are divided into:
by design into simple and complex;
according to the method of lifting loads into movable and stationary ones.
Let's start getting acquainted with the design of blocks with simple block, which is a wheel rotating around its axis, with a groove around the circumference for a cable (rope, chain) Fig. 1 and it can be considered as an equal-armed lever in which the arms of forces are equal to the radius of the wheel: OA=OB=r. Such a block does not provide a gain in strength, but allows you to change the direction of movement of the cable (rope, chain).
Double block consists of two blocks of different radii, rigidly fastened together and mounted on common axis Fig.2. The radii of the blocks r1 and r2 are different and, when lifting a load, they act like a lever with unequal shoulders, and the gain in force will be equal to the ratio of the lengths of the radii of the block of larger diameter to the block of smaller diameter F = Р·r1/r2.
Gate consists of a cylinder (drum) and a handle attached to it, which acts as a block large diameter, The gain in force given by the collar is determined by the ratio of the radius of the circle R described by the handle to the radius of the cylinder r on which the rope is wound F = Р·r/R.
Let's move on to the method of lifting a load with blocks. From the design description, all blocks have an axis around which they rotate. If the axis of the block is fixed and does not rise or fall when lifting loads, then such a block is called fixed block single block, double block, gate.
U moving block the axle rises and falls together with the load (Fig. 10) and it is intended mainly to eliminate the bending of the cable at the place where the load is suspended.
Let's get acquainted with the device and method of lifting a load; the second part of a simple lifting mechanism is a cable, rope or chain. The cable is made of steel wires, the rope is made of threads or strands, and the chain consists of links connected to each other.
Methods for hanging a load and gaining strength when lifting a load with a cable:
In Fig. 4, the load is fixed at one end of the cable, and if you lift the load by the other end of the cable, then to lift this load you will need a force slightly greater than the weight of the load, since a simple block of gain in strength does not give F = P.
In Fig. 5, the worker lifts the load by a cable that goes around a simple block from above; at one end of the first part of the cable there is a seat on which the worker sits, and by the second part of the cable the worker lifts himself with a force 2 times less than his weight, because the worker’s weight was distributed into two parts of the cable, the first - from the seat to the block, and the second - from the block to the worker’s hands F = P/2.
In Fig. 6, the load is lifted by two workers using two cables and the weight of the load will be distributed equally between the cables and therefore each worker will lift the load with a force of half the weight of the load F = P/2.
In Fig. 7, workers are lifting a load that hangs on two parts of one cable and the weight of the load will be distributed equally between the parts of this cable (as between two cables) and each worker will lift the load with a force equal to half the weight of the load F = P/2.
In Fig. 8, the end of the cable, by which one of the workers was lifting the load, was secured on a stationary suspension, and the weight of the load was distributed into two parts of the cable, and when the worker lifted the load by the second end of the cable, the force with which the worker would lift the load was doubled less weight load F = P/2 and lifting the load will be 2 times slower.
In Fig. 9, the load hangs on 3 parts of one cable, one end of which is fixed and the gain in force when lifting the load will be equal to 3, since the weight of the load will be distributed over three parts of the cable F = P/3.
To eliminate the bend and reduce the friction force, a simple block is installed in the place where the load is suspended and the force required to lift the load has not changed, since a simple block does not provide a gain in strength, Fig. 10 and Fig. 11, and the block itself will be called moving block, since the axis of this block rises and falls along with the load.
Theoretically, a load can be suspended on an unlimited number of parts of one cable, but in practice they are limited to six parts and such a lifting mechanism is called chain hoist, which consists of fixed and movable clips with simple blocks, which are alternately wrapped around a cable, one end of which is fixed to a fixed clip, and the load is lifted using the other end of the cable. The gain in strength depends on the number of parts of the cable between the fixed and movable cages; as a rule, it is 6 parts of the cable and the gain in strength is 6 times.
The article examines the real-life interactions between the blocks and the cable when lifting a load. The existing practice in determining that “a fixed block does not give a gain in strength, but a movable block gives a gain in force by 2 times” erroneously interpreted the interaction of the cable and the block in lifting mechanism and did not reflect the full diversity of block designs, which led to the development of one-sided erroneous ideas about the block. Compared to the existing volumes of material for studying a simple block mechanism, the volume of the article has increased by 2 times, but this made it possible to clearly and intelligibly explain the processes occurring in a simple lifting mechanism not only to students, but also to teachers.
Literature:
- Pyryshkin, A.V. Physics, 7th grade: textbook / A.V. Pyryshkin. - 3rd ed., additional - M.: Bustard, 2014, - 224 p.,: ill. ISBN 978–5-358–14436–1. § 61. Application of the lever equilibrium rule to the block, pp. 181–183.
- Gendenstein, L. E. Physics. 7th grade. In 2 hours. Part 1. Textbook for educational institutions / L. E. Gendenshten, A. B. Kaidalov, V. B. Kozhevnikov; edited by V. A. Orlova, I. I. Roizen. - 2nd ed., revised. - M.: Mnemosyne, 2010.-254 p.: ill. ISBN 978–5-346–01453–9. § 24. Simple mechanisms, pp. 188–196.
- Elementary textbook of physics, edited by academician G. S. Landsberg Volume 1. Mechanics. Heat. Molecular physics. - 10th ed. - M.: Nauka, 1985. § 84. Simple machines, pp. 168–175.
- Gromov, S. V. Physics: Textbook. for 7th grade general education institutions / S. V. Gromov, N. A. Rodina. - 3rd ed. - M.: Education, 2001.-158 p.,: ill. ISBN-5–09–010349–6. §22. Block, pp.55 -57.
Key words: block, double block, fixed block, movable block, pulley block..
Annotation: Physics textbooks for the 7th grade, when studying a simple block mechanism, interpret in different ways the gain in force when lifting a load using this mechanism, for example: in the textbook by A. V. Peryshkin, the gain in force is achieved using the wheel of the block, on which the forces of the lever act, and in the textbook by Gendenstein L.E. the same gain is obtained using a cable, which is acted upon by the tension force of the cable. Different textbooks, different objects and different forces - to obtain a gain in strength when lifting a load. Therefore, the purpose of this article is to search for objects and forces with the help of which a gain in strength is obtained when lifting a load with a simple block mechanism.
Most often, simple mechanisms are used to gain power. That is, using less force to move a larger weight in comparison with it. At the same time, gains in strength are not achieved “for free.” The price to pay for it is a loss in distance, that is, you need to make a greater movement than without using a simple mechanism. However, when forces are limited, then “trading” distance for strength is beneficial.
Movable and fixed blocks are one of the types of simple mechanisms. In addition, they are a modified lever, which is also a simple mechanism.
Fixed block does not give a gain in strength, it simply changes the direction of its application. Imagine that you need to lift a heavy load upward using a rope. You will have to pull it up. But if you use a stationary block, then you will have to pull down while the load rises up. In this case, it will be easier for you, since the required strength will consist of muscle strength and your weight. Without the use of a stationary block, the same force would have to be applied, but it would be achieved solely through muscle strength.
The fixed block is a wheel with a groove for a rope. The wheel is fixed, it can rotate around its axis, but cannot move. The ends of the rope (cable) hang down, a load is attached to one, and a force is applied to the other. If you pull the cable down, the load rises up.
Since there is no gain in strength, there is no loss in distance. The distance the load rises, the rope must be lowered the same distance.
Usage moving block gives the gain in strength twice (ideally). This means that if the weight of the load is F, then in order to lift it, a force of F/2 must be applied. The moving block consists of the same wheel with a groove for the cable. However, one end of the cable is fixed here, and the wheel is movable. The wheel moves with the load.
The weight of the load is a downward force. It is balanced by two upward forces. One is created by a support to which a cable is attached, and the other by a cable pulling. The tension force of the cable is the same on both sides, which means that the weight of the load is equally distributed between them. Therefore, each force is 2 times less than the weight of the load.
In real situations, the gain in strength is less than 2 times, since the lifting force is partially “wasted” on the weight of the rope and block, as well as friction.
A moving block, while giving almost a double gain in strength, gives a double loss in distance. To lift a load to a certain height h, the ropes on each side of the block must decrease by this height, that is, the total is 2h.
Combinations of fixed and movable blocks - pulley blocks - are usually used. They allow you to gain strength and direction. The more moving blocks there are in the chain hoist, the greater the gain in strength.
