A block is a kind of lever, it is a wheel with a groove (Fig. 1), a rope, cable, rope or chain can be passed through the groove.

Fig.1. General form block

Blocks are divided into mobile and fixed.

At the fixed block, the axle is fixed; when lifting or lowering the load, it does not rise or fall. Let's denote the weight of the load that we lift, P, the applied force, denote F, the fulcrum - O (Fig. 2).

Fig.2. Fixed block

The arm of the force P will be the segment OA (the arm of the force l 1), arm of force F segment OB (arm of force l 2) (Fig. 3). These segments are the radii of the wheel, then the shoulders are equal to the radius. If the shoulders are equal, then the weight of the load and the force that we apply to lift are numerically equal.

Fig.3. Fixed block

Such a block does not give a gain in strength. From this we can conclude that fixed block it is advisable to use it for ease of lifting, it is easier to lift the load up, using a force that is directed downwards.

A device in which the axle can be raised and lowered together with the load. The action is similar to the action of a lever (Fig. 4).

Rice. 4. Movable block

For this block to work, one end of the rope is fixed, we apply force F to the other end to lift a load of weight P, the load is attached to point A. The fulcrum during rotation will be point O, because at each moment of movement the block turns and point O serves as a fulcrum (Fig.5).

Rice. 5. Moving block

The value of the shoulder of the force F is two radii.

The value of the shoulder of force P is one radius.

The arms of the forces differ by a factor of two, according to the lever balance rule, the forces differ by a factor of two. The force that is needed to lift a load of weight P will be half the weight of the load. The movable block gives the advantage in strength twice.

In practice, combinations of blocks are used to change the direction of the applied force for lifting and reduce it by half (Fig. 6).

Rice. 6. Combination of movable and fixed blocks

At the lesson, we got acquainted with the device of a fixed and movable block, dismantled that blocks are varieties of levers. To solve problems on this topic, it is necessary to remember the rule of balance of the lever: the ratio of forces is inversely proportional to the ratio of the shoulders of these forces.

1. Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7-9 of educational institutions. - 17th ed. - M.: Enlightenment, 2004.
2. Peryshkin A.V. Physics. 7 cells - 14th ed., stereotype. - M.: Bustard, 2010.
3. Peryshkin A.V. Collection of problems in physics, grades 7-9: 5th ed., stereotype. - M: Exam Publishing House, 2010.

1. Class-fizika.narod.ru ().
2. School.xvatit.com().
3. scienceland.info().

Homework

1. Find out for yourself what a chain hoist is and what kind of gain in strength it gives.
2. Where are fixed and movable blocks used in everyday life?
3. How easy is it to climb up: climb a rope or climb with a fixed block?

Team "Physical Pirates"

Research task

Applying the system of blocks, get a gain in strength of 2,3,4 times. What's the other win? Present block connection diagrams and photos .

Target: Applying the system of blocks, get a gain in strength of 2,3,4 times.

Plan:

Learn what blocks are and what they are for.

Conduct experiments with blocks, get a gain in strength of 2,3,4 times.

File a job.

Make a photo report.

Report:

We studied that a fixed block does not give a gain in strength, and a moving block gives a gain in strength by 2 times.

Put forward a hypothesis :

Experience number 1. Gaining 2x Power Gain with Movable Block .

Equipment: tripod, 2 couplings, 1 foot, rod, 1 movable block, 1 fixed block, 1 kg weight (weighing 10 N), dynamometer, rope.

Conducting an experiment:

1. On a tripod, fix a fixed block, a rod, so that the plane of the fixed block and the end of the rod lie in the same plane.

2. Attach one end of the rope to the rod, throw the rope over the movable block and over the fixed block.

3. Hang a weight on the hook of the moving block, attach a dynamometer to the free end of the rope.

5. Make a conclusion.

Measurement results:

Output: F\u003d P / 2, the gain in strength is 2 times.

Equipment. Installation for experiment No. 1.

Conducting experiment No. 1.

Experience number 2. Gaining a 4x power gain with 2 movable blocks.

Equipment: tripod, 2 movable blocks, 2 fixed blocks, 2 weights weighing 1 kg (weighing 10 N) each, dynamometer, rope.

Conducting an experiment:

1. On a tripod, using 3 couplings and 2 legs, fix 2 fixed blocks and a rod, so that the planes of the blocks and the end of the rod lie in the same plane.

2. Fix one end of the rope on the rod, transfer the rope sequentially through the 1st movable block, 1st fixed block, 2nd movable block, 2nd fixed block.

3. Hang a weight to the hook of each movable block, attach a dynamometer to the free end of the rope.

4. Measure the traction force (arms) with a dynamometer, compare it with the weight of the weights.

5. Make a conclusion.

Installation for experiment No. 2.

Measurement results:

Output:F\u003d P / 4, gain in strength by 4 times.

Experience No. 3. Obtaining a gain in strength by 3 times with the help of the 1st moving block.

To get a gain in strength by 3 times, you need to use 1.5 moving blocks. Since it is impossible to separate half from the movable block, you should use the rope twice: once throw the rope over it completely, the second time attach the end of the rope to its half, i.e. to the center.

Equipment: tripod, 1 movable block with two hooks, 1 fixed block, 1 weight of 1 kg (weighing 10 N), dynamometer, rope.

Conducting an experiment:

1. Attach 1 fixed block to the tripod using a coupler.

2. Attach one end of the rope to the upper hook of the movable block, attach a weight to the lower hook of the movable block.

3. Throw the rope sequentially from the upper hook of the movable block through the fixed block, again around the movable block and again through the fixed block, hook the dynamometer to the free end of the rope. You should get 3 ropes on which the movable block rests - 2 at the edges (full block) and one towards its center (half block). Thus, we use 1.5 moving blocks.

4. Measure the traction force (of the arm) with a dynamometer, compare it with the weight of the kettlebell.

5. Make a conclusion.

Installation for experiment No. 3. Conducting experiment No. 3.

Measurement results:

Output:F\u003d P / 3, the gain in strength is 3 times.

Output:

Having done experiments No. 1-3, we tested the hypothesis put forward before the study. She confirmed. According to the results of the experiments, we found out the following facts:

to get a gain in strength by 2 times, you need to use 1 movable block;

to win in strength 4 times, you need to use 2 moving blocks;

to win 3 times, you need to use 1.5 moving blocks.

We also noticed that the gain in strength is equal to the number of ropes on which the moving blocks rest:

in experiment No. 1: 1 the movable block rests on2 ropes - gain in strength in2 times;

in experiment No. 2: 2 moving blocks are based on4 ropes - gain in strength in4 times;

in experiment No. 3, the movable block relies on3 ropes - gain in strength in3 times.

This pattern can be applied to obtain any number of gains in strength. For example, to get a win of 8 times, you need to use 4 moving blocks so that they rest on 8 ropes.

Appendix:

Block diagrams for experiments No. 1-3.

See next page.

IN modern technology for the transfer of goods at construction sites and enterprises, hoisting mechanisms are widely used, indispensable constituent parts which can be called simple mechanisms. Among them are the most ancient inventions of mankind: block and lever. The ancient Greek scientist Archimedes facilitated the work of man, giving him a gain in strength when using his invention, and taught him to change the direction of the force.

A block is a wheel with a groove around the circumference for a rope or chain, the axis of which is rigidly attached to a wall or ceiling beam.

Lifting devices usually use not one, but several blocks. The system of blocks and cables, designed to increase the carrying capacity, is called a chain hoist.

The movable and fixed block are the same ancient simple mechanisms as the lever. Already in 212 BC, with the help of hooks and grabs connected to blocks, the Syracusans seized the means of siege from the Romans. The construction of military vehicles and the defense of the city was led by Archimedes.

Archimedes considered the fixed block as an equal-armed lever.

The moment of force acting on one side of the block is equal to the moment of force applied on the other side of the block. The forces that create these moments are also the same.

There is no gain in strength, but such a block allows you to change the direction of the force, which is sometimes necessary.

Archimedes took the movable block as an unequal lever, giving a gain in strength by 2 times. Moments of forces act relative to the center of rotation, which should be equal at equilibrium.

Archimedes studied the mechanical properties of the moving block and put it into practice. According to Athenaeus, "many methods were invented to launch the gigantic ship built by the Syracusan tyrant Hieron, but the mechanic Archimedes, using simple mechanisms, alone managed to move the ship with the help of a few people. Archimedes came up with a block and through it launched a huge ship" .

The block does not give a gain in work, confirming the golden rule of mechanics. It is easy to verify this by paying attention to the distances covered by the hand and the kettlebell.

Sports sailing ships, like sailboats of the past, cannot do without blocks when setting sails and managing them. Modern ships need blocks for lifting signals, boats.

This combination of movable and fixed units on an electrified line railway to adjust the tension of the wires.

Such a system of blocks can be used by glider pilots to lift their vehicles into the air.

Blocks are classified as simple mechanisms. In addition to the blocks, the group of these devices, which serve to convert forces, includes a lever, an inclined plane.

DEFINITION

Block- a rigid body that has the ability to rotate around a fixed axis.

Blocks are made in the form of discs (wheels, low cylinders, etc.) with a groove through which a rope (torso, rope, chain) is passed.

A block is called fixed, with a fixed axis (Fig. 1). It does not move when lifting a load. A fixed block can be considered as a lever that has equal leverage.

The equilibrium condition for a block is the equilibrium condition for the moments of forces applied to it:

The block in Fig. 1 will be in equilibrium if the tension forces of the threads are equal:

since the shoulders of these forces are the same (OA = OB). A fixed block does not give a gain in strength, but it allows you to change the direction of the force. Pulling on a rope that comes from above is often more comfortable than pulling on a rope that comes from below.

If the mass of the load tied to one of the ends of the rope thrown over the fixed block is equal to m, then in order to lift it, a force F should be applied to the other end of the rope, equal to:

provided that we do not take into account the friction force in the block. If it is necessary to take into account the friction in the block, then the drag coefficient (k) is introduced, then:

A smooth fixed support can serve as a replacement for the block. A rope (rope) is thrown through such a support, which slides along the support, but the friction force increases.

The fixed block does not give a gain in work. The paths that pass through the points of application of forces are the same, the forces are equal, therefore, the work is equal.

In order to get a gain in strength, using fixed blocks, a combination of blocks is used, for example, a double block. When blocks must have different diameters. They are fixedly connected to each other and mounted on a single axis. A rope is attached to each block so that it can be wound on or off the block without slipping. Shoulders of forces in this case will be unequal. The double block acts as a lever with arms of different lengths. Figure 2 shows a diagram of a double block.

The equilibrium condition for the lever in Fig. 2 will become the formula:

Double block can transform force. By applying a smaller force to a rope wound around a large radius block, a force is obtained that acts from the side of the rope wound onto a block of a smaller radius.

A movable block is a block whose axis moves together with the load. On fig. 2 the movable block can be considered as a lever with arms of different sizes. In this case, point O is the fulcrum of the lever. OA - shoulder strength; OB - shoulder of strength. Consider Fig. 3. The arm of the force is twice as large as the arm of the force, therefore, for equilibrium it is necessary that the magnitude of the force F be two times less than the modulus of the force P:

It can be concluded that with the help of a movable block, we get a twofold gain in strength. The equilibrium condition of the moving block without taking into account the friction force can be written as:

If we try to take into account the friction force in the block, then we introduce the coefficient of resistance of the block (k) and get:

Sometimes a combination of a movable and a fixed block is used. In this combination, a fixed block is used for convenience. It does not give a gain in strength, but allows you to change the direction of the force. The movable block is used to change the magnitude of the applied force. If the ends of the rope enclosing the block make the same angles with the horizon, then the ratio of the force acting on the load to the weight of the body is equal to the ratio of the radius of the block to the chord of the arc that the rope covers. In the case of parallel ropes, the force required to lift the load will be required two times less than the weight of the load being lifted.

The golden rule of mechanics

Simple mechanisms of gain in work do not give. How much we gain in strength, how many times we lose in distance. Since the work is equal to the scalar product of force and displacement, therefore, it will not change when using movable (as well as fixed) blocks.

In the form of a formula "golden rule" can be written as follows:

where - the path that passes the point of application of force - the path passed by the point of application of force.

Golden Rule is the simplest formulation of the law of conservation of energy. This rule applies to cases of uniform or almost uniform movement of mechanisms. The translational distances of the ends of the ropes are related to the radii of the blocks ( and ) as:

We get that in order to fulfill the "golden rule" for a double block, it is necessary that:

If the forces and are balanced, then the block is at rest or moves uniformly.

Examples of problem solving

EXAMPLE 1

The task	Using a system of two movable and two fixed blocks, workers lift the construction beams, while applying a force equal to 200 N. What is the mass (m) of the beams? Friction in blocks is ignored.
Solution	Let's make a drawing. The weight of the load applied to the system of loads will be equal to the force of gravity that is applied to the lifted body (beam): Fixed blocks do not give a gain in strength. Each movable block gives a gain in strength twice, therefore, under our conditions, we get a gain in strength four times. This means that you can write: We get that the mass of the beam is equal to: Calculate the mass of the beam, take:
Answer	m=80 kg

EXAMPLE 2

The task	Let the height to which the workers raise the beams be equal to m in the first example. What is the work done by the workers? What is the work done by a load to move it to a given height?
Solution	In accordance with the "golden rule" of mechanics, if we, using the existing block system, received a gain in strength four times, then the loss in movement will also be four. In our example, this means that the length of the rope (l) that the workers should choose will be four times longer than the distance that the load will travel, that is:

The block consists of one or more wheels (rollers) wrapped around by a chain, belt or cable. Just like a lever, the block reduces the force required to lift the load, but in addition it can change the direction of the applied force.

You have to pay for the gain in strength with distance: the less effort is required to lift the load, the longer the path that the point of application of this effort must go through. The block system increases the gain in strength by using more load-carrying chains. Such power-saving devices have very wide range Applications range from lifting massive steel beams on construction sites to hoisting flags.

As with other simple mechanisms, the inventors of the block are unknown. Although it is possible that blocks existed earlier, the first mention of them in literature dates back to the fifth century BC and is associated with the use of blocks by the ancient Greeks on ships and in theaters.

Mounted on a suspension rail, movable block systems (figure above) are widely used on assembly lines, as they greatly facilitate the movement of heavy parts. The applied force (F) is equal to the weight of the load (W) divided by the number of chains used to support it (n).

Single fixed blocks

This simplest type block does not reduce the force required to lift the load, but it does change the direction of the applied force, as shown in the figures above and at the top right. Fixed block on the top of the flagpole makes it easier to raise the flag by allowing the cord to which the flag is attached to be pulled down.

Single moving blocks

A single moveable pulley cuts the effort required to lift a load by half. However, halving the applied force means that the point of its application must travel twice as far. In this case, the force is equal to half the weight (F=1/2W).

Block systems

When using a combination of a fixed block with a movable block, the applied force is a multiple of total load carrying chains. In this case, the force is equal to half the weight (F=1/2W).

Cargo, suspended vertically through the block, allows horizontal electrical wires to be pulled tight.

Overhead lift(picture above) consists of a chain wrapped around one movable and two fixed blocks. Lifting a load requires the application of a force that is only half of its weight.

Polyspast, commonly used in large cranes (figure on the right), consists of a set of moving blocks from which the load is suspended, and a set of fixed blocks attached to the crane boom. Getting a gain in strength from such a large number blocks, the crane can lift very heavy loads such as steel beams. In this case, the force (F) is equal to the weight of the load (W) divided by the number of supporting cables (n).