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:
Conclusion: 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:
Conclusion: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 to 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:
Conclusion:F\u003d P / 3, the gain in strength is 3 times.
Conclusion:
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.
Application:
Block diagrams for experiments No. 1-3.
See next page.
Blocks are used to lift loads. The block is a wheel with a groove, reinforced in the holder. A rope, cable or chain is passed along the gutter of the block. Motionless they call such a block, the axis of which is fixed and when lifting loads, it does not rise and does not fall (Fig. 1, a, b).
The fixed block can be considered as an equal-armed lever, in which the shoulders of the applied forces are equal to the radius of the wheel. Consequently, it follows from the rule of moments that a fixed block does not give a gain in strength. It allows you to change the direction of the force.
Figure 2, a, b shows movable block(the axis of the block rises and falls together with the load). Such a block rotates about the instantaneous axis O. The moment rule for it will look like
Thus, the movable block gives a gain in strength twice.
Usually, in practice, a combination of a fixed block with a movable one is used (Fig. 3). The fixed block is used for convenience only. It, by changing the direction of the force, allows, for example, to lift a load while standing on the ground.
The term "block" means some mechanical device, which is a roller, which is fixed on a perpendicular axis. This roller can either move freely, or vice versa - it is rigidly fixed. Let's simplify the definition - if the axis of rotation of the roller moves in space, then the block is movable. The roller has a groove into which a rope or cable is inserted. The picture below demonstrates appearance block.
If the roller is fixed, for example, on the ceiling, it is a fixed block. If the roller moves with the load, it is a moving block. In a general sense, the only difference is this.
The meaning of using a movable block is to gain strength when lifting or moving loads and physical bodies. A fixed block does not give a gain, however, it often greatly simplifies the movement of the body and is used in systems in conjunction with a movable block.
The use of movable and fixed blocks
The block system is ubiquitous. This and cranes, And various devices for moving goods in the garage, and even drive belts V modern car. Often the block is used even without a clear understanding that this is the same mechanism.
Surely on construction sites you have seen movable wheels fixed on the upper floors of a house under construction. A rope or chain is thrown over such a wheel and the worker, fixing the bucket on the first floor, raises it to the upper floor, moving the rope. This is a simple example of using a fixed block. If you add one more wheel to the bucket, you get a system of blocks - movable and stationary.
Another more rare example of using a fixed block. When a person pulls a car out of the mud, wrapping tow rope around the tree trunk. This is done for greater convenience, since the towing winch will easily catch on the small end of the cable wrapped around the trunk. There is no gain from such a block itself, and since the tree does not rotate around its axis, the resistance force increases the load.
There are a lot of examples of the use of these simple mechanisms around us.
The most famous device that works on the principle of blocks is the chain hoist. It is actively used in lifting mechanisms. Block system reduces strength and general work is reduced by 4-8 times.
Solving problems with moving and fixed blocks
In physics problems, it is often necessary to determine what total gain in strength will be obtained when using blocks. The student is offered complex scheme where several blocks of different types are connected in a row.
Key to the solution of such tasks lies in the ability to understand the interaction of these devices. Each block is calculated separately and then added to general formula. The calculation formula for the entire task is compiled according to the diagram that the student drew while reading the condition.
For a better understanding of such problems, it should be remembered that block is a kind of lever. The force gained gives a loss in distance (in the case of a moving block).
The calculation formula is very simple.
For fixed block F=fmg, where F is the force, f is the drag coefficient of the block, m is the mass of the load, g is the gravitational constant. In other words, F is the force that must be applied to lift, for example, a box from the ground using a fixed block. As you can see, the dependence is direct and there is no coefficient.
For moving block we have a double gain in strength. Calculation formula F=0.5fmg, where letter designations similar to the formula above. Accordingly, when using a movable block, such a box with a mass m will be twice as easy to lift with a block than using only one's own back.
note that drag coefficient- this is the resistance that occurs in the block when the rope moves along it. Usually these values are specified in the problem statement or are a tabular value. Sometimes in school tasks these coefficients are completely omitted and not taken into account.
Moreover, one must not forget that if the force is applied at an angle, then you need to use the standard method for calculating the triangle of forces. If the task says that a person is pulling a load by a rope that is at 30 degrees to the horizon line, then this should certainly be taken into account and indicated on the design diagram.
The moving block is different from immovable topics that its axle is not fixed, and it can rise and fall with the load.
Figure 1. Movable block
Like the fixed block, the movable block consists of the same wheel with a cable groove. However, one end of the cable is fixed here, and the wheel is movable. The wheel moves with the load.
As Archimedes noted, the movable block is essentially a lever and works on the same principle, giving a gain in strength due to the difference in leverage.
Figure 2. Forces and shoulders of forces in the moving block
The movable block moves along with the load, as if it lies on a rope. In this case, the fulcrum at each moment of time will be at the point of contact of the block with the rope on one side, the load will be applied to the center of the block, where it is attached to the axis, and the traction force will be applied at the point of contact with the rope on the other side of the block . That is, the shoulder of the body's weight will be the radius of the block, and the shoulder of the force of our thrust will be the diameter. The moment rule in this case will look like:
$$mgr = F \cdot 2r \Rightarrow F = mg/2$$
Thus, the movable block gives a gain in strength twice.
Usually, in practice, a combination of a fixed block with a movable one is used (Fig. 3). The fixed block is used for convenience only. It changes the direction of the force, allows, for example, to lift a load while standing on the ground, and the movable block provides a gain in strength.
Figure 3. Combination of fixed and movable blocks
We have reviewed perfect blocks, that is, those in which the effect of friction forces was not taken into account. For real blocks, it is necessary to introduce correction factors. The following formulas are used:
Fixed block
$F = f 1/2 mg $
In these formulas: $F$ is the applied external force (usually the force of the human hands), $m$ is the mass of the load, $g$ is the coefficient of gravity, $f$ is the coefficient of resistance in the block (for chains approximately 1.05, and for ropes 1.1).
With the help of a system of movable and fixed blocks, the loader lifts the box with tools to a height of $S_1$ = 7 m, applying a force of $F$ = 160 N. What is the mass of the box, and how many meters of rope will have to be chosen while the load rises? What work will the loader do as a result? Compare it with the work done on the load to move it. Ignore the friction and mass of the moving block.
$m, S_2 , A_1 , A_2$ - ?
The movable block gives a double gain in strength and a double loss in movement. A fixed block does not give a gain in strength, but changes its direction. Thus, the applied force will be half the weight of the load: $F = 1/2P = 1/2mg$, from which we find the mass of the box: $m=\frac(2F)(g)=\frac(2\cdot 160)(9 ,8)=32.65\kg$
The movement of the load will be half as much as the length of the selected rope:
The work performed by the loader is equal to the product of the applied effort and the movement of the load: $A_2=F\cdot S_2=160\cdot 14=2240\J\$.
Work done on the load:
Answer: The mass of the box is 32.65 kg. The length of the selected rope is 14 m. The work done is 2240 J and does not depend on the method of lifting the load, but only on the weight of the load and the height of the lift.
Task 2
What load can be lifted with a movable block weighing 20 N if the rope is pulled with a force of 154 N?
Let's write the rule of moments for the moving block: $F = f 1/2 (P+ R_B)$, where $f$ is the correction factor for the rope.
Then $P=2\frac(F)(f)-P_B=2\cdot \frac(154)(1,1)-20=260\ N$
Answer: The weight of the load is 260 N.
Block is a device in the form of a wheel with a groove through which a rope, cable or chain is passed. There are two main types of blocks - movable and fixed. At the fixed block, the axis is fixed and when lifting loads it does not rise or fall (Fig. 54), while at the movable block the axis moves along with the load (Fig. 55).
A fixed block does not give 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 make the load rise up (see Fig. 54). The situation is different with the moving block. This block allows a small force to balance a force 2 times greater. To prove this, let's turn to Figure 56. Applying a force F, we seek to rotate the block around an axis passing through the point O. The moment of this force is equal to the product of Fl, where l is the arm of the 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 shoulder 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 strength, obtained with the help of a movable block is 2. The experience shown in Figure 57 confirms this conclusion.
In practice, a combination of a movable block with a fixed one is often used (Fig. 58). This allows you to change the direction of the force action with a simultaneous double gain in strength. 
To obtain a greater gain in strength, apply lifting mechanism, called chain hoist. The Greek word "polyspast" is formed from two roots: "poly" - a lot and "spao" - I pull, so that in general it turns out "multi-thrust".
The chain hoist 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 chain hoist gives a sixfold gain in strength. 
1. What two types of blocks do you know? 2. What is the difference between a movable block and a fixed block? 3. For what purpose is a fixed block used? 4. What is the movable block used for? 5. What is a chain hoist? What power gain does it give?
