Since ancient times, mankind has sought by any means to facilitate their physical labor. Simple mechanisms have become a means to solve this problem. This article discusses such inventions as the lever and block, as well as the system of levers and blocks.
What is leverage and when was it used?
Probably everyone has been familiar with this simple mechanism since childhood. In physics, a lever is a combination of a beam (rod, board) and one support. Serves as a lever for lifting weights or for communicating speed to bodies. Depending on the position of the support under the beam, the lever can lead to a gain in either force or in the movement of loads. It should be said that the lever does not lead to a reduction in work as a physical quantity, it only allows you to redistribute its execution in a convenient way.
Man has been using leverage for a long time. So, there is evidence that it was used by the ancient Egyptians in the construction of the pyramids. The first mathematical description of the effect of the lever dates back to the 3rd century BC and belongs to Archimedes. A modern explanation of the principle of operation of this mechanism involvingthe concept of moment of force arose only in the 17th century, during the formation of Newton's classical mechanics.
Lever rule
How does the lever work? The answer to this question is contained in the concept of the moment of force. The latter is called such a value, which is obtained by multiplying the arm of the force by its modulus, that is:
M=Fd
The arm of force d is the distance from the fulcrum to the point of application of force F.
When a lever does its job, there are three different forces acting on it:
- external force applied, for example, by a person;
- the weight of the load that a person seeks to move with a lever;
- reaction of the support acting from the side of the support to the lever beam.
The reaction of the support balances the other two forces, so the lever does not move forward in space. In order for it not to also perform rotational motion, it is necessary that the sum of all moments of forces be equal to zero. The moment of force is always measured relative to some axis. In this case, this axis is the fulcrum. With such a choice of the axis, the leverage of the reaction force of the support will be equal to zero, that is, this force creates a zero moment. The figure below shows a typical lever of the first kind. The arrows mark the external force F and the weight of the load R.
Write down the sum of the moments for these forces, we have:
RdR+ (-FdF)=0
Equality to zero of the sum of moments ensures the absence of rotation of the lever arms. Momentforce F is taken with a negative sign because this force tends to turn the lever clockwise, while the force R tends to make this turn counterclockwise.
Rewriting this expression in the following forms, we obtain the equilibrium conditions for the lever:
RdR=FdF;
dR/dF=F/R
We have obtained the written equalities using the concept of the moment of force. In the III century BC. e. Greek philosophers did not know about this physical concept, nevertheless, Archimedes established an inverse relationship between the ratio of the forces acting on the arms of the lever and the length of these arms as a result of experimental observations.
The recorded equalities show that a decrease in the length of the arm dR contributes to the emergence of the possibility of lifting large weights with the help of a small force F and a long arm dF R cargo.
What is a block in physics?
Block is another simple mechanism, which is a round cylinder with a groove along the perimeter of the cylindrical surface. The furrow serves to secure the rope or chain. The block has an axis of rotation. The figure shows an example of a block that demonstrates how it works.
This block is called fixed. It does not give a gain in strength, but allows you to change its direction.
Besides the fixed block, there is a moving block. The movable and fixed block system is shown below.
If the rule of moments is applied to this system, then we getthe gain in strength is two times, but at the same time we lose the same amount on the way (in the figure F=60 N).
The system of levers and blocks
As mentioned in the previous paragraphs, leverage can be used to gain path or power, while block allows you to gain power and change the direction of its action. These properties of the considered simple mechanisms are used in systems of levers and blocks. In these systems, each element takes some force and transfers it to other elements so that we get the original force as an output.
The ease of operation of the lever and the block and the flexibility of their structural use make it possible to compose complex mechanisms from such a combination.
Examples of using systems of simple mechanisms
In fact, any machines that surround us are systems of levers and blocks. Here are the most famous examples:
- typewriter;
- piano;
- crane;
- folding scaffolding;
- adjustable beds and tables;
- a set of human bones, joints and muscles.
If the input force in each of these systems is known, then the output force can be calculated by successively applying the lever rule to each element of the system.
