Since ancient times, mankind has sought by any means to facilitate its physical labor. The means to solve this problem were simple mechanisms. This article discusses inventions such as a lever and a block, as well as a system of levers and blocks.
What is a lever and when did it start to be used?
Probably everyone from childhood is familiar with this uncomplicated mechanism. In physics, a lever is a combination of a beam (rod, board) and one support. It 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 either in strength or in the movement of goods. 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 implementation in a convenient way.
A system of levers has long been used by man. So, there is evidence that the ancient Egyptians used it in the construction of the pyramids. The first mathematical description of the leverage effect dates back to the 3rd century BC and belongs to Archimedes. A modern explanation of the principle of operation of this mechanism with the use of the concept of the moment of force arose only in the 17th century, during the formation of classical Newtonian mechanics.
Leverage rule
What is the principle of the lever? 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 shoulder strength by its module, that is:
M = F * d
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, three different forces act on it:
- external force applied, for example, by a person;
- the weight of the load that a person seeks to move with the help of a lever;
- support reaction acting from the support side to the lever beam.
The support reaction balances the other two forces, so the lever does not translate in space. So that he also does not rotate, it is necessary that the sum of all the 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 this choice of the axis of the shoulder, the influence of the reaction force of the support will be zero, that is, this force creates a zero moment. The figure below shows a typical lever of the first kind. The arrows indicate the external force F and the weight of the load R.
We write down the sum of the moments for these forces, we have:
R * d R + (-F * d F ) = 0
Equal to zero the sum of the moments ensures the absence of rotation of the shoulders of the lever. The moment of force F is taken with a negative sign because this force tends to turn the lever clockwise, while the force R tends to make this rotation counterclockwise.
Rewriting this expression in the following forms, we obtain the equilibrium conditions of the lever:
R * d R = F * d F ;
d R / d F = F / R
We got recorded equalities using the concept of moment of force. In the III century BC. e. Greek philosophers did not know about this physical concept, however, Archimedes established an inverse relationship between the forces acting on the shoulders of the lever arm and the length of these arms as a result of experimental observations.
The equalities recorded indicate that a decrease in the shoulder length d R contributes to the possibility of using the small force F and the long shoulder d F to lift large weights R of loads.
What is a block in physics?
A block is another simple mechanism, which is a round cylinder having a furrow along the perimeter of a cylindrical surface. A furrow serves to secure a rope or chain. The block has an axis of rotation. The figure shows an example of a block, demonstrating the principle of its operation.
This block is called motionless. It does not give a gain in strength, but allows you to change its direction.
Besides motionless, there is a mobile block. A system of movable and fixed blocks is shown below.
If the rule of moments is applied to this system, then we will get a gain in force twice, but at the same time we will lose as many times on the way (in the figure F = 60 N).
Lever and block system
As already mentioned in the previous paragraphs, the lever can be used to win on the way or in strength, while the block allows you to win in strength and change the direction of its action. These properties of the considered simple mechanisms are used in leverage and block systems. In these systems, each element takes some effort and transfers it to the other elements so that at the output we get the initial force.
The simplicity of the lever and block and the flexibility of their structural use allow complex mechanisms to be composed of 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;
- lifting crane;
- folding scaffolding;
- adjustable beds and tables;
- a set of bones, joints and muscles of a person.
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.