The golden rule of mechanics.

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Even in ancient times, when to use simple mechanisms (block, lever gate and so forth.), Was found a great feature of these machines.It turned out that all movements in simple mechanisms have a certain relationship with the forces that develop the car.It should be noted that the movement of a 2-all simple mechanism, which applied force is always the inverse relation of forces that are applied to these ends.

force affect the right arm, n times smaller than the force which acts on the left shoulder.Accordingly, the movement of the right arm (s2) is n times greater than the movement of the left arm (s1).

example, if in order to maintain a balance arm, the magnitude of force F2 must be n times smaller than the force F1.In this case, when the lever is rotated, the movement of the second end of s2 is n times greater than the movement s1 of the first end.If the unit is a double, then it actually is the same ratio between the forces that are attached to ropes that are wound on both the unit and keep it in a state of equilibrium, and the movements rope ends when the block is rotated.As the importance of this provision can not be overstated, it was called very nice, "the golden rule of mechanics".

Using symbols that have been introduced, the golden rule of mechanics can be expressed as a formula:

s1 / s2 = F2 / F1

or s1 * F1 = s2 * F2.

Subsequently, there was a gradual complication of the types of movements and nature of the machines that were used in mechanics.It so happened that the golden rule of mechanics is not always retains its relevance in a simple way.However, when it becomes difficult to machine types and kinds of movements happening at the same time and complexity of the golden rule of mechanics.Thus, under its influence began to get more difficult cases.It should be noted that the golden rule of mechanics became the basis for the emergence of various ideas about energy and work.This is usually the first, the simplest formulation of the law of conservation of energy, the continuing relevance for all natural phenomena.

use of "golden ruleĀ»

This rule still applies only in the case of uniform motion of simple machines (or with slight acceleration).For example, when rotated double block, there is movement of the ends of the ropes on the distances s1 and s2, which are wound into blocks radii r1 and r2, and also bonded to each other.These distances are proportional to the radii r1 / r2 = s1 / s2.

Thus, to the golden rule has been pressing for a double block, you need to meet the following specific conditions: F1 / F2 = r2 / r1.

In this case, happen equilibrium of forces F1 and F2.Therefore, the machine should perform or uniform motion or in a state of rest.However, in order to start a double block to be out of balance.To this end, any force, for example, to F1, a force should be added to f.The movement that occurs in the body, will be accelerated.

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