Golden rule of mechanics.

Even in ancient times, when simple mechanisms (a block, a lever, a gate, etc.) were used, an excellent feature of these machines was found. It turned out that all movements in simple mechanisms have a certain connection with the forces that the machine develops. It should be noted that the ratio of the movements of the 2 ends of a simple mechanism to which the forces are applied is always the inverse of the ratio of the forces that are applied to these ends.

The force affecting the right arm of the lever is n times less than the force that acts on the left shoulder. Accordingly, the displacement of the right arm (s2) is n times larger than the displacement of the left arm (s1).

Suppose, in order to maintain the balance of the lever, the force F2 must be a factor of n less than the force F1. In this case, when the lever rotates, the movement s2 of the second end will be n times larger than the movement s1 of its first end. If the block is double, then for it, the same relation between the forces that are applied to the ropes, which are wound on both blocks and keeps it in a position of equilibrium, and the movements of the rope ends when the block rotates, is actual. Since the importance of this provision can not be overemphasized, it was called very beautifully: the "golden rule of mechanics".

Using the notation that was introduced, the golden rule of mechanics can be expressed by the following formula:

S1 / s2 = F2 / F1

Or s1 * F1 = s2 * F2.

Subsequently, the types of movements and the nature of the machines that were used in mechanics gradually increased. It turned out that the golden rule of mechanics does not always remain relevant in a simple form. However, when the types of machines and types of movements became more complex, the golden rule of mechanics also became more complex. So under his influence, cases became more difficult. It should be noted that the golden rule of mechanics became the basis for the emergence of various ideas about energy and work. Moreover, this rule is the first, the simplest formulation of the law of conservation of energy, which remains relevant for any natural phenomena.

The application of the "golden rule"

This rule remains valid only in the case of uniform motion of simple machines (or with small accelerations). For example, when the double block rotates, the ends of the ropes move to distances s1 and s2, which are wound on the blocks of radii r1 and r2 and, moreover, are fastened together. These distances are proportional to the radii r1 / r2 = s1 / s2.

Thus, for the golden rule to be relevant for a double block, the following specific conditions must be met: F1 / F2 = r2 / r1.

In this case, the forces F1 and F2 will equalize. Consequently, the machine must either perform a uniform motion, or remain at rest. However, in order to run a dual unit, the balance must be disturbed. To do this, we need to add some force f to some force, say, F1. The movement that will arise in the body will be accelerated.

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