The lever — the most ancient mechanism for a raising of weights. It represents a crossbeam which rotates around a point of support. In spite of the fact that now there are a lot of any other devices, the lever of the relevance did not lose. It is a component of many modern devices. That these devices worked, it is necessary to calculate length of a shoulder of the lever just as it happened to be done still to Archimedes. Levers were used also in more ancient times, but the first written explanation was left just by the great Greek scientist. He connected together length of a shoulder of the lever, force and cargo.
It is required to you
- devices:
- - device for measurement of length;
- - calculator.
- mathematical and physical formulas and concepts:
- - law of energy conservation;
- - definition of a shoulder of the lever;
- - determination of force;
- - properties of similar triangles;
- - the weight of cargo which needs to be moved.
Instruction
1. Draw the scheme of the lever, having designated on it forces of F1 and F2 operating on both of his shoulders. Designate lever shoulders as D1 and D2. Shoulders are designated from a point of support to a point of application of force. On the scheme construct 2 rectangular triangles, their legs will be the distance on which it is necessary to move one shoulder of the lever and to which other shoulder and actually lever shoulders, and a hypotenuse — distance between a point of application of force and a point of support will move at the same time. At you similar triangles as in case of application of force to one shoulder the second will deviate an initial horizontal on just the same corner, as the first will turn out.
2. Calculate distance on which it is necessary to move the lever. If you were given the real lever which needs to be moved on real distance, just measure length of the necessary piece by means of a ruler or a roulette. Designate this distance as Δh1.
3. Calculate work which F1 force has to make to move the lever on distance necessary to you. Work is calculated on a formula A=F*Δh, In this case the formula will look as А1=F1*Δh1 where F1 is force operating on the first shoulder, and Δh1-distance already known to you. On the same formula calculate work which force operating on the second shoulder of the lever has to make. This formula will look as A2=F2*Δh2.
4. Remember the law of energy conservation for the closed system. Work which is made by force operating on the first shoulder of the lever has to be equal to that which is made by force counteracting it on the second shoulder of the lever. That is it turns out that A1=A2, and F1*Δh1 = F2*Δh2.
5. Remember ratios of the parties in similar triangles. The relation of legs of one of them is equal to the relation of legs of another, that is Δh1/Δh2=D1/D2 where D — length of one and other shoulder. Having replaced ratios with equal to them in the corresponding formulas, we receive the following equality: F1*D1=F2*D2.
6. Calculate transfer number I. It is equal to the relation of loading and the applied force for its movement, that is i=F1/F2=D1/D2.