Every modern person who hears the word "mechanism", imagines a set of screws, nuts, metal rods, springs, pistons, discs and shafts. In fact, by this word they usually understood simpler things, for example, a wooden wedge or an ordinary inclined plane. The mentioned mechanisms are called simple. One of them is leverage. Consider in the article that this is a lever.
The physical concept of leverage
The lever is a simple mechanism that serves to facilitate the performance of many types of work, for example, lifting weights or communicating to bodies the initial speed. The lever consists of two elements: a beam of a certain length and one support. The support located under the beam divides the lever into two shoulders. The ratio of their lengths is fundamental during the application of this mechanism.
The figure above shows the simple mechanism considered, which is a lever of the first kind (see below).
History reference
Every student already heard in the 7th grade about the famous lever of Archimedes. The Greek philosopher argued that, with a certain size of this simple mechanism, he could turn our Earth upside down, be the second such planet that could be used as a support. Archimedes really owes a great merit to the development of statics, since he was able to experimentally obtain mathematical equality, which is now called the "Equilibrium conditions of the lever."
However, the principle of leverage itself was used long before our era. So, it is known that this simple mechanism was used to draw water from rivers. There is historical evidence that the Egyptians also used a leverage system to build the pyramids.
The principle of operation of the lever
Having become acquainted with the question of what a lever is in physics (this is the simplest mechanism), we turn to the consideration of the principle according to which, with the help of a lever, a gain in strength or in the path of movement is obtained. For this, we recall that in physics there is a quantity called the moment of force. The latter is equal to the product of the force shoulder by the force modulus, i.e.:
M = d * F.
Where the shoulder of the force d is the distance from the support of the lever to the point of action of the force F.
If we recall the statics, then the second condition for the equilibrium of the system of solids in it states that the system will not perform rotational motion if the sum of all n moments of forces in it is equal to zero. I.e:
∑ i = 1 n M i = 0.
Before proceeding to the formulation of the condition of equilibrium of the lever, we note that the moment of force that tends to rotate the system counterclockwise is positive. The opposite moment will be negative.
The lever shown above is exerted by the external force F and the load force R. Given the value of the force shoulders and the direction of the moments, we can write the following equality:
R * d R - F * d F = 0.
Whence we obtain the condition of equilibrium of the lever obtained by Archimedes:
d R / d F = F / R.
This condition indicates that the longer the shoulder d F , the less force F should be applied to lift the weight R. Moreover, the lifting height of this weight will be less than the height to which the shoulder d F falls. Thus, for d F > d R , a gain in strength is obtained, but a loss in transit. With an inverse ratio of shoulders, a gain is already achieved along the way, but the force F will have to be applied more than the weight of R.
Thus, the lever can be used both for lifting weights and for communicating speed to a body weighing R. The latter was previously used in catapults.
Types of leverage and examples
Depending on the position of the support and the arrangement of the forces acting on the beam, the levers are of three kinds. Let's briefly talk about the features of each of them.
A lever is a device that can be of several types. The first kind of leverage is two shoulders. In accordance with the ratio of the lengths of the shoulders, it can give a gain in strength or in transit. Examples of the use of such levers are scissors, a swing for children, a nail clipper.
The lever is not only a two-shouldered mechanism. It can also have one shoulder when the support is near the edge of the beam. In this case, two options are possible in the arrangement of the points of application of the forces F and R, which were considered earlier. If F lies farther from the support than R, then we get a lever of the second kind, but if F is closer to the support than R, then we get a lever of the third kind. The levers of the second kind are a hand wheelbarrow for moving goods or a nut cracker.
As levers of the third kind, an example is a fishing rod, tweezers or a table fork.
It is easy to understand that the levers of the second kind give gain in strength, and the third kind - in the way.