The equilibrium in physics is the state of the system in which it is in relative peace with surrounding objects. The study of equilibrium is done by statics. One of the mechanisms, the knowledge of the equilibrium conditions for the operation of which is of fundamental importance, is a lever. Consider in the article what types of leverage are.
What is this in physics?
Before talking about the types of leverage (in physics 7th grade pass this topic), we give a definition of this device. A lever is a simple mechanism that allows you to convert force to distance and vice versa. The lever has a simple device, it consists of a beam (board, rod), which has a certain length, and from one support. The position of the support is not fixed, so it can be located both in the middle of the beam and at its end. Just note that the position of the support in general determines the type of lever.
The latter has been used by man since time immemorial. So, it is known that in ancient Mesopotamia or in Egypt with the help of it they raised water from rivers or moved huge stones during the construction of various structures. Actively used the lever in ancient Greece. The only written evidence that has been preserved about the use of this simple mechanism is Plutarch's Parallel Lives, where the philosopher gives an example of the use of the system of blocks and levers by Archimedes.
The concept of torque
Understanding the principle of operation of various types of levers in physics is possible if we study the question of the equilibrium of the mechanism under consideration, which is closely related to the concept of the moment of force.
The moment of force is the value that is obtained if we multiply the force by the distance from the point of its application to the axis of rotation. This distance is called the "shoulder of strength." Let F and d be the force and its arm, respectively, then we get:
M = F * d
The moment of force provides the opportunity to make a rotation around a given axis of the entire system. Vivid examples in which you can observe the moment of force in action are unscrewing a nut with a wrench or opening a door by a handle located far from the door hinges.
Torque is a vector quantity. In solving problems often have to take into account its sign. It should be remembered that any force that causes the rotation of the system of bodies counterclockwise creates a moment of force with a + sign.
Leverage Balance
The figure above shows a typical lever and indicates the forces that act on it. Further in the article it will be said that this is a lever of the first kind. Here, the letters F and R indicate the external force and some weight of the load, respectively. It is also seen that the support is offset from the center, so the shoulder lengths d F and d R are not equal to each other.
In statics, it is shown that the lever does not move as a whole mechanism, the sum of all the forces that act on it should be zero. We noted only two of them. In fact, there is also a third, which is the opposite of these two and equal to their sum - this is the reaction of support.
So that the lever does not make rotational movements, it is necessary that the sum of all the moments of forces be equal to zero. The shoulder of the reaction force of the support is zero, so it does not create a moment. It remains to write down the moments of forces F and R:
R * d R - F * d F = 0 =>
R * d R = F * d F
The written leverage equilibrium condition in the form of a formula is also given:
d R / d F = F / R
This equality means that in order for the lever not to rotate, the external force should be so many times (less) the weight of the load being lifted, how many times the shoulder of this force is less (more) than the shoulder that the weight of the load acts on.
The given formulation means that how many times we win on the way with the help of the mechanism in question, we lose in strength the same time.
Lever of the first kind
It was shown in the previous paragraph. Here we just say that for a lever of this type, the support is located between the acting forces F and R. Depending on the ratio of the lengths of the shoulders, such a lever can be used both to lift weights and to give the body acceleration.
Examples of levers of the first kind are mechanical scales, scissors, a nail puller, a catapult.
In the case of weights, we have two shoulders of the same length, therefore, the balance of the lever is achieved only when the forces F and R are equal to each other. This fact is used to weigh bodies of unknown mass by comparing it with a reference value.
Scissors and a nail clipper are vivid examples of a gain in strength, but a loss in transit. Everyone knows that the closer to the axis of the scissors a sheet of paper is laid, the easier it is to cut it. On the contrary, if you try to cut the paper with the tips of the scissors, then it is highly likely that they will begin to "chew" it. The longer the scissors handle or nail clipper, the easier it is to perform the appropriate operations with them.
As for the catapult, this is a vivid example of winning with the help of a lever in the path, and hence in acceleration, which his shoulder tells the projectile.
Lever of the second kind
In all levers of the second kind, the support is located near one of the ends of the beam. This location leads to the presence of only one shoulder at the lever. Moreover, the weight of the load is always located between the support and the external force F. The arrangement of forces in the lever of the second kind leads to the only useful result: gain in strength.
Examples of this type of lever are a manual wheelbarrow, which serves to transport heavy loads, as well as a nut cracker. In both cases, losing the way does not have any negative value. So, in the case of a manual wheelbarrow, it is only important to keep the load on weight during its movement. In this case, the applied force is several times less than the weight of the cargo.
Lever of the third kind
The design of the lever of this type is in many ways similar to the previous one. The support in this case is also located at one of the ends of the beam, and the lever has a single shoulder. However, the location of the acting forces in it is completely different than in the lever of the second kind. The point of application of force F lies between the weight of the load and the support.
Vivid examples of this type of lever are a shovel, a barrier, a fishing rod and tweezers. In all these cases, we win on the way, but there is a significant loss in strength. For example, in order to hold a heavy load with tweezers, it is necessary to apply a large force F, so using this tool does not imply holding heavy objects with it.
In conclusion, we note that all types of leverage work on the same principle. They do not give a gain in the work of moving goods, but only allow you to redistribute this work towards its more convenient implementation.