Humanity has long used simple machines and mechanisms to make physical labor easier and simpler. One of these mechanisms is the lever. What is a lever in physics, what formula describes its balance, and what types of levers are - all these questions are revealed in the article.
Concept
A lever in physics is a mechanism consisting of a beam or board and one support. The support generally divides the beam into two unequal parts, which are called lever arms. The latter can perform a rotational movement around the fulcrum.
Being a simple mechanism, the lever is designed to perform physical work with gain either in power or in transit. The applied forces act on the arms of the lever during its operation. One of them is the power of resistance. It is created by the weight of the load that needs to be moved (lifted). The second force is some external force, which in most cases is applied to the lever arm with the help of human hands.
The picture above shows a typical lever withtwo shoulders. Later in the article it will be explained why it refers to leverage of the second kind.
The lever rule looks like this:
ForceForce arm=LoadLoad arm
Moment of force
Let's make some digression from the theme of the lever in physics and consider an important physical quantity for understanding its operation. It's about the moment of force. It is the product of the force and the length of the arm of its application, which is mathematically written as follows:
M=Fd
It is important not to confuse, the arm of the force d and the arm of the lever, in general, these are different concepts.
The moment of force shows the ability of the latter to make a turn in the system. So, many people know that it is much easier to open the door by the handle than to push it close to the hinges, or it is easier to unscrew the nut on the bolt with a long wrench than with a short one.
Moment of force is a vector. To understand the operation of a simple lever mechanism in physics, it is enough to know that the moment is considered positive if the force tends to turn the lever arm counterclockwise. If it tends to make a turn in the direction of the clockwise direction, then the moment should be taken with a minus sign.
Lever balance in physics
To make it easier to understand under what condition the lever will be in balance, consider the following figure.
Two forces are shown here: a load R and an external force F applied to overcome thisloads. The arms of these forces are equal to dR and dF, respectively. In fact, there is another force - the reaction of the support, which acts vertically upwards at the point of contact between the beam and the support of the lever. Since the shoulder of this force is equal to zero, it will not be considered further when determining the equilibrium condition.
According to statics, the rotation of the system is impossible if the sum of the moments of external forces is equal to zero. Let's write the sum of these moments, taking into account their sign:
RdR- FdF=0.
The written equality reflects the sufficient equilibrium condition for the lever. If not two forces act on the lever, but more, then this condition will still remain. Only instead of the sum of two moments of forces, it will be necessary to find the sum of all the moments of the acting forces and equate them to zero.
The win is strong and on the way
The expression for the moments of lever forces in physics, which was written in the previous paragraph, will be rewritten in the following form:
RdR=FdF
From the above formula follows:
dR / dF=F / R.
This equality says that in order to maintain balance, it is necessary that the force F be as many times greater than the weight of the load R, how many times its arm dFless than the arm d R. Since the larger arm travels a longer path during the movement of the lever than the smaller arm, we get the opportunity to perform the same work using the lever in two ways:
- apply more force F and move the shoulder toshort distance;
- apply a small force F and move the shoulder a long distance.
In the first case, one speaks of a gain on the way in the process of moving the load R, in the second case, one obtains a gain in strength, since F < R.
Where is leverage used and what are they?
Depending on the point of application of lever forces in physics and on the position of the support, the simplest mechanism can be of three types:
- This is a two-arm lever, in which the support position is equally removed from both ends of the beam. Depending on the ratio of the lengths of the arms, this type of lever allows you to win both in the way and in strength. Examples of its use include scales, pliers, scissors, a nail puller, a baby swing.
- The lever of the second kind is one-arm, that is, the support is located near one of its ends. In this case, the external force is applied to the other end of the beam, and the load force acts between the support and the external force, which allows you to win in this very force. A wheelbarrow or a nutcracker are prime examples of this kind of leverage.
- The third type of mechanism is represented by examples such as a fishing rod or tweezers. This lever is also single-armed, but the external applied force is already closer to the support than the point of application of the load. This design of a simple mechanism allows you to win on the road, but lose in strength. That is why it is difficult to hold a small fish on the weight at the end of a fishing rod or a heavy object with tweezers.
To reiterate, a lever in physics only allowsmake it convenient to perform this or that work of moving goods, but does not allow you to win in this work.
