Lever balance rule and its application

hasenasJune 9, 2021

1,178 4 minutes read

In everyday life, people often have to use the rule of leverage in order to perform a wide variety of tasks that serve to facilitate physical labor when lifting weights. To understand how this rule works, you should familiarize yourself with the areas of its possible application, the types of mechanism and the wording of the definition.

Characterization of the concept of lever equilibrium

The described device is quite simple. But understanding the intricacies of the lever rule in physics, it is worth noting that it has several components:

A beam or plank that is acted upon by two opposing forces.
Supports representing the axis of rotation. The definition of the type of lever depends on its placement under the beam (there are three of them).
Shoulder, which is understood as the section of the board between its end and the support (while the acting forces must be applied along the edges of the beam). The equilibrium conditions of the mechanism depend on the length of the arm.

A lever is used to convert movement to force and vice versa. Thus, it is possible to achieve a redistribution of the work performed in favor of the displacement produced or the applied force.

If we consider the structure of the human skeleton, we can come to the conclusion that all people are given the ability to use a system of levers from birth. In this case, the shoulders and forearms act as a mechanism.

The beginning of the use of the device to facilitate physical work dates back to ancient times. There is evidence that even in Ancient Egypt, these devices were used when people raised a vessel filled with water from a river or well.

In 100 BC, a work by Plutarch was published called Parallel Lives. It says that Archimedes managed, without any help, to raise a ship above the water, on board which at that time there were passengers and cargo. For this, blocks and levers were used.

Moment of power

When studying the rule of equilibrium of the lever, you should separately understand what the unit of measurement, called the moment of force (or torque), means. To depict it using the formula, you must directly multiply the magnitude of the force (F) by the shoulder of the force (d).

Schematically, this will be depicted as follows: M = d x F. The axis of rotation is very important. Without its definition, the acting moment of force is meaningless. The use of M indicates the ability of the force to turn the system around an axis. You can apply it in practice using the example of a nut, if you try to unscrew the latter without the help of a wrench, but only with one hand. The same effect will be observed when you try to open the door by pushing near the hinges, and not by the handle.

When solving problems, the value of M is capable of causing the mechanism to rotate both clockwise and counterclockwise. Moreover, in the first case, the moment is negative, and in the second, it is positive.

Leverage rule

To understand what the leverage rule is, consider an example of a classic mechanism with two arms and a support located far from both ends of the board. During the use of the device, the action of two forces on it is noted:

External F, applied to carry out useful work.
R, resisting F and doing negative work.

How to calculate leverage

Usually human effort is applied to create F, and R is determined by the mass of the load being lifted. The mechanism will reach equilibrium only if the moments acting on it in the sum are equal to zero. Taking into account the moment of force, the formula for the lever rule can be written as follows: R x DR – F x DF = 0, where D is the force arm. F is negative due to the fact that it tends to wrap the arm of the device in a circle in the clockwise direction. If you write the formula in the form of equality, it will look like this: R x DR = F x DF.

It follows that in order to achieve equilibrium with a simple lever, it is enough to achieve equality of the moments of the forces of action F and reaction R. When using the mechanism, the energy of the system is saved, indicating the need to do a certain work while lifting the load to any height.

Since the length of the arm is multiplied by the force to obtain the value of the lever rule, it is possible to carry out work both with the use of more and less force. But with the first option, the arm of the mechanism will have to be set to a smaller value in the vertical direction, and the second case involves the movement of the arm by a larger amount. This feature is called leverage win and lose.

It should be noted that the values of the moments do not affect the operation in any way. The implementation of an action due to the moment of force is noted only in those cases when the system begins to rotate by a certain angle clockwise.