Of all the simple mechanisms that a person has been using since ancient times to perform physical work, perhaps the most famous is leverage. In physics, the formula of the lever (basic) is an expression that describes its balance. Consider this formula in an article.
The concept of leverage
In the general case, we are talking about a simple structure, which is formed by a beam lying on one support. We will explain further. The support divides the beam into two shoulders. It also provides an axis of rotation. The beam may be a board or a solid rod. Levers are of three types, which differ from each other in the number of shoulders (one or two) and the position of forces acting on this system.
The lever in the general case can fulfill two functions: provide a gain in force in moving the cargo or lead to it in the way to give these loads the initial speed. An example of a two-shouldered lever is shown in the figure below.
What forces are acting?
Most physics textbooks talk about the presence of only two forces - this is the weight of the load R and the external influence F aimed at overcoming it. Both forces can act on different shoulders or on one. However, the points of their application to the lever beam are always different.
In fact, there is also a third force. It is directed vertically upward at the point of contact of the beam and the base - this is the reaction of the support, providing a resting state of the lever. It does not play any role in the work of the forces mentioned above, since it is directed against R and F.
Leverage Formula in Physics
Next, consider mathematical expressions. The lever has a rotation axis, therefore, to describe its equilibrium, the sum of the moments of forces that act on its shoulders should be equal to zero.
Specify. The moment is considered to be the value that is obtained by multiplying the effective force by the value of the shoulder. The latter is the distance from the axis of rotation to the point to which it is attached. The formula for moment M is written as follows:
M = d * F
It was shown above that three forces act on a lever. The reaction of the support is applied directly to the axis of rotation, so it does not create a moment. The forces F and R remain. Using their moments, we can write the following equality:
d R * R - d F * F = 0
We draw attention to the appearance of different signs at the moments, which is associated with the creation by the forces under consideration of opposite directions of rotation of the lever arms. This expression translates to the following:
d R / d F = F / R
This is the main lever formula, which means that with a smaller force F it is possible to balance or raise a larger weight of the load R only if the shoulder d F is greater than the distance d R. Moreover, any gain in strength is accompanied by a loss in displacement, so that as a result the gain in work is not achieved.