Since ancient times, mankind has used simple machines and mechanisms to make physical labor easier and easier. One such mechanism is leverage. What constitutes a lever in physics, with the help of which formula describes its equilibrium, and what types of levers are - all these issues are revealed in the article.
The 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 the shoulders of the lever. The latter can rotate around the fulcrum.
Being a simple mechanism, the lever is designed to perform physical work with a gain, either in strength or in transit. The applied forces act on the shoulders of the lever during its operation. One of them is the resistance force. It is created by the weight of the cargo that needs to be moved (raised). The second force is some external force, which in most cases is applied to the shoulder of the lever with the help of human hands.
The figure above shows a typical two-arm lever. The rest of the article will explain why it refers to leverage of the second kind.
The leverage rule looks like this:
Strength * Leverage strength = Load * Leverage load
Moment of power
Let us make a digression from the topic of leverage in physics and consider the physical quantity important for understanding its operation. It's about a moment of power. It is a product of force by the shoulder length of its application, which is mathematically written as follows:
M = F * d
It is important not to confuse, the shoulder of the force d and the shoulder of the lever, in general, these are different concepts.
The moment of power 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 pushing 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.
The moment of power is a vector. To understand the operation of the 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 she wants to make a turn in the direction of the clockwise movement, then the moment should be taken with a minus sign.
Leverage balance in physics
To make it easier to make out under what condition the lever will be in equilibrium, consider the following figure.
Two forces are shown here: the load R and the external force F applied to overcome this load. The shoulders of these forces are equal to d R and d F , respectively. In fact, there is another force - the reaction of the support, which acts vertically upward at the point of contact of the beam and the support of the lever. Since the shoulder of this force is zero, it will not be considered further in determining the equilibrium condition.
According to statics, rotation of the system is impossible if the sum of the moments of external forces is zero. We write down the sum of these moments, taking into account their sign:
R * d R - F * d F = 0.
The recorded equality reflects a sufficient condition for the equilibrium of the lever. If more than two forces act on the lever, then this condition will still remain. Only instead of the sum of the 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.
Winning in power and on the go
The expression for the moments of leverage in physics, which was written in the previous paragraph, is rewritten in the following form:
R * d R = F * d F
From the above formula it follows:
d R / d F = F / R.
This equality suggests that for equilibrium it is necessary that the force F be so many times greater than the load weight R, how many times its shoulder d F is less than the shoulder d R. Since the larger shoulder during the movement of the lever goes a longer way than the smaller shoulder, we get the opportunity to do the same job using the lever in two ways:
- apply a large force F and move the shoulder a small distance;
- apply a small force F and move the shoulder a long distance.
In the first case, they speak of a gain in travel in the process of moving the load R, in the second case, a gain in strength is obtained, since F <R.
Where are the levers used, and what are they?
Depending on the point of application of the 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 position of the support is equally remote from both edges of the beam. Depending on the ratio of the lengths of the shoulders, this type of lever allows you to both win on the road and in strength. Examples of its use include scales, pliers, scissors, a nail puller, a children's swing.
- The lever of the second kind is one-armed, that is, the support is located near one of its ends. An 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 same force. A wheelbarrow or a nut cracker are prime examples of using this kind of lever.
- The third kind of mechanism is represented by such examples as a fishing rod or tweezers. This lever is also single arm, 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 along the way, but lose in strength. That is why it is difficult to hold a small fish in weight at the end of a fishing rod or a heavy object with tweezers.
Once again, the lever in physics allows us to only make it convenient to carry out one or another job of moving goods, but it does not allow us to win in this job.