The lever is one of the simple mechanisms that has served and continues to serve people to facilitate their physical labor. In the article, we will consider what leverage is, what types of it are and where they are used, as well as explain what the rule of leverage is.
Leverage in Physics
Despite the fact that we are talking about a simple mechanism, it still has its own components. Firstly, it is a beam or board, which is designed to influence two opposing forces on it. Secondly, it is a support, which, from a geometric point of view, represents the axis of rotation around which the beam can move. Depending on the location of the support under the beam, three types of lever are distinguished, which will be discussed below.
Another important concept for any leverage is shoulder. By it is meant the part of the beam that is between its end and the support, provided that the acting forces are applied to the ends of the beam. The length of the shoulder plays an important role in determining the conditions of equilibrium of the lever.
The lever is designed to convert force into displacement or, conversely, displacement into force. In other words, the simple mechanism under consideration is used to redistribute the work to be performed, in favor of the applied force or in favor of the movement being carried out. The figure below shows an example of a lever of the first kind.
When did humanity start using leverage?
One cannot confidently answer this question. It is known that levers from ancient times were used in Mesopotamia and Ancient Egypt to lift containers with water from wells and rivers.
The only written evidence that has survived to this day, indicating the use of the mechanism in question, is the well-known lever of Archimedes. Plutarch's work, Parallel Lives (100 BC), states that Archimedes alone was able to lift a ship with cargo and passengers above the surface of the water. In this case, the philosopher used a system of blocks and levers.
If we approach the question posed in the title of the paragraph more strictly, we can say that a person has been using the lever since he first appeared in this world, because our forearms and shoulders work according to the principle of this simple mechanism.
The concept of the moment of force
Before proceeding to the formulation of the rule of equilibrium of the lever, we consider the concept of torque or torque. In physics, it is understood as a quantity equal to the product of the shoulder of force by the force itself. Mathematically, it is written like this:
M = d * F.
Where, F is the acting force, d is the arm of the force, which corresponds to the distance from the point of application F to the axis of rotation. The last element of the system, that is, the axis of rotation, plays a fundamental role in determining the moment M. Without the presence of the axis of rotation, there is no point in talking about the current moment of force.
The physical meaning of the quantity M is to reflect the ability of the force F to rotate the system around its axis. In practice, this ability can be felt if you try to unscrew the nut not with a wrench, but with your hands, or if you try to open the door not by the handle, but pushing it near the hinges.
When solving problems, the moment of force M can lead both to the rotation of the system clockwise and against its course. In the first case, the moment is considered negative, in the second - positive.
Moments of power and the rule of leverage
Consider a classic two-arm lever when the support is away from the ends of the beam. An example of such a mechanism is shown below.
We see that when this lever is used to perform physical work, then two forces act on it:
- external force F, which is applied to perform useful work;
- force R, which resists force F (it performs negative work).
In most cases, the force F is created by human effort, and the force R is the weight of some load.
The lever in question will be in equilibrium, and will cease to experience rotation only when the sum of the moments acting on it is zero. Using the notation of the figure above, and applying the formula for M, we write the rule of equilibrium of the lever:
R * d R - F * d F = 0.
We note that the moment of force F is written with a minus sign, since it tends to turn the lever arm clockwise. It remains to transfer the second term to the right side of the equality in order to write down the rule of leverage:
R * d R = F * d F.
Thus, the equality of the moments of the action force F and the reaction force R is a sufficient condition for the equilibrium of the simple mechanism under consideration.
Who established the rule of balance of leverage? This question partially overlaps with the historical one discussed above. Since only written evidence of Archimedes' scientific activity related to this mechanism has been preserved, it is he who is currently considered the philosopher who established the rule of leverage.
The equilibrium of the system under consideration is ensured not only by the vanishing of the sum of the moments, but also by the vanishing of all the acting forces. Only two forces (F and R) were named above. In fact, there is still a reaction force of the support, directed against the forces F and R. The reaction of the support of the moment of force does not create due to the zero length of its shoulder.
Win and lose using leverage
It should be clearly understood that when using the lever, the full energy of the system is saved. To raise the load to a certain height, it is necessary to do some work. Since the formula for the rule of leverage is the product of force by the length of the shoulder, then the noted work can be performed both with the help of a greater force, and with the help of a smaller one. However, in the first case, it will be necessary to move the lever arm in the vertical direction by a small amount, in the second case, by a large amount. This is the gain and loss in using leverage.
Note that in the formula of the rule of leverage are the values โโof the moments. They have nothing to do with work. The moment of force performs work only when the system, due to its action, rotates around an axis by some angle.
Types of levers
It was already mentioned above that all levers belong to one of three types. The classification is based on the relative position of the forces R, F and the support. We characterize all three types:
- A lever of the 1st type, or genus, was shown above. The support is located between the forces R and F. Depending on the length of the shoulders d R and d F, it can be used both to win on the way and to gain in strength. An example of this type of lever are scissors, scales, a nail clipper.
- A lever of the 2nd kind assumes that the force R is applied between the support and the force F. In this case, the gain is only in the force. Examples of such levers in everyday life are a nutcracker or hand wheelbarrow.
- A lever of the 3rd kind assumes that the force F is located between the support and the load R. In this case, winning is possible only on the way. The use of a shovel, compass or fishing rod for fishing are vivid examples of a lever of the 3rd kind in work.
Simple block mechanism
Considering the rules of leverage, it is useful to say a few words about another simple mechanism - the block. It is an ordinary cylinder with an axis of rotation, which has a recess along the perimeter of its side surface. An example of using a fixed unit is shown below.
As you can see, there is no gain in strength and path, however, the fixed block allows you to change the direction of the acting force F.
The application of the rule of equilibrium of the lever to the block is made when it is necessary to calculate the gain in strength when using moving blocks. One such block allows you to win 2 times in strength and lose as many times on the way.
The solution of the problem
The hand wheelbarrow is made in such a way that the center of mass of the load in it is at a distance of 1/3 * l from the wheel, where l is the length of the wheelbarrow. What mass can a person move with a wheelbarrow if it is known that he can exert a maximum vertical force F = 200 N.
We use the rule of leverage, we get:
F * l = R * 1/3 * l
F = m * g / 3
m = 3 * F / g = 3 * 200 / 9.81 โ 61 kg.
Note that the force F = 200 N is equal to the weight of a body weighing only 20.4 kg. Thus, this hand wheelbarrow allows you to win 3 times in strength.