Modern machines have a fairly complex design. However, the principle of operation of their systems is based on the use of simple mechanisms. One of them is the lever. What does it represent from the point of view of physics, and also, under what condition is the lever in balance? We will answer these and other questions in the article.
Lever in physics
Everyone has a good idea what kind of mechanism it is. In physics, a lever is a structure consisting of two parts - a beam and a support. A beam can be a board, a rod, or any other solid object that has a certain length. The support, located below the beam, is the equilibrium point of the mechanism. It ensures that the lever has an axis of rotation, divides it into two arms and prevents the system from moving forward in space.
Humanity has been using the lever since ancient times, mainly to facilitate the work of lifting heavy loads. However, this mechanism has a wider application. So it can be used to give the load a big impulse. A prime example of such an applicationare medieval catapults.
Forces acting on the lever
To make it easier to consider the forces that act on the arms of the lever, consider the following figure:
We see that this mechanism has arms of different lengths (dR<dF). Two forces act on the edges of the shoulders, which are directed downward. The external force F tends to lift the load R and perform useful work. The load R resists this lift.
In fact, there is a third force acting in this system - the support reaction. However, it does not prevent or contribute to the rotation of the lever around the axis, it only ensures that the entire system does not move forward.
Thus, the balance of the lever is determined by the ratio of only two forces: F and R.
Mechanism equilibrium condition
Before writing down the balance formula for a lever, let's consider one important physical characteristic of rotational motion - the moment of force. It is understood as the product of the shoulder d and the force F:
M=dF.
This formula is valid when the force F acts perpendicular to the lever arm. The value d describes the distance from the fulcrum (axis of rotation) to the point of application of the force F.
Remembering statics, we note that the system will not rotate around its axes if the sum of all its moments is equal to zero. When finding this sum, the sign of the moment of force should also be taken into account. If the force in question tends to make a counterclockwise turn, then the moment it creates will be positive. Otherwise, when calculating the moment of force, take it with a negative sign.
Applying the above condition of rotational equilibrium for the lever, we obtain the following equality:
dRR - dFF=0.
Transforming this equality, we can write it like this:
dR/dF=F/R.
The last expression is the lever balance formula. Equality says that: the greater the leverage dF compared to dR, the less force F will need to be applied to balance the load R.
The formula for the equilibrium of a lever given using the concept of the moment of force was first experimentally obtained by Archimedes back in the 3rd century BC. e. But he got it exclusively by experience, since at that time the concept of the moment of force had not been introduced into physics.
The written condition of the balance of the lever also makes it possible to understand why this simple mechanism gives a win either in the way or in strength. The fact is that when you turn the arms of the lever, a greater distance travels a longer one. At the same time, a smaller force acts on it than on a short one. In this case, we get a gain in strength. If the parameters of the shoulders are left the same, and the load and force are reversed, then you will get a gain on the way.
Equilibrium problem
The length of the arm beam is 2 meters. Supportlocated at a distance of 0.5 meters from the left end of the beam. It is known that the lever is in equilibrium and a force of 150 N acts on its left shoulder. What mass should be placed on the right shoulder to balance this force.
To solve this problem, we apply the equilibrium rule that was written above, we have:
dR/dF=F/R=>
1, 5/0, 5=150/R=>
R=50 N.
Thus, the weight of the load should be equal to 50 N (not to be confused with mass). We translate this value into the corresponding mass using the formula for gravity, we have:
m=R/g=50/9, 81=5.1kg.
A body weighing only 5.1 kg will balance a force of 150 N (this value corresponds to the weight of a body weighing 15.3 kg). This indicates a threefold gain in strength.
