The problems of equilibrium in physics are considered in the section of statics. One of the important forces that is present in any mechanical system that is in equilibrium is the reaction force of the support. What is it and how can it be calculated? These issues are described in detail in the article.
What is a support reaction ?
Each of us walks daily on the surface of the earth or on the floor, opens the door, sits on a chair, leaning on the table, goes up the landing. In all these cases, there is a reaction force of the support, which makes it possible to carry out the above actions. In physics, this force is denoted by the letter N and is called normal.
According to the definition, the normal force N is the force with which the support acts on a body in physical contact with it. It is called normal because it is directed along the normal (perpendicular) to the surface.
A normal reaction of a support always arises as a response of an external force to one or another surface. To understand this, one should recall Newton’s third law, which states that there is opposition to any action. When the body presses on the support, the support affects the body with the same modulus of force as the body on it.
The reason for the appearance of a normal force N
This reason lies in the strength of elasticity. If two solids, regardless of the materials from which they are made, are brought into contact and slightly pressed against each other, then each of them begins to deform. Depending on the magnitude of the acting forces, the deformation changes. For example, if you put a load weighing 1 kg on a thin board that is on two supports, then it will slightly bend. If this load is increased to 10 kg, the strain will increase.
The resulting deformation tends to restore the original shape of the body, while creating some elastic force. The latter has an effect on the body and is called a support reaction.
If you look at a deeper, scale level, you can see that the elastic force appears as a result of the approach of atomic shells and their subsequent repulsion due to the Pauli principle.
How to calculate normal strength?
It has already been said above that its magnitude is equal in magnitude to the resulting force directed perpendicular to the surface under consideration. This means that in order to determine the reaction of the support, it is first necessary to draw up an equation of motion, using Newton’s second law, along a line that is perpendicular to the surface. From this equation we can find the value N.
Another way to determine the force N is to use the physical condition of the equilibrium of the moments of forces. This method is convenient to use if the system has rotation axes.
The moment of force is called the value, which is equal to the product of the acting force by the length of the lever relative to the axis of rotation. In a system in equilibrium, the sum of the moments of forces is always zero. The last condition is used to find an unknown value N.
Note that if there is one support in the system (one axis of rotation), the normal force will always create a zero moment. Therefore, for such problems, the above methodology should be applied using Newton's law to determine the support reaction.
There is no specific formula for calculating the force N. It is determined by solving the corresponding equations of motion or equilibrium for the considered system of bodies.
Below are examples of problem solving, where we show how to calculate the normal reaction of the support.
Inclined plane problem
The beam is at rest on an inclined plane. The mass of the timber is 2 kg. The plane to the horizon is inclined at an angle of 30 o . What is the normal force N?
This task is not difficult. To get an answer to it, it is enough to consider all the forces that act along a line perpendicular to the plane. There are only two such forces: N and the projection of gravity F gy . Since they act in different directions, the Newton equation for the system will take the form:
m * a = N - F gy
Since the beam is at rest, the acceleration is zero, so the equation is converted into the following form:
N = F gy
The projection of gravity on a normal to the plane is not difficult to find. From geometric considerations we find:
N = F gy = m * g * cos (α)
Substituting the data from the condition, we obtain: N = 17 N.
Two-pillar task
A thin board is laid on two supports, the mass of which is insignificant. 1/3 of the left support on the board put a weight of 10 kg. It is necessary to determine the reactions of the supports.
Since there are two supports in the problem, to solve it, one can use the equilibrium condition through the moments of forces. To do this, we first assume that one of the supports is the axis of rotation. For example, the right one. In this case, the moment equilibrium condition will take the form:
N 1 * L - m * g * 2/3 * L = 0
Here L is the distance between the supports. From this equality it follows that the reaction N 1 of the left support is equal to:
N 1 = 2/3 * m * g = 2/3 * 10 * 9.81 = 65.4 N.
Similarly, we find the reaction of the right support. The equation of moments for this case has the form:
m * g * 1/3 * L - N 2 * L = 0.
Where do we get:
N 2 = 1/3 * m * g = 1/3 * 10 * 9.81 = 32.7 N.
Note that the sum of the found support reactions is equal to the gravity of the load.