Principles Of Statics
The statics is based on the following principles of mechanics:
1. Newton’s laws of mechanics
2. Law of transmissibility
3. Parallelogram law of forces
4. Principles of physical independence
5. Principles of superposition.
Newton’s Laws of Mechanics
As already discussed in first chapter, Newton’s first law gave definition of the force and second law gave basis for quantifying the force. There are two more Newton’s laws:
a. Newton’s Third Law
b. Newton’s Law of Gravitation
These laws are explained in this article.
(a) Newton’s Third Law
It states that for every action there is an equal and opposite reaction. Consider the two bodies in contact with each other. Let one body apply a force F on another. According to this law the second body develops a reactive force R which is equal in magnitude to force F and acts in the line same as F but in the opposite direction. Figure 2.1 shows the action of a ball on the floor and the reaction of floor to this action. In Fig. 2.2 the action of a ladder on the wall and the floor and the reactions from the wall and the floor are shown
(b) Newton’s Law of Gravitation
It states that everybody attracts the other body. The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to the square of the distance between them. Thus the force of attraction between the bodies of mass m1 and mass m2 at distance ‘d’ between them as shown in Fig. 2.3 is
Similarly 1 kg-mass on earth surface experiences a force of
This force of attraction is always directed towards the centre of earth.
In common usage the force exerted by a earth on a body is known as weight of the body. Thus weight of 1 kg-mass on/near earth surface is 9.80665 N, which is approximated as 9.81 N for all practical problems. Compared to this force the force exerted by two bodies on each other is negligible. Thus in statics:
a. Weight of a body = mg
b. Its direction is towards the centre of the earth, in other words, vertically downward.
c. The force of attraction between the other two objects on the earth is negligible.
Law of Transmissibility
According to this law the state of rest or motion of the rigid body is unaltered, if a force acting on the body is replaced by another force of the same magnitude and direction but acting anywhere on the body along the line of action of the replaced force.
Let F be the force acting on a rigid body at point A as shown in Fig. 2.4. According to this law, this force has the same effect on the state of body as the force F applied at point B, where AB is in the line of force F
In using law of transmissibility it should be carefully noted that it is applicable only if the body can be treated as rigid. Hence if we are interested in the study of internal forces developed in a body, the deformation of body is to be considered and hence this law cannot be applied in such studies.
Parallelogram Law of Forces
This has been already explained in chapter 1 along with the derived laws i.e., triangle and polygonal law.
Principles of Physical Independence of Forces
It states that the action of a force on a body is not affected by the action of any other force on the body
Principles of Superposition of Forces
It states that the net effect of a system of forces on a body is same as the combined of individual forces acting on the body. Since a system of forces in equilibrium do not have any effect on a rigid body this principle is stated in the following form also: ‘The effect of a given system of forces on a rigid body is not changed by adding or subtracting another system of forces in equilibrium.’
