8.4 Fundamental force types  (Page 78/2)

There are different types of forces that may operate on a body. The forces are different in origin and characterization. However, there are only four fundamental forces. Other force types are simply manifestation of these fundamental forces.

In this module, we shall describe the four fundamental force types. The other force types, which are required to be considered in mechanics, will be discussed in a separate module. In this sense, this module is preparatory to the study of dynamics. The treatment of the force types, however, will be preliminary and limited in scope to the extent which fulfills the requirement of dynamics.

The four fundamental force types are :

• Gravitational force
• Electromagnetic force
• Weak force
• Strong force (nuclear force)

Gravitational force

The force of gravitation is a long distance force, arising due to the very presence of matter. Netwon’s gravitation law provides the empirical expression of gravitational force between two point like masses $m_1$ and $m_2$ separated by a distance “r” as :

where “G” is the universal constant. $G=6.7x{10}^{-11}N-m^2/{\mathrm{kg}}^2$ .

Gravitational force is a pair of pull on the two bodies directed towards each other. It is always a force of attraction. Gravitation is said to follow inverse square law as the force is inversely proportional to the square of the distance between the bodies.

Since the force of gravitation follows inverse square law, the force can be depicted as a conservative force field, in which work done in moving a mass from one point to another is independent of the path followed. The gravitation force is the weakest of all fundamental forces but can assume great magnitude as there are truly massive bodies present in the universe.

In the case of Earth (mass “M”) and a body (mass “m”), the expression for the gravitational force is :

where “g” is the acceleration due to gravity.

The most important aspect of acceleration due to gravity here is that it is independent of the mass of the body “m”, which is being subjected to acceleration. Its value is taken as 9.81 $m/s^2$ .

Gravitation force has a typical relation with the mass of the body on which its effect is studied. We know that mass (“m”) is part of the Newton’s second law that relates force with acceleration. Incidentally, the same mass of the body (“m”) is also a part of the equation og gravitation that determines force. Because of this special condition, bodies of different masses are subjected to same acceleration. Such is not the case with other forces and the resulting acceleration is not independent of mass.

Consider for example a body of mass "m'" instead of "m". Then,

$$\begin{array}{l}{F}_G=\frac{GM\mathrm{m\text{'}}}{r^2}=\mathrm{m\text{'}}g\end{array}$$

$$\begin{array}{l}\Rightarrow g=\frac{GM}{r^2}\end{array}$$

We see here that gravitational force on the body is proportional to the mass of the body itself. As such, the acceleration, which is equal to the force divided by mass, remains same.

Knowing that acceleration due to gravitational force in the Earth’s vicinity is a constant, we can calculate gravitational pull on a body of mass "m", using relation second law of motion :