What is force? This basic important question about force remains unanswered even today. We do not know : what is force and how does it come into existence ? Our best guess today is that it arises from some short of change in the characterization of vacuum around us or according to quantum field theory, force is mediated by exchange of particles called "gravitons" (gravitational force), "photons" (electromagnetic force), "gluons" (strong nuclear force) and "bosons" (weak force). One thing common to all quantum models attempting to explain existence of force is that it propagates at the speed of light. For the time being, however, it would be better if we simply ignore this question and proceed ahead with what we know about force. We shall return to this topic once we familiarize ourselves with other aspects of force.

What we know today with definite authority about force is actually its effect on interaction with a particle or a body. Newton’s laws of motion precisely provide this information. The laws tell us about the change in the motion (velocity) of the body on which force is applied. An important description of force is that it is a "push” or “pull” on a body. Importantly, this is the nature of all types of force, irrespective of their class or genesis (gravitational, physical, mechanical, chemical, nuclear, electrical, etc.).

We can measure force in exact terms as ”acceleration produced in unit mass”. Using Newton’s second law,

For m = 1 kg,

F (Newton) = ma = 1 x a = a ( m / s 2 m / s 2 )

But, this measurement of force would essentially be in terms of what it does (acceleration) rather than in terms of what it is.

The question “what is force?” is, therefore, unanswered as we actually do not know.

Exercise 1

A bob of mass 0.1 kg is hung from a mass-less string of 1 m length. The bob is set in oscillation. Then, the string is cut and the trajectory of the bob is observed. The bob takes different trajectory depending on the position of bob when the string is cut. It is found that the path is parabolic for the position(s) of bob :

(a) at mean position

(b) at extreme position

(c) while it is moving up towards extreme position

(d) while it is moving down towards mean position

Solution

Force has no past or future. The moment the string is cut, there is no tension force on the bob. Only gravity acts on the bob. If the bob is at extreme position, then its velocity is zero and there is downward acceleration due to gravity. As a result, the bob falls vertically down.

Figure 1: Path of pendulum bob

Path of pendulum bob

In all other cases, the bob has certain velocity. Its direction is horizontal at mean position. It makes certain angle with horizontal when bob is moving either towards extreme position or mean position. In all these cases, velocity is in a direction which is not vertical. The bob is worked down by gravity acting downward. As such, there is downward acceleration due to gravity. This results in a parabolic trajectory.

Hence, options (b), (c) and (d) are correct.

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Study of force and related phenomena is facilitated with certain classifications. One of the basic classifications is based on our experience with force. In our day to day life, we experience force when objects or particles are in contact. At the same time, we are aware that there are gravitational and electromagnetic forces, which come in to being without contact. These forces can change velocity of an object acting from a distance.

Contact forces : friction, tension, spring, muscle force etc.

“Action at a distance” forces : gravitational, Electromagnetic

We should understand that “contact” is a relative concept. What appears to be in contact is actually not in contact at atomic or sub-atomic levels. Further, this classification is also in the root of other important classification that divides force types between “fundamental” and “non-fundamental or other force types” :

Fundamental force : gravitational, Electromagnetic, weak force and strong force (nuclear force)

Other force types : friction, tension, spring, muscle force etc.

The important interpretation of this classification is that all other forces are actually macroscopic manifestation of fundamental forces. For example, we push an object with our hand using muscle. This muscle force is a macroscopic outcome of chemical force, which in turn is outcome of electromagnetic force. Also, we should keep in mind that the “effect of force” is same. It either pulls an object or pushes an object. In inertial frame of reference (non-accelerated frame of reference), the effect of force is determined by Newton’s laws of motion.

Newton’s laws of motion form the basic framework in which interaction of force with a particle or a body is studied. As a matter of fact, these are the only laws other than conservation laws which govern whole of kinematics and dynamics i.e. study of motion. Newton’s laws of motion are historically postulated for pure translational motion of a particle and that of a body by extension. We, however, employ a similar set of Newton’s laws for studying rotational motion.

There are three corresponding Newton’s laws of motion for pure rotation. Newton’s first law for rotation, for example, states that a body in rotation remains in rotation unless there is an external torque is applied on it. Similarly, Newton’s second law of motion for rotation relates torque, moment of inertia and angular acceleration as :

τ = I α τ = I α

This relation is very much like the famous relation F = m a F = m a for pure translational motion. Clearly, “force” is replaced by “torque”, “mass” by “moment of inertia” and “linear acceleration” by “angular acceleration”.

We have worked with Newton’s laws with fair degree of accuracy as far as “effect of force” i.e. “change in velocity” i.e. “acceleration" is concerned. It is true when we consider interaction at speeds, which are fraction of the speed of light. At higher speed, it is seen that we need a greater force to accelerate a body than that required to accelerate it by the same degree at a lower speed. The special theory of relativity quantifies (or accounts) this difference. The form of Newton’s law in momentum form remains unaltered even at higher speed and is given by :

F = đ P đ t F = đ P đ t

However, the definition of linear momentum is different at higher speed :

P = m v ( 1 - v 2 c 2 ) P = m v ( 1 - v 2 c 2 )

where “m” is the invariant mass, “v” is velocity and “c” is speed of light. Clearly, the new definition of momentum reduces to classical definition as product of mass and velocity when v<<c. For this reason, we can say that Newton’s laws are subset of more general “special theory of relativity”.

P = m v P = m v

The realization that all forces are manifestation of few fundamental forces, gives rise to a temptation to conclude that all fundamental forces may have a unifying origin or model of description. This tempting idea to unify fundamental forces has led many different approaches and models to describe force. The foremost among these has been the successful unification of electrical and magnetic forces via electromagnetic theory. Both these forces are now considered to be manifested due to the presence of charge and its motion. However, no further progress towards unifying other fundamental forces could be made based on this model.

Two promising theories which attempt to unify fundamental forces are “quantum field theory” and “string theory”. The quantum field theory describes force in terms of the exchange of “momentum carrying” particles (photons, bosons etc). According to this theory, the very idea of force is redundant and is replaced by "momentum".