Representation of Force

Force is denoted by the symbol (F). The quantity of force can be expressed by the vector product of mass (m) and acceleration (a). So the mathematical representation of the force can be written as follows:

F = m × a                                                                                            

where, F is the force, m is the mass of the object and a is the acceleration obtained. 

Now, since acceleration is the change in the velocity of the moving body, hence other mathematical representation of the force can be written as follows:

F = m × a   

Since,

a = (v-u)/t 

So, 

F = m × (v-u)/t

where, u and v are the initial and final velocities respectively and t is the time taken.

In our everyday life, it is observed that some effort is required to put an object in a rest state into motion or to stop a moving body. it is experiencing this as a muscular effort and say that we must push or pull on an object to change its state of motion. The concept of force is based on this push, hit, or pull only. 

Hence, Force can be defined as a push, pull, or hit on any object that brings a change in its state of motion. A force is exerted on one object by another. 

e.g,: When a box is pushed, it moves forward and changes its state of motion, hence we can say that when a force was applied to the box in the form of a push, it changed its state from rest to motion. Similarly, suppose a box is tied with a rope and is pulled by a person, then the box will change its state of rest and will start moving in the direction of the pull. This is another example of Force. 

Force can also change the shape and size of any object. The greater the force is applied, the more the changes will be observed in the shape and size of any object. 

e.g:, When a force is applied to a spherical rubber ball, it changes its shape from spherical to oblong. 

Another example can be of a rubber spring, as when a force is applied to a spring in the form of a pull, it gets expanded and hence changed its shape. 

In this way, the force has many applications in our everyday lives such as the force due to one’s foot pushing on the pedal when riding a bicycle, the force applied of the bat by the ball. A general case for the existence of the normal force is when a person stands on the ground i.e. the ground exerts a force on the person that is equal in magnitude to the person’s weight.