# Force definition and force formula in Physics

In this post, we will discuss the fundamentals of Force in physics which will include the definition of force and force formula.

## What is a force?

Force is a push or pull that causes change of velocity of an object i.e. force is a kind of interaction that causes an object with mass to accelerate or retard. This is a simple definition of force in physics. A force is a Vector quantity as it has both magnitude and direction. The SI unit of force is Newton. Dyne is its CGS unit. Force is generally represented by the symbol F.

### Give a few examples of force

As we have covered the force definition in physics now its time to mention a few common examples of force.

If you are pushing a box, you are certainly applying a force. If you are pulling a rope you are again applying a force.

As a force is applied to a body, it results in an acceleration of the body. Force can be of different types like friction or frictional force, gravitational force, the tension in the string, etc.

## Force Formula

It can be proved from Newton’s 2nd Law of motion that, magnitude of a force is obtained by multplying mass of the object (on which the force is applied) and the acceleration of that object caused by the force.
The force formula is expressed as:
Force(F) = Mass x Acceleration
=> F = m * a, (here m=mass and a =acceleration)
This is also known as force equation.

[ see the derivation of the force formula here: Newton’s 2nd Law and equation of force ]

### How does a force impact a motion?

If we kick a ball at rest, it starts moving. That means a change in its velocity happens and it took some time for this change. That means an acceleration of the ball is generated by the kick (a push). That’s an example of a force that generates an acceleration of the body on which the force is applied.

Similarly, if we kick a moving ball and its velocity changes (change in magnitude or direction or both of velocity) then it’s because of the force applied through the kick.

And if we stop a running ball, similarly we are applying a force, as its velocity of the ball changes in a given time.

### What is Net Force?

Force is a Vector Quantity as we need to mention both the magnitude and direction of a force to define it.

And Net force on a system is the vector summation of all components of all forces acting on a system.

This is also called the Resultant force.

### How can you derive Newton’s first law of motion from the force formula?

If there is no net force acting on a system i.e. if net force is 0 then from the formula of Force above, acceleration is also 0. (considering a non zero mass).

[ F= 0 , hence F = m a = 0. Considering, mass m is non-zero, so obviously a = 0 ]

Note that we are saying ‘no net force” which means this is true even when there are multiple components of force working in or on a system but eventually they nullify after vector summation and net effort or force on the system is zero. This system where all forces got balanced and the net force is zero that system is known as a balanced system. Similarly, an unbalanced system has a net force working on it.

#### Newton’s first law from force formula – one example

As an example, say two teams in a tug of war are pulling each other in opposite direction with equal forces. In this case, the net force on the rope is zero.

In details using equation of force derived from Newton’s second law,

F= m * a;

when a net force (F) is zero then we can write,

0=m * a

or, a=0 (considering mass m is non-zero)

So when the net force is zero on a body or a system, the acceleration of the body is also zero. This is exactly what is expressed by the First Law of Motion.

## Unit of Force – Newton

We mentioned about the units of force when we discussed the force definition in physics. Lets revise once more.

In SI the unit of force is Newton.

Newton: One Newton is the amount of force which can generate an acceleration of 1 meter/second^2 when applied on a mass of 1 Kg.

### Force cgs unit – Dyne

CGS unit of force is Dyne.

Dyne: One Dyne is the amount of force which can generate an acceleration of 1 centimeter/second^2 when applied on a mass of 1 gm.

### Relation between Newton and Dyne

1 Newton = 10^5 Dyne

## formula of force in numerical problems

This force equation or formula is profusely used to solve numerical problems based on force and laws of motion. Get some numerical with the solution here.

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