# Force in Physics

In this post, we will discuss the fundamentals of Force in physics which will include the definition of force and force formula, types and examples of force, reference to Newton’s laws of motion, and units of force.

## What is a force?

Force is a push or a pull that causes a 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 simple examples of force from daily life

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

If you are pushing a box, you are certainly applying 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.

## Types of force

There are different types of force. We will discuss a few selected forces.

### Tension

If we attach a rope to a body and pull it, the rope is in tension. This is also the name of the force exerted on the body. It’s a contact force.

### Normal force

Whenever two surfaces are in direct contact, there will be a force between them (if not then they are not in contact). This force acts at right angles to the surface so is called the normal force. Normal force opposes force i.e. it’s a response force.
For example: When a block is kept on a table (as shown in the diagram), its weight W works downwards (as shown 10N downwards). The table, in turn, applies a normal force N equal to 10N normally (making a 90-degree angle to the common surface) upwards.

The normal force is a contact force.

### Gravitational force

Every object in this universe attracts every other object with this force. Newton’s universal law of gravitation talks about this force. Gravity is also an example of gravitational force. It’s a non-contact force.

We know that all objects on the earth experience gravity that pulls them downwards; we call this force the weight. The direction of this force is always towards the center of the Earth. The weight (W) of a body is directly proportional to the mass (m) of the body.
W = mg where g = the acceleration due to gravity. Know more about the gravitational force

### Friction force

Whenever two touching surfaces move or attempt to move, relative to each other, there is a force that opposes the motion. This is called frictional force. It’s a contact force.

The size of this force is dependent on the material of the surfaces and how much force is used to push them together. Read more about friction here

### Upthrust or Buoyant Force

Upthrust is the name of the force experienced by a body immersed in a fluid (gas or liquid). This is also known as Buoyant Force. This is the force that pushes up on a boat enabling it to float in water. The size of this force is equal to the weight of the fluid displaced by the boat. It’s a contact force. Read more about the Upthrust

### Air resistance or drag

Air resistance is the force that opposes the motion of bodies through the air. This force is dependent on the speed, size, and shape of the body. It’s a contact force. Know more about drag

Also Read this relevant post: 8 common forces

## Contact forces & Non-contact forces

Contact force – A force that can be exerted between two objects when they touch. Examples: Friction, Air resistance, Tension, Normal contact force are examples of Contact forces.
Non-contact force – A force that can sometimes be exerted between two objects that are physically separated. Examples: Gravitational, electrostatic, and magnetic forces are examples of non-contact forces.

## Force Formula

It can be proved from Newton’s 2nd Law of motion that, the magnitude of a force is obtained by multiplying the 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 or resultant 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.

### Examples of the Resultant force or Net force

1) A body is pulled by two forces in two opposing directions as shown in the adjacent Figure. The resultant force acting is the vector sum of the forces.
The sum is found by arranging the vectors point to tail. This gives a resultant of 2 N to the left.

2) If a body is pulled by two perpendicular forces as in the adjacent Figure, then the vector addition gives a triangle that can be solved by Pythagoras. Read about Vector Physics and Vector Addition here

## 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 directions with equal forces. In this case, the net force on the rope is zero.

Now using the equation of force derived from Newton’s second law we can write:

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

Related Post:

The 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 on Force formula with the solution here.

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