Unit of Force

As per the second law of motion proposed by Newton, force is defined or expressed as the product of mass and acceleration.

In both the SI system (the International System of Units) and in the MKS system, the unit of mass is kilogram, abbreviated as kg, and the unit of acceleration is m/s². Therefore, the unit of force is kg m/s², which is what we refer to as Newton or N.

In the CGS system of units, the unit of mass is gram or g, and the unit of acceleration is cm/s². Therefore, the CGS unit of force is g cm/s², which is called dyne or Dyn.

In the FPS system of units, the unit of mass is pound or lb, and the unit of acceleration is feet per second squared or ft/s². Therefore, the FPS unit of force is lb-ft/s², which is called poundal or pdl.

Derivation of SI Unit of Force:

From Newton’s Second Law of motion, force is equal to the rate of change in momentum (P). We also know that momentum (P) is the product of mass(m) and velocity(v) .

Force = Rate of change of momentum

          = P/ t               {where  P stands for momentum and t for time}

          = mv/ t            { P= mv}

Force= mass*velocity / time             -- (replacing terms with their respective units)   

Newton = (kg*m)/sec⁻²                 

Where,

Unit of Force = Newton

Unit of mass = Kilogram

Unit of time = Second

Unit of velocity = Metre / Second

NOTE: Displacement is the shortest distance from the initial to the final point. Inshort,displacement is distance in vector form(same as how velocity is speed in vector form), So displacement is measured in metres.

Other Units of Force:

There are two other units of force in Physics; however, they are not as commonly used as the SI unit of force Newton. 

1. Dyne: A dyne is a force required to give a mass of 1 gram (1 g) an acceleration of 1 centimetre per second squared (1 cm/s²). 1 N = 100,000 dynes. You might use the dyne if you are working with very small objects.

2. Poundal and Pound: A poundal is a force required to give a mass of 1 pound (1 lb) an acceleration of 1 foot per second squared (1 ft/s²). 1 poundal = 0.1382 N. A pound is a force applied on a mass of 1 pound (1 lb) by the acceleration due to gravity, that is, g. It is a non-technical unit of force and is also referred to as the weight. These units of force are in the English system and are rarely used in scientific measurements.

3. Gram Force: It is defined as the force of standard gravity on a gram, that is, acceleration due to gravity (g)*gram.  

4. Pond: It is another term for the gram force.   

5. Sthene: It is defined as a tonne meter per second squared.

6. Ounce-force: An ounce-force is defined as the force of gravity on an avoirdupois ounce (mass = 1 ounce), that is, acceleration due to gravity (g)*ounce.      

7. Ton-force: A Ton-force is defined as the force of standard gravity on 1 ton, that is, acceleration due to gravity (g)*ton.        

8. Kip or Kipf: A Kip or Kipf is defined as 1000 pound forces.

What is Force? 

Force is an external agent that is applied to a body to change the state of a body, speed of the body, direction of the body or position of the body. Force is a vector quantity, it has both magnitude and direction. The direction towards which the force is applied is known as the direction of the force and the application of force is the point where force is applied. It is measured using a spring balance and the unit in which force is measured in Newton(N).

What are the Effects of Force? 

1. Change in state of the body of position 

2. To change the speed of the body 

3. To change the direction of the body 

4. To accelerate the moving body 

5. To decelerate or bring it to stop

Force Formula Derivation 

Force is a product of mass and acceleration. It is a vector quantity that has both magnitude and direction. 

F=ma 

Where F= Force

             m= Mass

              a= Acceleration 

Acceleration can be defined as the rate of change of velocity of an object in a particular specified time. It can be expressed as,  

a= v/t 

Where v= Velocity 

              t= Time 

So, Force can be rewritten as, 

 F=mv/t 

It is known that P=mv, where p is the momentum, 

Therefore,  

 F= p/t = dp/dt 

Force formula is helpful in finding out the force, mass, acceleration, momentum, velocity in any given problem.

Unit of Force 

Force is represented as,

                              Force = (Mass)(Acceleration)

Unit of force is Newton 

Unit of Mass is Kilograms 

Unit of Acceleration is Meter/second^2

Types of Forces 

The two categories of forces are- Contact forces and non-contact forces 

1. Contact Forces 

Forces that are directly in touch with the body where the force is to be applied or is in touch through a medium are known as contact forces such as muscular forces, mechanical force or frictional force. 

2. Non-contact Forces 

Forces that act without any medium or any direct contact with the body are termed as non-contact forces and under these forces are Magnetic forces, Electrostatic forces, gravitational forces etc. 

SI Unit 

The International System of units is an internationally accepted metric system established in 1960, the standard for measurement which is approved by scientific researchers everywhere making it easier for people to understand or express the magnitude or quantity of a natural phenomenon.

SI units are important because they are based on precise standards and the base used in SI units is 10 which makes it easier for conversion. 

There are a total of 7 base units and 22 derived units. 

In the table given below is the base SI Units 

Other Units of Force

Force is measured in kilograms and is denoted by kg. However, there are also smaller measures called the cgs system. If we talk about force in a centimetre gram second system of unit CGS units, it is measured in dynes and is denoted as gf. 

Other units of force are- Dyne, Gram-force, Poundal, Poundal-force, Kilogram-force. 

Poundal-force is the gravitational unit of force.