What is the 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.
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.
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.
Gram Force: It is defined as the force of standard gravity on a gram, that is, acceleration due to gravity (g)*gram.
Pond: It is another term for the gram force.
Sthene: It is defined as a tonne meter per second squared.
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.
Ton-force: A Ton-force is defined as the force of standard gravity on 1 ton, that is, acceleration due to gravity (g)*ton.
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?
Change in state of the body of position
To change the speed of the body
To change the direction of the body
To accelerate the moving body
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
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.
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.
FAQs on Unit of Force
1. What is force, and what is its standard unit of measurement in physics?
In physics, a force is an interaction, such as a push or a pull, that can change the motion of an object. According to Newton's Second Law of Motion (F = ma), force is the product of mass and acceleration. The standard or SI unit of force is the Newton, which is denoted by the symbol N.
2. How is one Newton (N) of force defined?
One Newton (N) is defined as the amount of force required to give a mass of 1 kilogram (kg) an acceleration of 1 metre per second squared (m/s²). This definition comes directly from the formula for force, F = m × a, where 1 N = 1 kg · m/s².
3. What are the SI and CGS units of force, and how are they related?
The two primary systems for measuring force have different units:
- The SI unit of force is the Newton (N).
- The CGS (Centimetre-Gram-Second) unit of force is the Dyne.
The relationship between them is that 1 Newton is equal to 100,000 Dynes (1 N = 10⁵ dyne). The Newton is the more commonly used unit in scientific and engineering applications worldwide.
4. What are some real-world examples that illustrate the concept of one Newton of force?
It can be hard to visualize the magnitude of one Newton. Here are a few relatable examples:
- The force of gravity on a small apple is approximately 1 Newton.
- The force you exert to press a key on a typical computer keyboard is about 0.5 to 1.5 N.
- Holding a stack of ten standard A4 paper sheets exerts a downward force of roughly 0.5 N.
5. Why is the unit of force considered a derived unit and not a fundamental unit?
The unit of force, the Newton, is a derived unit because its definition is based on a combination of fundamental SI units. The seven fundamental units in physics (like the kilogram for mass, the metre for length, and the second for time) are independent. The Newton (N) is derived from these three, as shown by its formula: kg·m/s². It is not an independent base quantity but is calculated from them.
6. How are the units of force (Newton) and mass (kilogram) different?
This is a common point of confusion. The key difference is what they measure:
- Kilogram (kg) is the SI unit of mass, which measures the amount of matter in an object. An object's mass is constant regardless of its location.
- Newton (N) is the SI unit of force, which is an interaction that causes acceleration. An object's weight, for example, is a force that depends on both its mass and the acceleration due to gravity (W = mg).
Therefore, an object has a mass of 1 kg on both Earth and the Moon, but the force of its weight in Newtons is much less on the Moon.
7. Is there a difference between the unit of force and the unit of weight?
No, there is no difference in the unit itself, because weight is a type of force. Weight is specifically the gravitational force exerted on an object by a celestial body like Earth. Since weight is a force, its SI unit is the Newton (N). The general term 'force' can refer to any push or pull, such as friction, tension, or an applied push, all of which are also measured in Newtons.
8. Besides the Newton and Dyne, what are other practical units of force used in some contexts?
While Newton and Dyne are the standard scientific units, other units, known as gravitational units, are sometimes used in specific engineering or regional contexts. These include:
- Kilogram-force (kgf): Also called kilopond (kp), it is the force exerted by Earth's gravity on a one-kilogram mass. 1 kgf is approximately equal to 9.8 N.
- Pound-force (lbf): Used in the imperial system, it is the force exerted by Earth's gravity on a one-pound mass. 1 lbf is approximately equal to 4.45 N.
