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### Work, Energy and Power

Work - When a force acts upon an object and displaces it from its original position, it is said that work was done upon the object. There associates three key component to work - force, displacement, and reason or source.

Some of the examples of work are-

• A horse pulling a plow through the field
• A shopper pushing a grocery cart down the aisle of a grocery store
• A traveler lifting a backpack full of books upon his shoulder
• A weightlifter lifting a barbell above his head
• An Olympian launching the shot-put, etc.

In each of the example above there is a force exerted upon an object to cause that object to be displaced.

Mathematically, work can be expressed by the following equation.

W = Fd Cosθ, where F is the force, d is the displacement, and the angle θ is defined as the angle between the force and the displacement vector.

Units of Work- The SI Unit of work is Joule. One Joule is equivalent to one Newton of force causing a displacement of one meter.

Energy- Energy Is the Ability to Do Work. This is most popular definition of energy. Energy has different forms-

•    Chemical energy,
•    Electrical energy,
•    Heat energy or thermal energy,
•    Light energy or radiant energy,
•    Mechanical energy,
•    Nuclear energy

Types of Energy – Energy is something responsible behind every event happening. In principle, energy can be divided over two types-
• Potential Energy - Stored energy is called potential energy.
• Kinetic Energy - Moving energy is called kinetic energy.
Unit of Energy – The unit of energy is Joule. 1000 joules make 1 BTU i.e. British Thermal Unit.

The term "joule" is named after an English scientist James Prescott Joule who lived from 1818 to 1889. He discovered that heat is a type of energy.

Potential Energy - Potential Energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system. The SI unit for measuring work and energy is the joule (symbol J).

The term "potential energy" was coined by the 19th century Scottish engineer and physicist William Rankine.

Mathematically, potential energy can be expressed as -
Potential Energy: PE = m x g x h
where, PE = Potential Energy, m = Mass of object, g = Acceleration due to Gravity and h = Height of object,

Examples of Potential Energy:
•    A car parked at the top of a hill

•    A boulder sitting at the top of a mountain.

•    Water behind a dam

•    Pressure in an un-opened soda bottle, gas cylinder, etc.

•    A truck loaded with explosives.

Kinetic Energy - The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy of a point mass m is given by

K.E. = ½ mv2

Types of Kinetic Energy
Basically Kinetic Energy has four types -

Translational Kinetic energy - The Energy possessed by the body when the body is moving along the straight line is called Translational Kinetic energy.

Turbulent Kinetic energy - Turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow.

Relativistic kinetic energy - Relativistic Kinetic energy is the Kinetic energy possessed by the body acquiring velocity comparable to the velocity of light.

Negative kinetic energy- Negative kinetic energy is the kinetic energy possessed by the body when its velocity decreases as compared to its initial Velocity.

Examples of Kinetic Energy
Some of the examples of Kinetic Energy are -

Orbital motion: moons about the planets, or the planets around the sun. The motion of the stars in a galaxy, orbiting satellites and space vehicles.

Random linear motion: On a molecular level, vibrations of molecules, gas molecules bouncing around a room.

Rotational or torquing motion: spinning flywheels, rolling balls or wheels

Projectile (parabolic) motion: a fired bullet, a thrown ball, a boy jumping

Linear motion: running, bowling, aircraft in flight, a moving car or train, a boy skateboarding

### The Principle of Conservation of Energy

The law of conservation of energy states that the total amount of energy in an isolated system remains constant over time. For an isolated system, this law suggests that energy can change its location within the system, and that it can change form within the system. For example, chemical energy can change into electrical energy and vice versa but it can be neither created nor destroyed.

Relation between momentum and kinetic energy
The  kinetic energy of a particle in terms of the momentum can be expressed as follows-
Since Momentum (P) = mv so v = P/m …..(i)
and Kinetic Energy (KE) = ½ mv2  ………. (ii)
Replacing the value of v from equation (i) into equation (ii), we will get
K = ½m (P/m)2 = P2 /2m

Power- Power is the rate at which energy is transferred, used, or transformed. The unit of power is the joule per second (J/s) also known as the watt in honor of James Watt.