Physics

# Work, Energy and Power

## Definition of Work:

The act of displacing an object in the direction of force by applying a force is called work. For work to happen, it is necessary that there must be a displacement of the object when a force is applied.

The work done on an object is equal to the product of the force acting on the object and the displacement of the object in the direction of that force.

Work = Force × Displacement in the direction of force

[ W = F × S]

If on applying force F, the object does not move in the direction of the force but moves S distance making θ angle with it,

then the work W done = Force × Component of displacement in the direction of force

or,  [W = F × S Cos θ]

if,   θ = 900

then  cos 900 = 0

W = F × S × 0 = 0  (Total work is zero)

it means if the displacement is perpendicular to the direction of the force, then the work will be zero.

if θ = 0

then  cos 0 = 1

W = F × S

It means if displacement in the direction of force θ = o then work will be maximum.

### Examples of Directions of Applied Force for Works:

1. The direction of centripetal force acting on a body moving in a circular path is towards the centre, which is perpendicular to the displacement, so no work is done by the force due to the value of displacement in the direction of the force being zero.
2. Similarly, when an object moves in the same direction with a uniform speed, then according to Newton’s first law of motion, no work is done because the value of force is zero.
3. If a person tries to push a wall but the wall does not move from its place, no work is done by the person because the displacement is zero.

### Difference between work done by an object and work done on an object:

When a force is applied by an object, work is done by that object and work is done on the object when a force is applied on it. For example, when we lift a stone, the hand exerts a force on the stone, so in this action the hand acts on the stone, on the contrary, when the stone falls down, the force on it due to gravity is applied downwards, in this action the work is done by the stone.

### Unit of Work

unit of work = unit of force × unit of distance = Newton-meter

The unit of work in M.K.S. system is also called joule, it is represented by the letter J.

It is worth noting here that although force and displacement are both vector quantities, work is a scalar quantity.

Other unit of work:

Work = power × time = watt × hour = watt.hour

1 watt. hour = (1 Jule / 1 second) × 3600 second = 3600 Jule

## Energy

The capacity of working of an object is called energy. It may exist in kinetic, thermal, electrical, chemical, nuclear, or other various forms. Like work, energy is also a scalar quantity. Actually work is done by energy transfer. There are always two factors involved in doing work – one who does the work and the one on whom the work is done. The energy of the object doing work decreases as much as the energy of the other object increases. The entire energy of the system remains constant. The work done is equal to the energy transferred.

### Difference Sources of Energy:

#### 1) Solar Energy:

Actually the Sun is the fundamental source of all types of energy. Human invented all other sources of energy are only ​transform of solar energy. For example, growth in plants is due to solar energy. We obtain food and wood from these plants that contain chemical energy.In ancient era the plants were buried inside the Earth due to extreme temperature and pressure that were converted into coal, petroleum etc which are sources of energy. Like this, the water from oceans evaporate due to solar energy and this evaporated water falls on the earth in the form of rain. This rainwater is used to production of electricity through turbines.

The fundamental source of solar energy is nuclear fusion. In this process, four nuclei of hydrogen combine to form one nucleus of helium. Whatever mass is lost in this reaction is converted into energy according to Einstein’s mass-energy equation. The Sun is 99 percent hydrogen, due to which the process of nuclear fusion on the Sun will continue to provide additional energy to the Earth for millions of years in the future.

#### 2) Water Energy:

Under this, hydroelectric energy is obtained mainly by dynamo by dropping high potential energy water obtained by making dams on rivers and tidal water of the sea on turbine blades. Hydroelectric power is the leading renewable energy source used to generate electricity in most countries. The first commercial U.S. power station using ocean waves to generate electricity is in the works in Oregon. Apart from this, water energy is also used in transportation.

#### 3)  Air Energy:

Moving air has kinetic energy due to its velocity. Many mechanical works can be done with this. For example, separating straw from grain, sailing boats, generating electricity by a windmill, etc.

#### 4) Fossil Fuel Energy:

Energy sources that were formed from ancient plants and organisms during the Carboniferous Period, approximately 286 – 360 million years ago are called fossil fuel energy. There are three major types of fossil fuels:

• Coal: Due to pressure and heat ferns, plants and trees were hardened and converted into coal.
• Petroleum: Intense amounts of pressure caused smaller organisms, like zooplankton and algae to decompose into petroleum.
• Natural Gas undergoes the same process as oil; however, the process is long and subject to higher amounts of heat and pressure, causing further decomposition.

#### 5)  Biomass:

Biomass is renewable organic material that comes from plants and animals. The decomposition of those parts of trees-plants and animals which are discarded as waste releases methane gas which is flammable. It is used as fuel. Biomass continues to be an important fuel in many countries, especially for cooking and heating in developing countries.

#### 6) Nuclear Energy:

When the nuclei of many radioactive substances (especially uranium) are fissioned by the bombardment of neutrons, some amount of nuclear mass is converted into energy according to Einstein’s theory, releasing a large amount of nuclear energy. This action takes place in a nuclear reactor.

#### 7) Geothermal Energy:

Geothermal energy is heat within the earth. It is a renewable energy source because heat is continuously produced inside the earth. People use geothermal heat for bathing, heating buildings, and generating electricity.

### Different Form of Energy:

1) Mechanical Energy, 2) Thermal Energy, 3) Light Energy, 4) Electric Energy,

5) Magnetic Energy,  6) Sound Energy, 7) Chemical Energy, 8) Nuclear Energy

#### Mechanical energy:

Some of the kinetic energy, and the potential energy. Actually, the ability of an object to do work only due to mechanical reasons (position or motion) is called mechanical energy.

##### Kinetic Energy:

The ability of an object to do work due to its motion is called kinetic energy.

Kinetic energy is measured by the work that an object does to come from its moving state to a standstill.

If an object of mass m is moving with a velocity v, then its kinetic energy K.E. = 1/2 m v2.

The kinetic energy of an object = work is done by object = F × s

##### Potential Energy:

The ability of an object to do work due to its particular position is called potential energy. There are many transforms of potential energy, some of them are given below:

###### A) Gravitational potential energy:

The work done against the force of gravity in raising an object above the earth’s surface is stored in the object in the form of potential energy. This is called gravitational potential energy.

###### B) Elastic potential energy:

The energy possessed by an object due to its shape (like; spring) is called elastic potential energy.

###### C) Electrostatic potential energy:

Electric potential energy is the energy that is needed to move a charge against an electric field.

###### D) Chemical potential energy:

This type of energy is stored in the chemical bonds of a substance. For example; gasoline contains a large amount of chemical potential energy that is released when the gasoline is burned in a controlled way in the engine of the vehicles.

###### E) Magnetic potential energy:

When a magnetic dipole moves in a magnetic field it possesses potential energy which depends upon its orientation with respect to the magnetic field.

###### F) Nuclear potential energy:

This type of potential energy is found among particles such as protons and neutrons that are present inside the nucleus of an atom. This energy holds protons and neutrons together to form the nucleus.

### Conversion of Energy:

Energy is not destroyed only it is transformed. According to the law of conservation of energy, “energy can neither be created nor destroyed, it can only be transformed from one form to another.” According to this law, the total amount of energy in the universe is always constant.
For example, when a body falls from a height, its gravitational potential energy decreases but the velocity of the body increases. Due to this the kinetic energy of the body increases as much as the potential energy decreases. That is, while falling from a height, the total energy in each position of the body remains constant.

#### Various examples of energy conversion:

##### 1. Conversion of electrical energy into light energy:

Light energy is produced when an electric bulb is lit.

##### 2. Conversion of electrical energy into thermal energy:

In an electric heater, electrical energy is converted into thermal energy.

##### 3. Conversion of kinetic energy into electrical energy:

In the dynamo, the kinetic energy of the coil is converted into electrical energy.

##### 4. Conversion of sound energy into electrical energy:

In the microphone, the conversion of sound energy into electrical energy takes place.

##### 5. Conversion of electrical energy into sound energy:

The electrical energy coming from the microphone by loudspeakers is converted into sound energy.

##### 6. Conversion of chemical energy into light and thermal energy:

When a candle or any other object is lit, chemical energy is converted into light and heat energy.

##### 7. Conversion of potential energy into kinetic energy:

By pouring the accumulated water from the dam built on the rivers and spinning it on the turbine, the potential energy is converted into kinetic energy.

##### 8. Conversion of Kinetic Energy into Potential Energy:

When a bullet released from a gun hits a target, its kinetic energy is converted into potential energy.

##### 9. Conversion of nuclear energy into electrical energy:

In nuclear reactors, the nuclear energy of an atom is converted into electrical energy.

##### 10. Conversion of nuclear energy into heat, light, and mechanical energy:

Nuclear energy is converted into heat, light, and mechanical energy in the atomic bombs, hydrogen bombs Sun, and other stars.

#### Mass-Energy Equation:

In 1905, the scientist Einstein said that every substance has energy due to its mass. Whenever there is a loss of mass we get energy. Mass can be converted into energy and energy into mass.

According to Einstein’s mass-energy equation, the total energy produced, (E) = mc2 when an object of mass m is completely converted into energy.
where c = 3 × 108 m/s (speed of light)

## Power:

Power is the rate at which a job is done or the rate at which power is moved from one location to one more or changed from one kind to one more. In various other words, power is the rate at which a job is done. It is the work/time proportion. Mathematically, it is calculated utilizing the list below formula.

Power = Work / time;   [ P = W/t]

or, Power = (Force x Displacement)/Time;    [P = (f x d)/t]

or, Power = Force x Velocity;  [ P = f x v ]

The S.I. unit of power is the Watt. As is suggested by the formula for power, a unit of power amounts to a unit of job split by a unit of time. Thus, a Watt amounts to a Joule/second. The horsepower is sometimes made use of to define the power supplied by equipment. One horsepower amounts to around 750 Watts.

Most equipment is made as well as developed to do service things. All equipment is commonly explained by a power ranking. The power ranking shows the rate at which that device can do function upon various other things. Thus, the power of the equipment is the work/time proportion for that certain device. An auto engine is an instance of equipment that is offered a power ranking. The power ranking connects to just how swiftly the cars and trucks can speed up the cars and trucks. Suppose that a 40-horsepower engine might speed up the cars and trucks from 0 mi/hr to 60 mi/hr in 16 secs. If this held true, after that an automobile with 4 times the horsepower might do the exact same quantity of operating in a quarter the moment. That is, a 160-horsepower engine might speed up the exact same cars and trucks from 0 mi/hr to 60 mi/hr in 4 secs. The factor is that for the exact same quantity of job, power, as well as time, are vice versa symmetrical. The power formula recommends that a much more effective engine can do the exact same quantity of operating in much less time.

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