## What is Energy?

The ability of an object to work is called **Energy**. The energy contained in an object is measured by the total work that the object can perform from its present state until it is in that state (while it can no longer work) until it reaches zero energy. Thus, the work done by an object is the measurement of energy. Because of measuring energy with work, the units of energy and work are the same. The **dimensional formula of energy** is [ML^{2}T^{-2}]. It has unit joule in the SI system and arg in the CGS method. Some other units of energy are calories, kilowatt-hours, and electron volts.

### Different Forms of Energy

Energy in nature is found in many forms, among which are some common forms of energy.

#### 1. Mechanical Energy

The energy, due to which an object can do mechanical work, is called mechanical energy. Examples- Energy of a moving car, energy of water in a water tank, etc. Mechanical energy consists of kinetic energy and potential energy.

#### 2. Internal Energy

The energy stored in an object due to its heat or intermittent forces is called internal energy. Hence, there are molecules present in each object, which are vibrational with respect to each other. The kinetic energy due to the motion of the molecules in the object and the potential energy due to the molecular forces are present. In fact, the internal energy of an object is the sum of the kinetic energy and potential energy of the molecules.

#### 3. Heat Energy

The energy due to which we feel the heat of an object or the energy obtained due to the heating of an object is called thermal energy. The thermal energy in an object arises due to the disordered variance of the molecules. Steam contains thermal energy. In steam engines, heat is used to perform useful mechanical work.

#### 4. Chemical Energy

The difference between the energy of a chemical compound and the energy of the elements that make up that chemical compound is called chemical energy, that is, chemical energy is due to the bonds in the atoms of a chemical compound. Chemical energy is present in a chemical reaction.

Energy is either absorbed or emitted in chemical reactions. If the total energy of the reactants present in the chemical reaction is less than the total energy of the products, the energy is absorbed and in the opposite case, energy is emitted.

Examples- The energy of a power cell, the energy contained in coal or oil, which is obtained by combustion, etc.

#### 5. Electric Energy

Equal electric charges repel each other and uneven electric charges attract each other, ie the charges exert forces on each other. Hence, the electric field has to move the electric charge from one point to another, which is stored in the form of energy. Examples - electric motors, electric bulbs, etc.

#### 6. Nuclear Energy

The nucleus of an atom is formed by neutrons and protons. The energy through which neutrons and protons are stored in the nucleus is called nuclear energy. Nuclear energy is expressed in nuclear fusion and nuclear fission.

#### 7. Light Energy

The energy that causes things to be seen clearly to us is called light energy.

Examples: Energy derived from electric bulbs, candles, etc.

#### 8. Sound Energy

The energy that causes us to feel heard is called sound energy.

#### 9. Wind Energy

There is kinetic energy in the fast-flowing air. This energy of wind is called wind energy. Wind energy is used in windmills, water pumps, etc. Currently, wind energy is also used to generate electricity.

#### 10. Hydro Energy

Energy derived from flowing water is called water energy. With its help, the electric currents produce electricity through the generator. About 25% of the water in India is derived from sources of water.

#### 11. Bio-mass Energy

Energy derived from cow dung gas or waste etc. is bio-weight energy. It produces methane gas which is used as fuel.

#### 12. Solar Energy

The energy received by the sun every day is called solar energy. The Sun is directly or indirectly the basis of all the energy sources found on the Earth. The Sun is the biggest source of energy.

## What is Mechanical Energy?

The energy present in an object with the help of which it can do any mechanical work is called mechanical energy. For example, the energy of water in a water tank on the roof of a house is mechanical energy, the energy of a moving car is also mechanical energy.

### Types of Mechanical Energy

There are mainly two types of mechanical energy.

- Kinetic Energy
- Potential Energy

#### 1. Kinetic Energy

The ability of any object to perform its work due to its speed is called the object's kinetic energy. The value of kinetic energy is always positive, ie its value cannot be obtained negative under any circumstances. The kinetic energy is the scalar amount. If the mass of an object is (m), which is moving with v velocity, then the kinetic energy of that object

The unit of kinetic energy in the SI system is Joule and arg in the CGS method. Its dimensional formula is [ML^{2}T^{-2}].

##### Examples of kinetic energy

- The shot fired by the gun has kinetic energy, due to which it can penetrate the target for some distance.
- The running water has kinetic energy, which can be used to rotate a turbine, flush large wooden logs.
- A moving hammer has kinetic energy, due to which it can hit the nail and bury it in the wall.
- Dynamic air also contains kinetic energy, by which the operation of windmills and boats can be accelerated.

##### Expression of Kinetic Energy

The speed energy of any moving object is measured by two following methods.

- By measuring the work done in moving an object from a pause to a dynamic state.
- By measuring the work done in resting a moving object.

##### First Method

Suppose an object of mass m is displaced to an s distance by exerting an external force F. If the acceleration of the object is a and the velocity v, then

From Newton's Second Law of Motion,

Force (F) = ma ...1

From the third equation of motion v^{2} = u^{2} + 2as,

Here, u = 0

Hence, v^{2} = 2as

Work done by force (F)

W = F × s …3

Putting the values of equation 1 and equation 2 in equation 3,

Therefore, the kinetic energy of a moving object is directly proportional to the square of its mass (m) and velocity (v).

##### Second Method

Suppose an object of mass m is moving with v velocity. A restraining force F is applied to this object in the opposite direction of motion, which produces the dilution a in the object.

Due to which the object s stops after traveling a distance, so

Blocking force (F) = mass × acceleration …1

By the third equation of motion,

v^{2} = u^{2} + 2as

0 = u^{2} + 2as

-2as = u^{2} a = -v^{2}/2s ...2

Putting the value of equation 2 in equation 1,

The kinetic energy of the object (K) = the work done to bring the object from the dynamic state to rest = inhibitory force × displacement in the direction of the force

K = F × (-s) ...4

Putting the value of equation 3 in equation 4

#### 2. Potential Energy

The energy due to its position or configuration in an object or body is called its potential energy. Potential energy is inherent in many forms; Such as - Gravitational, Elastic, Chemical, Electrical, etc. The potential energy is displayed as the signal energy of the signal U.

##### Examples of Potential Energy

- Water stored at high altitudes in the dam has gravitational potential energy through which the turbine rotates.
- When the hammer is lifted, the gravitational potential energy is conserved in it, through which the wedge falls into the wood.
- When the key is loaded in the clock, the elastic energy stored in the spring corresponding to the clock, through which the clock needles move.
- When the bowstring is pulled, the elastic potential energy is stored in the string, through which the arrow moves.

##### Measurement of Potential Energy

The potential energy of an object is also measured by the work done to move that object from a zero-position to its present state or to move that object from its current position to a zero-position. The potential energy is explained only for the protective force field. This has no significance for the non-conservative force field.

There is a change in potential energy (dU) of the object corresponding to the Conservative internal force,

Normally, the directions take the point to infinity, and there the potential energy is assumed to be zero i.e

If r_{i} = ∞ (infinite) and U_{i} = 0, then

Therefore the potential energy is at the negative value of the work done by the conservative force, which is done to bring that object from the eternal to the present position.

##### Types of Potential Energy

##### 1. Gravitational Potential Energy

When an object is lifted above the surface of the earth, it has to work against the gravitational force. This work is contained in the object in the form of gravitational potential energy, so the ability to work to lift an object above the surface of the earth is called gravitational potential energy.

**The formula for Gravitational Potential Energy**

Suppose an object of one m mass is raised to h height as per the picture, then the potential energy of the object = work done to move the object to h height against the force of gravity.

U = F×h

U = mg×h

Where F = mg

U = mgh

##### Relation between Gravitational Force and Gravitational Potential Energy

Let an object of mass m lie on the surface of the earth, the force of gravity acting on the object,

F = -mg ...1

The work done in moving the object to h height against the force of gravity,

W = (-mg)×h

W = -mgh

Therefore, we can say that the gravitational potential energy of a body at h height above the earth's surface is equal to the negative value of the work done by the force of gravity in lifting the same body to the same height. If the gravitational potential energy is a function of height above the earth plane, this can be represented by U (h). If the value of height varies from the surface of the earth, then

It is clear from the above equation that the gravitational force (F) is equal to the negative derivative of the gravitational potential energy U (h) relative to height (h).

##### 2. Elastic Potential Energy

The energy present in the object due to its elasticity (ie in its compressed or stretched state) is called elastic energy. If the spring force is F = -kx, then the elastic potential energy of the spring

Where k, the force of spring is constant and x is the change in length of spring. If the length of a spring is changed from the initial state x_{1} to the final state x_{2},

Then increase the elastic potential energy is

##### Elastic Potential Energy of a Spring

If a spring is compressed or propagated, an afferent force is generated in the spring. Suppose a spring is pulled or pressed from its normal position (x = 0), then the external force is acted against the afferent force.

If the length of the spring is increased x, then the force acting on it

F α –x

F = -kx

Here k is a constant called spring force constant or spring constant.

To increase the length of the spring, a force has to be applied against the force of the afferent,

Hence the external force acting on the spring

F_{External} = -F = -(-kx) = kx

If there is a very small increase dx in the spring by applying external force, then the work done

dW = F_{External} xdx = kxdx

The work done by the force to increase the length of the spring from 0 to x,

This work is stored in the spring in the form of elastic potential energy,

Hence the elastic potential energy of the spring

If the spring is compressed by x length, then the direction of external force F is to the left, and the direction of spring force F_{a} is to the right. In this case, vector F being θ = 180^{o} and the work done is -½kx^{2} and the work done by F is -½kx^{2}, so the spring's recalcitrant potential energy is U = -½kx^{2}.

If the spring is displaced from the equilibrium position O to the other kinetic energy again, the elastic potential energy converts, and when the displacement is maximum, the full kinetic energy is converted to potential energy again. Therefore, the kinetic energy and potential energy changes mutually when the object makes a simple periodic motion and the total mechanical energy of the object is always fixed.

The change of energy with distance is shown in the diagram below.

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