Understanding Energy: Types, Formulas, and Applications

Energy in physics is defined as the ability or capacity of a body to perform work. In simple terms, it is what enables an object to carry out any task or activity. Broadly, energy is categorized into two main types: kinetic energy and potential energy.

In this article, we’ll explore the concept of energy, its types, the law of conservation of energy, and much more in detail.

But before diving into energy itself, it’s important to understand the concept of work done—so let’s begin there.

What is Work in Physics?

Work is said to be done when a force is applied to an object, and the object moves in the direction of that force. In other words, work done is the product of the magnitude of the force applied and the displacement of the object in the direction of the force.

Formula for Work Done

Work (W)=Force (F)×Displacement (d)×cos⁡(θ)

Where:

• W is the work done (in joules),
• F is the applied force (in newtons),
• d is the displacement (in meters),
• θ is the angle between the force and the direction of displacement.

Sign Conventions for Work Done

Understanding the sign of work done is crucial in physics, as it tells us whether energy is being transferred to or from an object.

1. Positive Work

Work is positive when the force and the displacement are in the same direction. W=F×s

Example: Pulling a cart forward — both force and movement are in the same direction.

2. Negative Work

Work is negative when the force acts in the opposite direction to the displacement.

W=−F×s

This occurs when the angle between the force and displacement is 180°.

Example: Frictional force acting against a moving object.

3. Work at an Angle

When force and displacement are inclined at an angle θ (where 0° < θ < 180°), the work done is given by:

W=F⋅s⋅cos⁡θ

This equation accounts for the component of force in the direction of displacement.

4. Zero Work

Work done is zero in the following cases:

• When the angle between the force and displacement is 90° (perpendicular),
• Or when no displacement occurs at all.

Example: Pushing against a rigid wall that doesn’t move.

Key Points:

• Work is positive if the force and displacement are in the same direction.
• Work is negative if the force and displacement are in opposite directions.
• If there is no displacement, no work is done—even if a force is applied.

Unit of Work Done

The SI unit of work is the Joule (J).

Definition:

One Joule of work is said to be done when a force of 1 Newton displaces an object by 1 meter in the direction of the force.

1 Joule=1 Newton×1 meter

Quick Insight:

• Joule (J) is a derived unit in the SI system.
• It is also used to measure energy, as work and energy are closely related in physics.

Dimensional Formula of Work Done

The dimensional formula of work is:

[M L²T⁻²]

Explanation:

Work is defined as:

Work (W)=Force (F)×Displacement 

Now,

• Force F=Mass×Acceleration=[M][L][T⁻²]
• Displacement d=[L]

So, the dimensional formula of Work=[M][L][T⁻²]×[L]=[ML²T⁻²]

This dimensional formula helps in verifying the correctness of equations in physics through dimensional analysis.

What is Energy?

In physics, energy is defined as the capacity of a body to perform work. It is a fundamental concept that explains how things move and change. Since energy and work are closely related, they share the same unit—the Joule (J), which is equivalent to Newton-meter (N·m).

There are various forms of energy, including:

• Mechanical Energy
• Heat (Thermal) Energy
• Light (Radiant) Energy
• Chemical Energy
• Electrical Energy

Source of Energy

In simple terms, energy is the ability of an object to do work. On Earth, the Sun is considered the primary and ultimate source of energy, powering most life and natural processes.

Units of Energy

The SI unit of energy is the Joule (J), named after the English physicist James Prescott Joule.

Definition:

One Joule is the energy transferred when a force of 1 Newton moves an object by 1 meter in the direction of the force.

Other common units of energy include:

• Calorie
• Kilowatt-hour (kWh)
• Erg

Dimensional Formula of Energy

Since energy and work are measured in the same unit, they also share the same dimensional formula: [M L²T⁻²]

Where:

• M = Mass
• L = Length
• T = Time

Energy Conversion: Transfer and Transformation

Energy can neither be created nor destroyed, but it can be transferred or transformed from one form to another. This principle is a cornerstone of the Law of Conservation of Energy.

Types of Energy Transformation:

1. Mechanical Energy Conversion
   (e.g., Moving vehicles, turbines)
2. Electrical Energy Conversion
   (e.g., Generators converting mechanical energy into electricity)
3. Energy Conversion by Radiation
   (e.g., Solar panels converting sunlight into electricity)
4. Energy Conversion by Heating
   (e.g., Boilers converting electrical energy into thermal energy)

Law of Conservation of Energy

The Law of Conservation of Energy states:

“Energy can neither be created nor destroyed; it can only be transformed from one form to another.”

In simpler terms:

“In a closed and isolated system, the total energy remains constant over time.”

This is one of the most fundamental laws in physics. It helps explain countless phenomena, from how stars shine to how machines work on Earth.

Different Types of Energy

All forms of energy can broadly be grouped into two main categories:

• Kinetic Energy (K.E.) – Energy due to motion
• Potential Energy (P.E.) – Energy stored due to position or configuration

Let’s dive into kinetic energy in more detail.

Kinetic Energy

Kinetic Energy is the energy an object possesses due to its motion. Any object that moves—whether it’s a running athlete or a speeding car—has kinetic energy. The faster an object moves or the more massive it is, the more kinetic energy it has.

Kinetic Energy Formula

K_E=1/2mv²

Where:

• m = mass of the object
• v = velocity of the object

Units of Kinetic Energy

• SI Unit: Joule (J) → 1 J = 1 kg·m²/s²
• CGS Unit: Erg → 1 erg = 10⁻⁷ J

Derivation of Kinetic Energy Formula

Let’s derive the formula using the concept of work done:

Work Done (W) = Force (F) × Displacement (s)

From Newton’s Second Law:

Using the equation of motion:

Now, substitute:

If the object starts from rest (u = 0):

Since work done = change in kinetic energy,

Types of Kinetic Energy

Kinetic energy appears in several different forms depending on the type of motion:

Radiant Energy

Energy carried by electromagnetic waves (like sunlight). It doesn’t need a medium to travel.

Thermal Energy

Energy due to the movement of particles in matter. Examples include heat from fire or geothermal sources.

Sound Energy

Energy from vibrating objects transmitted through a medium (like air). It enables hearing.

Electrical Energy

Energy from moving electrons. It powers our homes, electronics, and appliances.

What is Potential Energy?

Potential Energy is the stored energy in an object due to its position or state. When work is done on an object to change its position or shape, this energy is stored and referred to as potential energy.

For example:

• A stretched rubber band stores elastic potential energy.
• A rock held at a height stores gravitational potential energy.

Potential Energy Formula

The potential energy due to gravity is given by: PE=m⋅g⋅h\text{PE} = m \cdot g \cdot hPE=m⋅g⋅h

Where:

• m = mass of the object
• g = gravitational acceleration (9.8 m/s²)
• h = height above the ground

This equation tells us that the higher or heavier an object is, the more potential energy it stores.

Units of Potential Energy

Just like Kinetic Energy, the unit of Potential Energy is:

• SI Unit: Joule (J) → 1 J = 1 kg·m²/s²
• CGS Unit: Erg → 1 erg = 10⁻⁷ J

Types of Potential Energy

Potential energy comes in various forms, depending on how the energy is stored:

1. Gravitational Potential Energy

Energy stored due to an object’s position relative to Earth (or any gravitational source).

Example: A rock at the edge of a cliff.

2. Elastic Potential Energy

Energy stored in stretched or compressed objects.

Example: A stretched rubber band or compressed spring.

3. Electric Potential Energy

Energy stored due to the position of charged particles in an electric field.

Example: Charges in a capacitor or ends of a battery.

4. Chemical Potential Energy

Energy stored in the bonds of chemical substances.

Example: Batteries, food, or fuel like gasoline.

Work-Energy Theorem

The Work-Energy Theorem is a fundamental concept in physics that relates the net work done on an object to the change in its kinetic energy.

Statement: The net work done by all the forces acting on an object is equal to the change in its kinetic energy.

Mathematically:

W_net=ΔKE=KE_final−KE_initial

Using the formula for kinetic energy:

Where:

• Wnet = Net work done
• m = Mass of the object
• u = Initial velocity
• v = Final velocity

Interpretation: This theorem tells us that whenever work is done on an object, it results in a change in its kinetic energy. If the object speeds up, kinetic energy increases. If it slows down, kinetic energy decreases.

For example:

• Pushing a car makes it accelerate — positive work increases its kinetic energy.
• Friction slows it down — negative work reduces its kinetic energy.

Mechanical Energy

Mechanical Energy is the total energy possessed by an object due to its motion and position. It is the sum of Kinetic Energy (KE) and Potential Energy (PE).

Definition: The total energy of an object, combining both its kinetic energy (due to motion) and potential energy (due to position), is called its mechanical energy.

Formula for Mechanical Energy:

Where:

• m = Mass of the object
• v = Velocity of the object
• g = Acceleration due to gravity (9.8 m/s²)
• h = Height of the object from the ground

Key Points:

• Mechanical energy is conserved in the absence of non-conservative forces like friction or air resistance.
• It plays a crucial role in systems like pendulums, projectiles, machines, and roller coasters.

What is Power?

Power is the rate at which work is done or the rate at which energy is transferred. It measures how quickly work is completed or how rapidly energy is used. Power is typically denoted by the symbol P.

Definition: In simple terms, power is the ratio of work done to the time taken to do that work:

P=Wt

Where:

• P = Power
• W = Work done
• t = Time taken to do the work

Units of Power:

• The SI unit of power is the Watt (W), which is defined as 1 Joule per second (Js⁻¹).
• In commercial contexts, Power is often measured in kilowatt-hours (kWh), which refers to the amount of energy consumed or transferred in 1 hour at a rate of 1000 Joules per second.

Conversion:

1 kWh = 3.6 × 10⁶ Joules (J)

Key Points:

• Power tells you how fast an object or system can perform work.
• Common devices like motors, light bulbs, and engines have their power measured in watts or kilowatts.

Examples on Energy Formula

Example 1: How much work is required to stop the car in 20 s if the kinetic energy of the car is 5000 J and what is its power?

Given:

• Kinetic energy of the car K_E=5000 J
• Time to stop the car t=20 s

Solution:

Work required to stop the car:

The work done to stop the car is equal to the change in its kinetic energy. Since the car is coming to a stop, the final kinetic energy is zero, so:

(The negative sign indicates that the work is done against the car to stop it.)

Power:

Power is defined as the rate at which work is done. The formula for power is:

Substituting the values:

So, the power required to stop the car is 250 W (the negative sign indicates that the energy is being used to stop the car).

Final Answer:

• Work done: -5000 J
• Power: 250 W

Example 2: Two passengers of mass 50 kg each sit in the car then find the Kinetic energy of car if the mass of the car is 800 kg and velocity of the car is 15 km/h.

Let’s solve this step by step:

Given:

• Mass of the car m_car=800 kg
• Mass of each passenger m_passenger=50 kg
• Velocity of the car v=15 km/h

First, we need to convert the velocity from km/h to m/s:

Now, let’s calculate the total mass of the car and the passengers:

Formula for Kinetic Energy: The kinetic energy K_E is given by the formula:

Substituting the values:

Final Answer: The kinetic energy of the car with two passengers is 7815 J.

Read Next:

1. MTOE: Million Tons of Oil Equivalent 
2. Global Primary Energy Reserves
3. Various Forms of Energy
4. Energy Management