Conservation of Mechanical Energy: Definition, Formulas, Principles and More

Updated on Sep 1, 2025 10:19 IST

Mechanical Energy is defined as the energy obtained by a body due to its motion or position. As we have studied before, the energy possessed by an object due to its motion is called Kinetic Energy and the energy possessed through position is known as Potential Energy. Therefore, to sum up, Mechanical Energy is the resulting sum of both kinetic and potential energies of a particular object. Mechanical Energy is one of the core fundamental topics of physics and is used to solve a vast range of numerical problems which are frequently asked in JEE MAINS.

Studying Mechanical Energy will help you gain a clear understanding of how energies are converted between different forms and utilized efficiently by the systems. Let us understand the concept deeply through this article.

Relevant Suggestion: NCERT Solutions

Table of content

What is Mechanical Energy?
Conservation of Mechanical Energy
Important Formulas used in Mechanical Energy
Applications in Real World
Physics Class 11 Notes for Revision
Physics Class 11 NCERT Solutions

What is Mechanical Energy?

In simple terms, Mechanical energy is the total sum of both the kinetic energy $(K)$ and potential energy $(U)$ of an object. The SI unit for energy is the joule (J), with dimensions $M^{1} L^{2} T^{- 2}$ .

Mathematical Representation:

$E = K + U$

Where Kinetic Energy: $K = \frac{1}{2} m v^{2}$ ,

And Potential Energy = ( $U = m g h$ )

Example: A ball thrown in the air will gain high potential energy due to its height and comparatively low kinetic energy. And when it starts moving down, the potential energy gradually starts reducing and converting back into kinetic energy. As soon as it reaches the ground, the lost kinetic energy is regained (due to the motion) and there is decline in the potential energy of the ball.

Conservation of Mechanical Energy

Conservation of mechanical energy is a core concept of physics defined by the scientists for studying and observing the motion of an object. What it states is that the total mechanical energy will always remain constant in the absence of some non-conservative forces like friction, air resistance, etc.

This can be explained further with the help of Work-Energy Theorem:

As per the work-energy theorem, Total Work done on an object = Change in the object's Kinetic Energy

For conservative forces, Work done will be:

Wconservative=−ΔPE

As per the Work Energy Theorem,

Wtotal=ΔKE

When we substitute the values of 1 and 2, we get –

−ΔPE=ΔKE

ΔKE+ΔPE=0

(KE_final−KE_initial)+(PE_final−P_Einitial)=0(KE_final+PE_final)=(KE_initial+PE_initial)(KE_final+PE_final)

=(KE_initial+PE_initial)

Great! Value of the initial mechanical energy turns out to be equal to the value of the final mechanical energy, which in turn proved our belief that mechanical energy always remains preserved inside the system.

Important Formulas used in Mechanical Energy

Here are some of the useful formulas used in the numerical problems which the candidates can go through:

1. Kinetic Energy:

This is the energy possessed by the body through its motion and is represented by:

$K = \frac{1}{2} m v^{2}$ ,

where 𝑚 is mass of the object,

and 𝑣 is velocity of the body.

2. Potential Energy:

This is the energy stored in the body, or the energy possessed due to its position. This energy can be further classified into 2 types:

Gravitational Potential Energy:

Gravitational Potential Energy is gained due to height of the body and is represented by:

P = mgh

Where m = mass of the body,

g = 9.8 m/s^2,

and h = height of the body.

Elasticity:

Elastic Potential Energy is another type of energy which is gained by a body while being stretched or compressed. Mathematical representation of this energy will be:

𝑈=1/2*𝑘*𝑥^2

Where k = spring constant,

And x = displacement from the original position.

Applications in Real World

The conservation of mechanical energy has various applications in our day to day lives, with some most common ones as follows:

Roller Coasters
Construction Sites
Automobiles
Wind Turbines
Power Plants
Electric Generators
Sports

Physics Class 11 Notes for Revision

You can refer to these notes which are specifically designed to ease the preparation process for competitive exams:

Units and Measurements Class 11 Notes	Mechanical Properties of Solids Class 11 Notes
Motion in a Straight Line Class 11 Notes	Mechanical Properties of Fluids Class 11 Notes
NCERT Class 11 Notes for Motion in a Plane	Thermal Properties of Matter Class 11 Notes
Laws of Motion Class 11 Notes	Thermodynamics Class 11 Notes
Work, Energy, and Power Class 11 Notes	Kinetic Theory of Gas Class 11 Notes
System of Particles and Rotational Motion Class 11 Notes	Oscillations Class 11 Notes
Gravitation Class 11 Notes	Waves Class 11 Notes

Students may also like:

NCERT Class 11 Notes for PCM

NCERT Class 11 Physics Notes

Physics Class 11 NCERT Solutions

NCERT forms the base of any topic and should be thoroughly studies before looking out for high level concepts. Check these solutions for various important topics in the physics subject:

NCERT Solutions for Physics Class 11

Units and Measurements Class 11 NCERT Solutions	Mechanical Properties of Solids Class 11 NCERT Solutions
Motion in a Straight Line Class 11 NCERT Solutions	Mechanical Properties of Fluids Class 11 NCERT Solutions
Motion in a Plane Class 11 NCERT Solutions	Thermal Properties of Matter Class 11 NCERT Solutions
Laws of Motion Class 11 NCERT Solutions	Thermodynamics Class 11 NCERT Solutions
Work, Energy, and Power Class 11 NCERT Solutions	Kinetic Theory Class 11 NCERT Solutions
System of Particles and Rotational Motion Class 11 NCERT Solutions	Oscillations Class 11 NCERT Solutions
Gravitation Class 11 NCERT Solutions	Waves Class 11 NCERT Solutions

Commonly asked questions

How is conservation of mechanical energy related to newton's law of motion?

Conservation of Mechanical Energy is linked to newton's second law of motion (F = ma) in combination with work energy theorem. The work energy theorem states that total work done on an object equals to change in kinetic energy. This theorem is used to prove that the sum of kinetic energy and potential energy remains constant.

Does the concept of conservation of mechanical energy also apply to the real-world situations?

Not in all cases. This happens due to the interruption of non conservative forces like friction, air resistance, etc. which are responsible for decreasing the mechanical energy by converting it into other forms of energy such as heat, noise, etc.

Can Mechanical Energy be negative?

Yes. Mechanical energy is the sum of both kinetic and potential energies. Kinetic energy cannot be a negative value since mass is always positive and velocity square leads to a positive value. However, potential energy can be negative depending on the reference point.

Physics Work, Energy and Power Exam