# Conservation of Mechanical Energy of a system

Energy is a basic physical property of a system. Physics defines energy as the ability to do work. That means a system or a body can do work only if it has some energy. A system can store energy in many forms like Mechanical energy, Chemical Energy, Electrical energy, etc. Again, energy can be transformed from one form to another. For example, a microphone converts electrical energy into sound energy. What a system can do all due to its energy. In this article, I’m going to explain the basic concepts of Mechanical energy of a system and the law of conservation of mechanical energy.

1. Definition of Mechanical Energy in Physics
2. Types of Mechanical Energy
3. Formula of Mechanical Energy of a system
4. Examples of Mechanical Energy
5. Conservation of Mechanical Energy

## Definition of Mechanical Energy in Physics

The Mechanical energy of a system is defined as the total energy of the system available for mechanical work. In simple words, the energy of a system with which it can do mechanical work is the Mechanical energy of the system.

## Types of Mechanical Energy

The mechanical energy of a body has two types – Kinetic energy and Potential energy.

• Kinetic energy is the ability to do work due to motion.
• Potential energy is the ability to do work due to the position above the ground.

The sum of kinetic energy and potential energy gives the total mechanical energy of the body.

Read a detailed article on Kinetic energy and Potential energy.

## Formula of Mechanical energy of a System

The total Mechanical Energy of a body is the sum of its kinetic energy and potential energy.

So, Total Mechanical Energy = Kinetic Energy + Potential Energy

If an object of mass m is moving with a velocity v, then the equation of its kinetic energy is $\color{Blue}\small K.E. = \frac{1}{2}mv^{2}$………(1)

Again, if an object of mass m is positioned at a height h from the ground then its potential energy is, $\color{Blue}\small P.E. = mgh$…..(2)

Thus, the formula for Mechanical energy of an object of mass m moving with a velocity v at a height h above the ground is Mechanical Energy = K.E. + P.E.

or, Mechanical energy = $\color{Blue}\small \frac{1}{2}mv^{2} + mgh$………..(3)

## Examples of Mechanical Energy

There is a number of examples of Mechanical energy that we see in our daily life. What are those? The energy of all moving bodies is kinetic Mechanical energy. Again, the potential energy of a body at a height is potential Mechanical energy. Check the following list of examples of mechanical energy –

1. A moving vehicle has mechanical energy in the form of kinetic energy.
2. A moving baseball has mechanical energy in the form of kinetic energy.
3.  If we throw a ball in the vertical direction, it will have mechanical energy in the form of both kinetic and potential energy.
4. A swinging pendulum is a good example where Mechanical energy is present in the form of both kinetic energy and potential energy.
5. Water flow has kinetic energy along the length of the pipe or tube.

These are 5 examples of mechanical energy in everyday life.

## Conservation of Mechanical Energy

Total Mechanical energy is a conserved quantity for an isolated system where only gravitational force acts. Friction force and air resistance should be neglected for this. The law of conservation of mechanical energy states that the total mechanical energy of a system is always constant. However, it can be transferred from one form to another. For example, the kinetic energy of a particle can be changed to its potential energy and vice-versa. Here is a full article on the Transformation of Energy and its examples.

If we throw a particle with an initial velocity in the vertical direction, then at the moment of throwing it will have kinetic energy only. As it goes up, its potential energy increases and its kinetic energy decreases as the velocity decreases. This is because the kinetic energy of the particle converts into its potential energy. At the maximum height, its entire kinetic energy converts into potential energy. However, during the entire journey of the particle, its total mechanical energy remains conserved i.e. the sum of kinetic and potential energy will remain constant.

## Summary

1. The mechanical energy of a system is the sum of the kinetic energy and potential energy of the system.
2. Kinetic energy is the energy of motion and potential energy is due to the position at a height.
3. Total Mechanical energy is conserved in an isolated system where only the gravitational force acts.

This is all from this article on definition, types, formula, examples and law of conservation of total Mechanical energy of a mechanical system. If you still have any doubts on this topic you can ask me in the comment section.

Thank you!

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