conservation of mechanical energy

Introduction

Energy is a property of physics that must be transferred to a physical system or a body to work on and/or heat it. Movement is simply the result of energy. Energy is a conserved quantity. The law of conservation of energy states that energy cannot be created or destroyed. Energy can be transformed into other forms. Energy is measured by the joule in the International System of Units. Energy is required by living organisms, just as humans acquire oxygen from breathing and food by eating. Fossil fuels, nuclear energy, and renewable energy sources must be available for civilization to flourish.

Let us first define energy and its various forms before discussing the conservation of mechanical energy. Energy is the capability to accomplish work. There are many types of energy, including light energy, mechanical energy, sound energy, chemical energy, atomic energy, and others. Each of these forms can be converted into another form. The two most important forms of energy are Kinetic and Potential Energy, although there are many different types. Kinetic energy is the energy involved in objects in motion and mass. Examples of kinetic energy are electrical energy and mechanical energy. Any form of energy capable of being used in the future is potential energy. Examples include nuclear energy and chemical energy.

Many forms of energy exist. Among the most familiar are:

• Chemical energy

A chemical compound’s bonds store energy as chemical energy. The chemical energy of a reaction is usually released as heat during the reaction. For instance, you can burn wood or coal to release chemical energy.

• Mechanical energy

It refers to the energy that is generated by the motion of a substance or system. Mechanical energy, for example, is used to make machines work.

• Electrical energy

Electrical energy, carried by electrons moving through an electric conductor, is one of the most common and crucial forms of energy. For instance: Lighting a bulb.

• Thermal energy

It is the energy of moving or vibrating molecules that determines the temperature of a substance or system. Solar radiation is used for cooking food, for instance.

• Nuclear energy

Fission and fusion are the processes that produce nuclear energy, which is the energy trapped inside each atom. Fission is the method most commonly used.

• Gravitational energy

Objects in a gravitational field carry gravitational energy; for example, water falling down a waterfall carries gravitational energy.

Here is a detailed discussion of mechanical energy conservation. 

In order to perform a particular function, an object must not only possess kinetic energy but also potential energy. The motion or position of an object causes it to generate energy. If we state the law of conservation of energy, the overall mechanical energy of a system is conserved. Due to the inability to create and destroy energy simultaneously, energy can only be changed internally by conservative forces acting on the system. If energy is lost in a part of an isolated system like the universe, then energy must be gained in another part. Though the principle of conservation of energy cannot be proven, the principle has never been demonstrated to be violated. 

In any system, we can calculate the amount of energy by using the equation below: 

Ut= Ui+W+Q

Ut=total energy of the system

Ui= A system’s initial energy

W= Work done by or on the system 

Q= Addition or removal of heat

An overall system with only conservative forces is characterized by the fact that each force has an associated potential energy form, and the energy changes only between kinetic energy and potential energy types. Therefore, the overall energy remains constant. When an object is moved in the opposite direction of a conservative net force, its potential energy increases; however, if the object’s speed changes, its kinetic energy also changes. The conversion of mechanical energy between forms involves a variety of devices. Electrical energy is converted to mechanical energy by electric motors, for instance.

The frictional forces in mechanical systems subject to conservative gravitational forces, such as a swinging pendulum, are negligible. Kinetic and potential energy are exchanged constantly but never leave the system. In the vertical position, the pendulum will possess the greatest kinetic energy and the most potential energy, since it is moving at high speed and is closest to the Earth. Moreover, even when frictional forces are taken into account, the system will lose mechanical energy with each swing, because these non-conservative forces will cause negative work to be done on the pendulum.

Law of conservation of energy derivation 

Let’s take an example where a fruit falls from a tree with zero potential energy at the surface. The fruit at the point A on the tree at the height ‘H’ from the ground is at maximum potential energy since the fruit velocity is zero. As the fruit falls, its kinetic energy increases, and its potential energy decreases. As the fruit approaches point B, it is falling freely from the tree at a height of X above the ground. As it gets closer to point B, its speed increases. In the same way, if we consider the energy at point C at the tree’s bottom, we find that it is mgH. Here, potential energy is being converted into kinetic energy as the fruit falls to the bottom. Thus, kinetic energy must equal potential energy at some point.

Conclusion:

According to this law, forces must be conservative in nature to be considered. Total kinetic energy plus total potential energy is what we define as mechanical energy. A system’s mechanical energy can be characterised as macroscopic. We are constantly surrounded by energy – even inside ourselves. All of our movements are powered by energy. We move because we eat food that provides the chemical energy that fuels our muscles and keeps us moving. Despite having mastered many aspects of the physics of energy, humans continue to search for ways to use and store energy more efficiently.