The Principle Of Conservation Of Mechanical Energy

Energy surrounds the activities and the work that we do. The steps you take to school or the plant that you grow, every activity involves energy. In the simplest sense, energy refers to the ability to do work. Energy in physics can be of various kinds. There is kinetic energy, potential energy, mechanical energy and more. 

In the below information, there will be a complete elucidation on what mechanical energy is. further , there will be a detailed understanding provided for the principle of conservation of mechanical energy and the law of conservation of mechanical energy. Lastly, there will be a complete understanding of what conservative force and conversion of energy is. 

Mechanical Energy- An Overview

Have you ever wondered about the energy of a ball when you throw it? Or the car that moves at a ferocious speed? In all these movements and positioning, there is a form of energy that is present. It is defined as the mechanical energy. Physics defines mechanical energy to be an energy that is achieved when the object is in motion or at a particular position. The principle of mechanical energy indicates that there is energy present, when a work is done on the object. 

The Principle Of Conservation Of Mechanical Energy

Mechanical energy is the sum total of the potential and kinetic energy that is used and remains unchanged after work is done.

A good way of explaining the conservation of mechanical energy is by considering a round trip. If the kinetic energy is remaining the same after the round trip this means it is a conservative force or is at least acting like one.

When you throw a ball straight up, it has a little bit of kinetic energy the moment you throw it out. At the top of its path though, it has no kinetic energy but potential energy (which is equal to the kinetic energy before). Thus when you catch it back in your hand, it has the same kinetic energy as before. Thus we can say that the sum of the potential and kinetic energy remains unchanged i.e the mechanical energy. 

Mechanical energy is the aggregate of potential and kinetic energies. Kinetic energy is the object’s motion energy and potential is the energy that is stored in the object when resting.

To be able to understand the conservation of mechanical energy we must understand the system that is being recognized. In physics, a system is a group of objects which is under observation, and with a closed system, the objects under conservation have no contact with external forces whatsoever.

The fact that the total mechanical energy of a closed system remains unchanged throughout is known as the law of conservation of energy. Thus the preservation of mechanical energy is also observed.

The Law Of Conservation Of Mechanical Energy

The total amount of energy in the universe is unchanged. Energy cannot be created nor can it be destroyed. Energy is thus among the handful of physical quantities that we say are conserved.

Conservation of energy is not an intuition-based derivation that everybody just accepts as a conjecture. This is based on scientific experiments. Even with the discovery of new advanced forms of energy, conservation of energy has always been found to apply to everything.

Maybe Einstein gave us a lot of insight in such ways when he suggested that mass is equivalent to energy by his famous equation E = mc².

For us to get hold of this statement more vividly we can consider the following things –

Hereafter the force F is applied to a body it is getting displaced by Δx. So mathematically speaking –

ΔKE = F(x) Δx

ΔKE is the net swap in the total kinetic energy. So if we consider only conservative forces are at work only then,

W_net = W_c

W_c = ΔKE is being concluded. 

If conservative forces are present in a system, the system cuts potential energy the same to the work done. Therefore we can say that, W_c = -PE.

This only says that the aggregate kinetic energy and potential energy of the system remain unchanged.

KE + PE = constant

KE_i+ PE_i = KE_f+ PE_f

Here i signifies the initial energy and f represents the final energy of the system.

However, one thing to note is that this law is only applicable to forces that are conservative in nature. The mechanical energy of the system is described as the aggregate of the absolute kinetic energy and the absolute potential energy.

In a system that consists of only conservative energies, each energy is manifested with a form of potential energy and the energy only changes itself between the kinetic energy and different kinds of potential energy, so that ultimately, the total energy remains the same.

Let us discuss this with a good example. For example, a ball of mass m is released from a building of height H,

At height H:

Potential energy (PE) = m×g×H, where  g is the acceleration due gravity.

Kinetic energy (K.E.) = 0

Total mechanical energy = mgH

At height h:

Potential energy(PE) is given s = m×g×h

Kinetic energy (K.E.) is given as =1/2(mv²)

The velocity v₁ at a height h for an object of mass m released from the height H can be