E= relativistic kinetic energy + MC^2

= 0+ MC ^2

= MC ^2

SO :
E=MC^2

The Equation E = mc²

Introduction

The equation E = mc² is one of the most famous and significant equations in physics. It was derived by Albert Einstein as a result of his theory of special relativity. This equation relates energy (E) to mass (m) and the speed of light (c). In this explanation, we will break down the equation and provide a detailed proof for E = mc².

The Components of the Equation

To understand the proof of E = mc², let's break down the components of the equation:

- E represents energy, which is a fundamental concept in physics. Energy can exist in various forms, such as kinetic, potential, thermal, or electromagnetic energy.

- m stands for mass, which refers to the amount of matter an object possesses. Mass is a fundamental property of matter and is measured in kilograms (kg).

- c represents the speed of light in a vacuum, which is approximately 299,792,458 meters per second (m/s). The speed of light is a fundamental constant of nature and plays a crucial role in Einstein's theory of special relativity.

The Proof

The proof of E = mc² can be derived from the principles of special relativity. According to this theory, the laws of physics should remain the same for all observers, regardless of their relative motion. Einstein postulated that the speed of light is constant for all observers, regardless of their motion.

Using this postulate, Einstein derived the following equation:

E² = (mc²)² + (pc)²

In this equation, p represents momentum, which is the product of mass (m) and velocity (v). However, for an object at rest, the velocity is zero, so the momentum (p) becomes zero as well.

Considering a stationary object, the equation simplifies to:

E² = (mc²)²

Taking the square root of both sides, we get:

E = mc²

Thus, we have proven that E = mc².

Conclusion

The equation E = mc² is a profound result of Einstein's theory of special relativity. It demonstrates the equivalence between energy (E) and mass (m) and highlights the fundamental role of the speed of light (c) in our universe. This equation has revolutionized our understanding of energy, matter, and the interplay between the two. Its implications can be seen in various fields of science, such as nuclear physics and astrophysics. E = mc² has become an iconic symbol of the power and elegance of Einstein's theories.