Mass energy Equivalence

Introduction

Measurement denotes the comparison of an unknown quantity with a known quantity. It is the measure of quantity. Length, mass, time, electric current, temperature, amount of substance, and luminous intensity are the seven fundamental quantities. There are many systems of units used such as the KGS system, CGS system, and International SI system.

Different systems assign different units for basic elements. If the quantity has only magnitude then it is called a scalar quantity. Example mass, distance, time, etc. If the quantity has both direction and magnitude then it is called a vector quantity.

Example velocity, displacement, force, etc. Every matter in the universe is composed of tiny particles called molecules. They attract each other with some attractive force. There exists an intermolecular force of attraction between molecules.

What is mass?

It is the property of a body that refers to the amount of matter that the body constitutes. It is the fundamental quantity. The resistance offered by the body to the motion or velocity of the body. Everything around us has mass. A chair, football, glass, and even air have mass. The mass of a body is measured as

$$\mathrm{mass\:=\:density\:\times\:volume}$$

Mass of the body is constant. The S.I unit of mass is the kilogram.

According to Newton’s law of motion the force applied to the body is given by,

$$\mathrm{Force\:=\:mass\:\times\:acceleration}$$

$$\mathrm{F\:=\:ma}$$

The force that acts on the body is the rate at which the momentum changes with time. Thus the force acting on the body also be written as

$$\mathrm{F\:=\:\frac{dp}{dt}}$$

P denotes the momentum of the body and it denotes as $\mathrm{P\:=\:mv}$

$$\mathrm{F\:=\:\frac{d(mv)}{dt}}$$

$$\mathrm{F\:=\:\:m\:\frac{dv}{dt}}$$

$$\mathrm{F\:=\:ma}$$

What is energy?

The capacity of the physical system that needs to do work is called the energy of the system and it is a scalar quantity. It occurs in many forms. The S.I unit for energy is Joule. Energy is used to power the devices that we are using such as heat, light, etc. The different types of energy sources are used mainly for the production of electricity. Energy sources can be divided into two categories such as renewable and non- renewable sources. Renewable sources of energy are the energy that is obtained from flow sources such as wind, tide, sunlight, etc. The energy that is obtained from natural resources which cannot be replaced is called non-renewable sources of energy. Fossil fuels and nuclear energy are some examples of non-renewable sources.

Types of energy

Energy is very important and it occurs in nature in many forms. There are different kinds of energy. They are mechanical energy, thermal energy, nuclear energy, chemical energy, electromagnetic energy, sonic energy, gravitational energy, kinetic energy, potential energy, and ionization energy. Generally, all energy comes under potential or kinetic energy.

What is mass-energy equivalence

The energy and mass of the objects are interchangeable is the basic concept of Einstein's mass-energy equivalence. According to his theory, they were denoted as the same thing. Einstein describes the relation between the energy and the mass of the object by using his theory of relativity. To his theory, the mass-energy equivalence of the object is given by,

$$\mathrm{E\:=\:mc^{2}}$$

E denotes the energy of the object, m denotes the mass of the object and c denotes the velocity of light which is known as $\mathrm{c\:=\:3\times\:10^8\:m/s}$.

Derivation of mass-energy equivalence

Derivation of mass-energy equivalence >

Let us assume that an object that moves at the speed of light. If a uniform force is applied to the object, then it induces energy and momentum. energy and work done are the same. Thus the energy that is exerted on the object is,

$$\mathrm{energy\:=\:force\:\times\:displacement}$$

$$\mathrm{E\:=\:F\:\times\:S}$$

The displacement of the object is the product of velocity and time taken

$$\mathrm{E\:=\:ct}$$

$$\mathrm{E\:=\:F\:\times\:ct----------------(1)}$$

According to Newton’s law of motion the force that acts on the object is

$$\mathrm{force\:=\:mass\:\times\:acceleration}$$

$$\mathrm{F\:=\:ma}$$

The acceleration of the object is the velocity of the object per second. Thus

$$\mathrm{a\:=\:\frac{c}{t}}$$

$$\mathrm{F\:=\:\frac{mc}{t}-------------(2)}$$

By substituting the value of F in equation (1) we get, these two equations we get,

$$\mathrm{E\:=\:m\:(\frac{c}{t})\:\times\:ct}$$

The energy is equal to $$\mathrm{E\:=\:mc^{2}}$$

This equation denotes Einstein's mass-energy equivalence.

Conclusion

Mass is the quantity of the object that it holds. Energy is the capability of the object to do work. They are interconnected by mass-energy equivalence. This equation was proposed by Albert Einstein. So it is also denoted as Einstein’s mass-energy equation. The equation proposed by him is $\mathrm{E\:=\:mc^{2}}$.

Conclusion

In this tutorial, the facts about mass and energy were discussed in detail. The mass- energy equivalence, the derivation for mass-energy equivalence, and its conclusions were also discussed in detail.

FAQs

1. What is the law of conservation of energy?

Energy is a fundamental quantity that is very important for life. Energy conversion is the process of conversion of one form of energy into another form of energy. All forms of energy-related to motion. By the conservation of energy law, one form of energy can be transformed into another form and the energy cannot be destroyed or formed. In other ways, it can also be stated that if the system is isolated then the total energy of the system does not change and it remains constant.

2. Why is there a need for an alternate source of energy?

Fossil fuels are non-renewable sources of energy that are reducing in quantity for continuous usage. These sources need thousands of years to form again. So they are exhausted. To save these sources for the future it is better to go for an alternate source.

3.What are the differences between mass and volume?

Mass	Volume
It is the quantity of matter in the body	It is the amount of space that is covered by the matter of the body
mass of the body is the constant	volume of the body that can change
S.I unit of mass is kg	S.I unit of volume is cubic meter

4. What are the applications of Einstein’s equation?

The applications of Einstein’s equation are given below.

• Einstein’s equation is used to understand the gravity in other planets and is also used in measuring the age of fossil fuels.

• It helps to understand nuclear fission and nuclear fusion. And it is used in the creation of nuclear reactors and nuclear power.

• It is the basis for the radioactivity of the elements.

• The binding energy of the atoms in the nucleus is determined using this equation.

5. What is known as relative mass?

In classical theory, the mass of the object does not depend upon the velocity of the object. But according to relativity which is formulated by Albert Einstein the mass varies with varying velocity. This states that the mass of the object that moves with the relative speed v to the observer is greater than the mass of the object when it is at rest.