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# Mechanics and Its Applications

## Introduction

Mechanics originated dates back from 384 B.C. to 322 B.C. The ancient Greek philosophers were the first to propose the principles that govern nature. Aristotelian mechanics was considered the main theory of mechanics until the medieval age. Today, the principles of Mathematical mechanics find application in our day-to-day activities. Let’s explore Mechanics in more detail.

## What is Mechanics?

Mechanics is one of the most important branches of Physics. It helps us in observing and analyzing the motion of any physical object under the influence of force or when the object is at rest (F=0). Mechanics helps us to establish a mathematical relation among the various terms such as Mass of the body, Force (or Torque) acting on it, its Linear velocity (or Angular velocity), etc.

It also involves the subsequent study of these physical objects in their environment. For example - Consider a body of mass m at rest or on the ground. Now, a force F (parallel to the ground) is applied to this body such that it starts to move in forward direction with acceleration a. We all know that the following relation exists between F,m and a:

$$\mathrm{F=ma}$$

**Figure 1 - Motion of Block **

What we have discussed above is an example of **Classical mechanics** (a sub-branch of Mechanics) that takes into account the study and analysis of objects in motion under the influence of force.

## Branches of Mechanics

### Classical Mechanics

Classical mechanics discuss the motion of objects under the influence of force. The example demonstrated in fig:1 belongs to Classical mechanics. When a body is at rest under the influence of many forces acting on it, then this state is called Equilibrium.

Classical Mechanics also deals with the objects or body in the equilibrium state.

**Classical mechanics** has been of great importance to mathematicians and physicists since time immemorial. It helped us in the mathematical analysis of the motion of macroscopic objects such as projectiles, planets, satellites, machinery parts, etc. It is also called **Newtonian Mechanics** as it largely involves the use of concepts and theories given by ,**Sir Issac Newton**.

### Quantum Mechanics

Classical mechanics failed to explain the wave nature of atomic and subatomic particles. Moreover, it failed to explain the concept of Blackbody radiation, **Photoelectric effect** and was found to be inconsistent with Maxwell’s Electrodynamics. Classical mechanics was superseded by **Quantum mechanics** in order to explain the behavior and state of particles at the bottom or foundation level i.e., atomic and subatomic particles.

The state of a particle includes its position, velocity (momentum), etc. The wavefunction of a particle is used to find the amplitude of the **de - Broglie wave** associated with it and is of great importance to define the state of the particle. It is denoted by ${\psi}$

### Relativistic Mechanics

Newtonian mechanics deals with the motion of objects at low velocity. But what if the object travels at the speed of light $\mathrm{(

u=c=3\times\:10^{8}\:m/s^{2})?}$ This is where the need for Relativistic mechanics is significant. **Albert Einstein’s Special theory of relativity** superseded the absoluteness of time. Einstein proved that the result of any physical measurement depends upon the choice of **frame of reference**.

The Special Theory of Relativity took **non-accelerating frames** into account. In 1916, Einstein proposed the **general theory of Relativity** which took accelerating frames and their relation to gravity into account. The General Theory of Relativity is important for explaining topics like Black Holes.

Basis | Special theory of relativity | General theory of relativity |
---|---|---|

Reference Frames | Takes into account non - accelerating frames of references. | Take into account the accelerating frame of references. |

The shape of Space-time | It predicted space-time to be flat. | It predicted spacetime to be curved due to the presence of heavy bodies. |

## Applications

Newton’s third law of motion (Classical Mechanics) is used for the mathematical analysis of the motion of rockets.

Free body diagrams (Classical Mechanics) help us in the mathematical understanding of the various forces acting on the body under the state of equilibrium.

The Equations of motion (Classical Mechanics) help to find the position, velocity, and acceleration of the body at any instant of time.

Quantum computers work on the principles of quantum mechanics. The processing power of quantum computers is quite fast as they use quantum bits.

World’s first entanglement-enhanced microscope was developed using the principles of quantum mechanics. It uses a differential interference contrast technique.

The world’s most accurate cesium clock utilizes quantum mechanics.

The phenomenon of quantum tunneling is used in many electronic devices. Flash memory chips use quantum tunneling to erase their memory.

Lasers work on the stimulated principle phenomenon, which originates in quantum mechanics.

## Conclusion

The principles of Mechanics are used in and by us daily. The sub-branches of Mechanics evolved over some time to mitigate the limitations of the previous sub-branch. Classical mechanics helps us to analyze the motion of macroscopic objects under the influence of force. Quantum mechanics takes into account the nature, behavior, and state of atomic and subatomic particles. Relativistic mechanics was developed to study the objects moving with or near the speed of light. Mechanics is used widely across various domains.

## FAQs

**Q1. What is the Frame of Reference?**

Ans. It is a Coordinate system in which the positions and velocities of objects are uniquely determined for some reference points.

**Q2. What are the types of Frames of Reference?**

Ans. Inertial and Non-inertial frame of reference.

**Q3. What is the relation between relativistic mass and rest mass?**

Ans. The relation between rest mass and relativistic mass is as follows-

$$\mathrm{m=\frac{m_0}{\sqrt{1-\frac{

u^{2}}{c^{2}}}}}$$

where $\mathrm{m_{0}}$ is the rest mass, and m is relativistic mass.

**Q4. What is the significance of $\mathrm{\lvert \psi^{2} \rvert}$**

Ans. $\mathrm{\lvert \psi^{2} \rvert}$ w.r.t quantum mechanics tells us about the probability of finding a particle at a specific point.

**Q5. What is Schrodinger's Cat?**

Ans. It was a thought experiment that depicted the paradox of quantum superposition. In this experiment, Schrodinger thought of an imaginary cat, if placed inside a box along with a poisonous fish as its food and sealed tightly for some time, then it is impossible to know the state of the cat (Alive or dead) without opening the box. Schrodinger underlined the fact that - the cat is both dead and alive at the same instant of time, unless and until we open the box to find the reality.

**Q6. What is Length Contraction?**

Ans. About the relativity theory- the length of anybody in motion looks shorter than its original length or proper length to the other person at rest. The length of the object when it is at rest is called its proper length. The following relation exists between length in motion and proper length -

$$\mathrm{L=L_0\sqrt{1-\frac{

u^{2}}{c^{2}}}}$$

Here, $\mathrm{L_0}$ is the proper length.