## What is Mechanics?

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

The mechanics are classified into three stages that are discussed in detail below:

### Statics

Statics is a state of mechanics that deals with forces operating on and in a body at rest.

### Kinematics

Kinematics describes the possible motions of a body or system without evaluating the force of motion.

### Kinetics

Kinetics described the effect of forces acting over the system performing the motion.

The simplest and the most accessible mechanical system is the particle or the smallest body whose shape and internal structure have no real-life impact. In contrast, the motion of a system that contains multiple particles exerting forces on each other and maybe experiencing forces exerted by bodies outside of the system is a complex mechanical system.

## Classical mechanics

In this part of mechanics, the motion of bodies under the influence of forces or in equilibrium state experiences all balanced forces are studied. Classical mechanics can be considered an approximation that arises from the more deep laws included in quantum mechanics and the theory of relativity. The central concepts discussed in classical mechanics are forces, mass, and motion.

## Quantum mechanics

It is a branch that can be defined as the study on very small scales in length. It is directly applied to some macroscopic systems. The word quantum in quantum mechanics emerges because some quantities only take the discrete values compared to classical mechanics. In quantum mechanics, particles show the nature and properties like a wave and have a particular wave equation.

## Statistical mechanics

Statistical mechanics is the branch that extends classical thermodynamics deals with temperature gradient, work done, and many more. It is also known as statistical thermodynamics or equilibrium statistical mechanics. Statistical mechanics is applied to obtain the solutions and the demands that the entropy is highest at equilibrium.

## Some important definitions

### Mass

Mass is an amount of matter possessed by a physical body, and that offers resistance to acceleration when a net force is applied. The mass of an object also helps identify the strength of the object's gravitational attraction to other bodies. The standardized unit used for the measurement of mass is a kilogram.

### Time

Time is described as a quantity that indicates a measure of successive events. The successive event is selected based on the earth's rotation on its axis.

### Space

Space is referred to as the confined region in which the analysis of the body or system is done.

### Length

Length is referred to as the distance measured about the largest dimension of an object.

### Distance

Distance is referred to as a numerical explanation or quantity that identifies how far apart the systems are.

### Displacement

Displacement is referred to as the minimum length among the body's initial to the final location.

### Velocity

The velocity is expressed as a term that gives a fractional relation of change in the object's position concerning a reference frame with time.

### Acceleration

An acceleration is referred to as the second derivative of displacement concerning time. It is a vector quantity, and negative magnitude acceleration is called deceleration.

### Momentum

The momentum is expressed as a characteristic feature of a system. Its magnitude is identified by a product of its mass and velocity.

### Force

A force is described as an influence that can change the state of an object. The force applied to an object will generate acceleration over the object.
Force is described as either of push or pull nature. A force has both magnitude and direction, assembling it as a vector quantity.

## Newton’s laws of motion

Newton's laws of motion are referred to as fundamental laws of classical mechanics that clarify the association between the object's motion and the forces acting over it.

### Newton’s first Law of motion

It states that a body at rest will remain at rest, and a body in motion will remain in motion unless an external force act over it. In other words, the system's state can only change by involving some external means.

### Newton’s second Law of motion

It states that the force acting on an object equals the fractional change of momentum or equal to the product of the system's mass and its gained acceleration.

### Newton’s third Law of motion

It states that there is always an equal magnitude and opposite direction reaction for every force effect.

## Stress

In mechanics, stress is identified as a fractional relation among force and unit area of the system.

### Types of stress

Stress applied to a material can be of two types as follows:

### Tensile stress

Tensile stress is described as the induced force in the component due to axially applied force that increases the length of a component. Objects under tensile stress become thinner and longer.

### Compressive Stress

Compressive stress is described as the induced force in the component due to axially applied force that decreases the length of a component. Objects under compressive stress become thicker and shorter.

## Strain

Strain is described as the fraction relation among deformation experienced by the system in the direction of force applied and the initial dimensions of the system.

### Types of strain

Strain experienced by a body can be of two types depending on stress application as follows:

### Tensile Strain

Tensile strain is described as the variation in length (or area) of a component due to the application of tensile stress.

### Compressive strain

Compressive strain is described as the variation in length (or area) of a component due to the application of compressive stress.

## Hooke’s law

While studying the springs and objects that possess elasticity, a scientist named Robert Hooke detected that many materials exhibited a similar property when the stress-strain relationship was observed.
In this, there was a linear region where the force required to stretch the material was proportional to the extension of the material, known as Hooke’s law.

### Particle

A particle is described as a body with a certain mass, but its dimensions can be neglected.

### Continuum

The body that consists of several matters is called a continuum.

### Rigid Body

A rigid body is described as a solid body in which deformation is zero or so small that it can be neglected.

## Common Mistakes

Students often get confused in thermodynamics and statistical mechanics. Thermodynamics is concerned about heat and the direction of heat flow, whereas statistical mechanics gives a microscopic perspective of heat in terms of the structure of matter and provides a way of evaluating the thermal properties of matter, e.g. heat capacity.

## Context and Applications

This topic is significant in the professional exams for both graduate and postgraduate courses, especially for

• Bachelor of Technology in Mechanical Engineering
• Bachelor of Science in Physics
• Master of Technology in Mechanics
• Electromagnetism
• Material Properties
• Yield point

## Practice Problems

Q1. Hooke’s law gives the relation between

1. Stress-Strain
4. Strain-Deformation

Correct option: (a)

Explanation: Hooke’s law gives the relation between the normal stress, and longitudinal strain that occurs due to applied normal stress.

Q2. The amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body, is called

1. Stress
2. Strain
3. Displacement
4. Distance

Correct Option: (b)

Explanation: The term strain can be defined as the ratio of change in the dimension of the body to its original dimension. It is of various types like longitudinal strain, lateral strain, etc.

Q3. “It deals with the motion of bodies under the influence of forces or with the equilibrium of bodies when all forces are balanced”, this definition is of

1. Classical Mechanics
2. Statistical Mechanics
3. Kinetics
4. Kinematics

Correct option: (a)

Explanation: The term classical mechanics deals with the motion of a body under equilibrium conditions, meaning when all the forces acting on the body would be balanced.

Q4. The quantity of motion of a moving body, measured as a product of its mass and velocity is called

1. Force
2. Momentum
3. Energy
4. Work

Correct Option: (b)

Explanation: The term momentum exists when an object of a specific mass moves in a particular direction. It consists of magnitude and direction, so that refers to vector quantity.

Q5. The area of mathematics and physics concerned with the motions of physical objects is called

1. Mechanics
2. Thermodynamics
3. Fluid Mechanics
4. Vibrations

Correct Option: (a)

Explanation: Mechanics deals with the motion of a physical body with the help of internal/external force acting on it, whereas thermodynamics deals with the properties associated with the temperature.

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### Basic Terminology in Mechanics

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