# Engineering Mechanics

In this tutorial, you will be studying the basics of Engineering Mechanics. This includes introduction to the subject, its usage in daily life, and most frequently used quantities, units and their usage of dimensions following a set of rules and guidelines.

Contents:

## What is Engineering Mechanics?

Mechanics is defined as the science that explains the conditions of rest or motion of a body, when a number of forces are acting on it. Engineering Mechanics is the branch of engineering which applies the principles of Mechanics to design by taking the effect of forces into account.

• The goal of Engineering Mechanics is to support the student by attacking with as many general methods of problems as possible, so that the student gets exactly where a problem lies and can solve it.
• Engineering Mechanics is the foundation for subjects like Machine Design, Machine Dynamics etc. It is divided into two types as well, one Statics and the other Dynamics.
• A mechanical engineer is always accompanied by several new problems. In order to cope up with the existing and upcoming problems, a man must require powerful fundamentals and must be very similar with various methods of attack as possible. One such subject which provides beautiful techniques is Engineering Mechanics.

The figure below is a mind-map of the types of Engineering Mechanics.

• Statics deals with the study of forces acting on material bodies which are at rest.
• Dynamics is the study of motion observed in rigid bodies which is caused by the action of several forces. It is classified into Kinetics and Kinematics.

## What Do We Study in Engineering Mechanics?

Basically, in almost every field, there is use of Engineering Mechanics. Just look at your surroundings, feel the existence of every object, you find everything inside the arena of Engineering Mechanics.

For example, tables and chairs in our room, electricals like switches, ball-bearing of fans etc.
Some more are bridges of a railway train, pillars of a flyover, mobile tower etc. Hence this is a subject of solving practical reality. We study the structure of almost each and every machine carefully to establish satisfactory results.

• All these mentioned applications have their own usage of the subject in different ways.
• Some use strengths and forces division, some may fail due to vibrations, some get affected due to friction etc.
• The examples mentioned above are just only a few. There is no dearth of examples.

Hence to solve each and every example carefully and successfully, we have been introduced a concept called Idealization. To perform various idealization concepts and theories, the units and dimensions play a crucial role in determining solutions. The Units and Dimensions are such a chapter which can severely damage the whole setting if mistaken.

Different Terms Used in Mechanics:

• Idealization in Mechanics
• Units and Dimensions

## Idealization in Mechanics

By knowing that mechanics is nothing but analysis of a system, now we need to know how to analyze it. Going straightaway blindly will make no sense. It is anyway necessary to develop a model that will produce the complete behavior of the system.

• The real-life situations are complex. They are not at all possible to analyze because by keeping each and every aspect of the actual situation led us to a worse condition.

The diagram below shows how different forces on different places act in real life. It is an example to describe that many forces act at one time and can bring huge losses.

In the above figure, we observe that forces can either be vertical, horizontal or inclined. Hence, we do take the components along horizontal and vertical axes to idealize the given mechanical problem. The procedure to find components will be further explained.

• Further, these aspects may not contribute to failure which we overlooked and entered. Hence what to study and what not to study is determined by some factors and by taking care of them, we can easily solve the problems. Hence idealization would reduce the effort, making it amenable for analysis to form the foundation of the design.

Some of the important idealizations are:

• Continuum – Defined as continuous distribution of matter with no empty spaces.
• Particle – A body of negligible dimensions but having a definite mass concentrated at a point.
• System of Particles – A system of particles is an idealization of point masses.
• Space – Space refers to the three dimensional region in which a body exists. Their positions are defined by linear and angular measurements relative to a co-ordinate system.
• Mass – It is the quantity of matter in a body.
• Force – It is defined as an action that tends to change the state of rest of a body to which it is applied.
• Time – Time is simply measure of sequence of events.

## System of Forces

When several forces of various magnitudes and directions act upon a body, they are said to constitute a system of forces. The system of forces is classified according to the orientation of lines of action of the forces as follows:

• Force Systems in Space
• Force Systems in Plane
• Both force systems in plane and force systems in space can further be classified into
• Concurrent Force System
• Parallel Force System
• Non Concurrent or General Force System

Given below is a diagram showing you different types of coplanar forces.

As per the given diagram, we observe that System of Forces can be classified into Coplanar and Non-Coplanar Forces. And again, both coplanar and non-coplanar forces are classified into Concurrent and Non-Concurrent Forces.

## What are Units and Dimensions?

Units:

Unit is defined as the numerical standard used to measure the qualitative dimension of a physical quantity. And the units are of two types, they are Fundamental Units and Derived Units.

Given below is a table which shows definitions and some differences between Fundamental Units and Derived Units

Parameters Fundamental Unit Derived Unit
Definition Fundamental Units are those units which are independent of any other unit. Derived Units are those units which are obtained by applying operations on fundamental units.
Components Fundamental Units cannot be converted into elementary level, since they stay at elementary level. Derived Units can be reduced to minimum levels since they are components of fundamental units.
External Conversions Cannot be expressed in terms of Derived Units. Can be easily expressed in terms of Fundamental units.
Abundance Only seven types of fundamental units are available. There are many derived units.
Examples Meter, kilogram, second, mole, kelvin, ampere, candela Newton, Watt, Henry, hertz etc.

## Coherent System of Units

A coherent system of units is defined as the system in which units of derived quantities are the multiples and sub-multiples of certain basic units.

SI Units

To bring out the marking of units everywhere in the world onto a single unified platform, an international system of units is implemented and accepted throughout the world. So, according to this system, the length is measured in meters, mass is measured in kilograms and time is measured in seconds.

• Meter: The meter is defined as approximately 1650763.73 wavelengths of a certain radiation of the Krypton-86 atom at 15 degree Celsius and 76 cm of mercury.
• Kilogram: The kilogram is the mass of a platinum-iridium cylinder of diameter equal to its height at IBWM, Paris.
• Second: The second is defined as around 9.192 billion periods of the radiation of the Cesium 133 atom.

S.I units are absolute system of units which are independent of the location where the measurements are made.

In the below table, there are some SI units shown. The system consists of 7 base units, 2 supplementary units and a lot of derived units. For studying Engineering Mechanics, the mass, the length and the time are sufficient.

SI Units from Fundamental Quantities
Quantity S.I Units Symbol
Mass kilogram kg
Length meter m
Time second s
SI Units from Some Derived Quantities
Derived Unit Symbol Physical Quantity
Newton N Force
Joule J Energy, Work, Heat
Watt W Power
Pascal Pa Pressure, Stress
Hertz Hz Frequency

## Rules for Using SI Symbols

The rules are introduced to implement uniformity in representing the units in same form all over the world. The following set of rules is described for the proper use of various symbols in the SI units.

• A symbol is never written in plural.
• Symbols are always indicated in lowercase letters except the symbols named after an individual.
• It is permissible that one space can be left between any two unit symbols.
• No space must be left after a multiple or submultiple symbol, e.g., kJ/kgK.
• A space must be left between the number and the symbol. e.g., 67 cm, 45 N.
• The exponential power represented for a unit having a prefix refers to both the unit and the prefix.
• In general, don’t use any prefix in the denominator of composite units.
• Compound and complicated prefixes should not be used.

Given below is a table showing different key prefixes used in Engineering Mechanics.

Multiplication Factor Prefix Symbol
1012 Tera T
109 Giga G
106 Mega M
103 Kilo k
10-3 Milli m
10-6 Micro µ
10-9 Nano n
10-12 Pico p

The table shows the prefixes and their values that are mainly used in the subject every time. A student will use the units in the range of 10 raised to power 12, to 10 raised to the power negative 12.

## Dimensions – Law of Dimensional Homogeneity

Dimensional Formula: A formula in which the given physical quantity is expressed in terms of the fundamental quantities rose to a suitable power.

Analysis of Dimensions

• Dimensional Analysis deals with dimensions of quantities.
• In order to completely define a physical quantity, the following are to be known:
• The unit of the quantity
• The number of times the unit contained in that quantity
• Dimensional Quantities – The quantities that have no dimension are called Dimensional Quantities.
• Law of Dimensional Homogeneity
• The law of Dimensional Homogeneity states that all equations which describe the physical process must be dimensionally homogenous.
• This means that in no equation separate terms having different dimensions can be physically valid.

## Key Points to Remember

Here is the list of key points we need to remember about “Engineering Mechanics”.

• Engineering Mechanics tells us about the rest or motion of bodies when various forces are acting on them.
• Basically, mechanisms of almost every object in this world are covered in this subject that may or may not be in our knowledge.
• Idealization in Mechanics is simply a process of technically separating the components of forces acting on a body in a way to solve them easily.
• “Units and Dimensions” is the most neglected chapter that results in bizarre circumstances in the life of an industrial engineer.
• A rigid body is the one in which the distance between any two arbitrary points is invariant. In this subject, we consider all the objects as rigid bodies while solving the problems.
• The system of forces is categorized into two types, such as coplanar and non-coplanar forces. If the forces acting on the body are lying on the same plane, then they are Coplanar Forces otherwise, they are said to be Non Coplanar.
• The basic concepts used in mechanics are space, time, mass and force.
• Units have a definite set of rules that are to be followed while denoting them. A mechanical engineer needs to follow every rule in his piece of work.
• The use of dimensions is similar to units, but they help us more efficiently while going through equalization of units in a given situation. Since they are denoted in powers of fundamental units it is easy for anybody to replace or change something that he wishes to.
• The dimensional formula is used to check the validity of a given equation only when it follows homogeneity.

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