# Mechanics for Engineers

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# Code(Credit) : CUTM1006(2-1-0)

## Course Objectives

• To provide the students with a clear and thorough understanding on fundamentals of mechanics as applied to solve real-world problems

## Learning Outcomes

Upon successful completion of this course student should be able to:

• Use scalar and vector analytical techniques for analyzing forces in statically determinate structures.
• Analyze the frictional forces involved in planes, ladder friction and belt friction.
• Determine the centroid and moment of inertia of composite shapes.
• Apply fundamental concepts of kinematics and kinetics of particles to the analysis of simple, practical problems.
• Apply basic knowledge of mathematics and physics to solve real-world problems

## Course Syllabus

Module I:

Force and Moment:
Law of Transmissibility of a Force, Composition and Resolution of Forces, Resultant and Equilibrant, Resultant of Two and Several Forces, Moment of a Force and a Couple, Varignon’s Principle of Moment
Practice-1: Verification of laws of parallelogram law of forces

Module II:

Equilibrium:
System Isolation and Free Body Diagram, Particle Equilibrium, Lami’s theorem, General Conditions of Equilibrium, Types of Supports and Support Reactions, Rigid Body Equilibrium.
Practice-2: To verify the condition of equilibrium by finding reactions at the support of a beam

Module III:

Friction:
Basic Terms used in Dry Friction, Laws of Coulomb Friction, Equilibrium of Bodies on a Inclined Plane, Ladder Friction, Belt Friction
Practice-3: Determination of Angle of Repose

Module IV:

Centroid:
Axis of Symmetry, Centroid of Lines, Areas and Volumes, Centroid of Composite Section.

Module V:

Moment of Inertia:
Rectangular and Polar Moment of Inertia, Radius of Gyration, Parallel Axis Theorem and Perpendicular Axis Theorem, Moment of Inertia of Composite Section
Practice-4: Determination of Moment of Inertia of a fly wheel.
Module VI:

Kinematics of Linear Motion:
Kinematics of a Particle, Uniform and Variable Acceleration, Motion under Gravity.

Module VII:

Kinetics of Linear Motion:
Principles of Dynamics such as Newton’s Second Law, Work-Energy Principle, Impulse-Momentum Principle, Law of Conservation Law of Momentum and Energy
Practice-5: Verification of Newton’s second law of motion
Practice-6: Verification of conservation of momentum in collision

Text Books:
Engineering Mechanics; Statics and Dynamics by A. K. Tayal, Umesh Publications
Reference Books:
Engineering Mechanics by S. Timoshenko, D.H. Young and J.V. Rao, Tata McGraw Hill
Engineering Mechanics by D.S. Kumar, S.K. Kataria and Sons

## Session 1

Introduction, Law of Transmissibility of a Force

You tube: https://youtu.be/HjFunNWJplI

Study Materials: MFE-1

## Session 2

Composition and Resolution of Forces, Resultant and Equilibrant

You tube: https://youtu.be/T8-g7stZwDs

Study Material: MFE-2

## Session 3

Resultant of Two and Several Forces

You tube: https://youtu.be/OxG4pBDOAJg

Study Material: MFE-3

## Session 4

Moment of a Force and a Couple, Varignon’s Principle of Moment

You tube: https://youtu.be/us7KNhguSuM

Study Material: MFE-4

## Session 5

Practice-1(2 hrs.):

Verification of laws of parallelogram law of forces

You tube: https://youtu.be/BSP-3J4H6pM

## Session 6

System Isolation and Free Body Diagram

You tube: https://youtu.be/go4vsgnb9jU

Study Material: MFE-6

## Session 7

Particle Equilibrium, General Conditions of Equilibrium

You tube: https://youtu.be/AZzFQDeeUBI

Study Material: MFE-7

## Session 8

Types of Supports and Support Reactions, Rigid Body Equilibrium

You tube: https://youtu.be/Bf4UrWfys5U

You tube: https://youtu.be/doY2MIsU2aQ

Study Material: MFE-8

## Session 9

Practice-2(2 hrs.)

To verify the condition of equilibrium by finding reactions at the support of a beam

You tube: https://youtu.be/swJULZs71Oo

## Session 10

Basic Terms used in Dry Friction, Laws of Coulomb Friction

You tube: https://youtu.be/XaFkPeW1d7k

Study Material: MFE-10

## Session 11

You tube: https://youtu.be/mWce2ZzfDiM

Study Material: MFE-11

## Session 12

Practice-3(2 hrs.):

Determination of Angle of Repose

You tube: https://youtu.be/ON8h8Tg65Sc

You tube: https://youtu.be/KWCb8U_T4Hc

## Session 13

Axis of Symmetry, Centroid of Lines, Areas and Volumes

You tube: https://youtu.be/R8wKV0UQtlo

Study Material: MFE-13

## Session 14

Centroid of Composite Sections

You tube: https://youtu.be/G2jhy-SXceQ

Study Material: MFE-14

## Session 15

Rectangular and Polar Moment of Inertia, Radius of Gyration

You tube: https://youtu.be/A4KhJYrt4-s

Study Material: MFE-15

## Session 16

Parallel Axis Theorem and Perpendicular Axis Theorem

You tube: https://youtu.be/_Kwel7lQNcA

Study Material: MFE-16

## Session 17

Moment of Inertia of Composite Sections

You tube: https://youtu.be/2TqDATuJU8k

Study Material: MFE-17

## Session 18

Practice-4(2 hrs.):

Determination of Moment of Inertia of a fly wheel.

## Session 19

Kinematics of a Particle, Uniform acceleration

You tube: https://youtu.be/4dCrkp8qgLU

Study Material: MFE-19

## Session 20

Variable Acceleration, Motion under Gravity

Study Material: MFE-20

## Session 21

Projectile Motion

You tube: https://youtu.be/aY8z2qO44WA

## Session 22

Newton’s Second Law

You tube: https://youtu.be/xzA6IBWUEDE

Study Material: MFE-22

## Session 23

Work-Energy Principle, Impulse-Momentum Principle

You tube: work-energy: https://youtu.be/zVRH9d5PW8g

You tube: Impulse-momentum:https://youtu.be/E13h1E_Pc00

Study Material: MFE-23

## Session 24

Law of Conservation of Momentum, Law of Conservation of Energy

You tube: https://youtu.be/OTK9JrKC6EY

Study Material: https://www.slideshare.net/eliseb/conservation-of-momentum

## Session 25

Practice-5(2 hrs.):

Verification of Newton’s second law of motion

## Session 26

Practice-6(2 hrs.):

Verification of conservation of momentum in collision