A TEXTBOOK APPLIED MECHANICS

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2 A TEXTBOOK OF APPLIED MECHANICS

4 A TEXTBOOK OF APPLIED MECHANICS (Including Laboratory Practicals) S.I. UNITS By R.K. RAJPUT M.E. (Heat Power Engg.) Hons. Gold Medallist ; Grad. (Mech. Engg. & Elect. Engg.) ; M.I.E. (India) ; M.S.E.S.I. ; M.I.S.T.E. ; C.E. (India) Principal (Formerly), Punjab College of Information Technology PATIALA (Punjab) LAXMI PUBLICATI TIONS (P) LTD BANGALORE CHENNAI COCHIN GUWAHATI HYDERABAD JALANDHAR KOLKATA LUCKNOW MUMBAI PATNA RANCHI NEW DELHI

5 Published by : LAXMI PUBLICATIONS (P) LTD 113, Golden House, Daryaganj, New Delhi Phone : Fax : info@laxmipublications.com All rights reserved with the Publishers. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Price : Rs Only. Third Edition: 2011 OFFICES Bangalore Kolkata Chennai Lucknow Cochin , Mumbai , Guwahati , Patna Hyderabad Ranchi Jalandhar EAM ATB APPLIED MECH-RAJ Typeset at : Goswami Associates, Delhi C 689/09/09 Printed at : Mehra Offset Printer, Delhi

6 CONTENTS Chapters INTRODUCTION TO S.I. UNITS AND CONVERSION FACTORS Pages (i) (v) Part I APPLIED MECHANICS THEORY 1. BASIC CONCEPTS Introduction to Mechanics Basic Definitions Rigid Body Scalar and Vector Quantities Fundamental Units and Derived Units Systems of Units... 6 Highlights... 7 Objective Type Questions... 8 Exercises LAWS OF FORCES Force Units of Force Characteristics of a Force Representation of Forces Classification of Forces Force Systems Free Body Diagrams Transmissibility of a Force Particle Resultant Force Component of a Force Principle of Resolved Parts Laws of Forces Resultant of Several Coplanar Concurrent Forces Equilibrium Conditions for Coplanar Concurrent Forces Lami s Theorem Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples MOMENTS Moments Clockwise and Anti-clockwise Moments (v)

7 (vi) 3.3. Principle of Moments Equilibrium Conditions for Bodies Under Coplanar Non-concurrent Forces Varignon s Theorem Parallel Forces Graphical Method for Finding the Resultant of any Number of Like or Unlike Parallel Forces Couple Properties of a Couple Engineering Applications of Moments Resultant of a Coplanar, Non-concurrent Non-parallel Force System Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples CENTRE OF GRAVITY AND CENTROID Centre of Gravity of a Body Determination of Centre of Gravity Centroid Positions of Centroids of Plane Geometrical Figures Positions of Centre of Gravity of Regular Solids (a) Centroids of Composite Areas (b) Centre of Gravity of Simple Solids Areas and Volumes Centroid Method Centre of Gravity in a Few Simple Cases Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples MOMENT OF INERTIA Moment of Inertia Theorem of Parallel Axes Theorem of Perpendicular Axes Radius of Gyration of the Section Moment of Inertia of Laminae of Different Shapes Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples

8 (vii) 6. FRICTION Concept of Friction Characteristics of Frictional Force Types of Friction Static and Dynamic Friction Limiting Friction Laws of Friction Angle of Friction Co-efficient of Friction Angle of Repose Cone of Friction Motion of Body on Horizontal Plane Motion up an Inclined Plane Motion Down an Inclined Plane Screw Friction Screw Jack Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples RECTILINEAR MOTION Concept of Motion Definitions Displacement-Time Graphs Velocity-Time Graphs Equations of Motion Under Uniform Acceleration Distance Covered in nth Second by a Body Moving with Uniform Acceleration Motion Under Gravity Some Hints on the use of Equations of Motion Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples LAWS OF MOTION Introduction Momentum Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion Gravitational and Absolute Units of Force Law of Conservation of Momentum Impulse and Impulsive Force

9 (viii) 8.9. D alembert s Principle Motion of a Lift Motion of two Bodies Connected by a String Passing over a Smooth Pulley Motion of two Bodies Connected at the Edge of a Horizontal Surface Motion of two Bodies Connected by a String One End of which is Hanging Free and the other Lying on a Rough Inclined Plane Motion of Two Bodies Connected Over Rough Inclined Planes Highlights Objective Type Questions Unsolved Examples WORK, POWER AND ENERGY Concept of Work Units of Work Graphical Representations of Work Power Law of Conservation of Energy Highlights Objective Type Questions Unsolved Examples SIMPLE MACHINES General Concept of a Machine Important Definitions Relation between M.A., V.R. and η Concept of Friction in a Machine Condition for Reversibility of a Machine Non-reversible/Irreversible or Self-locking Machine Law of a Machine Maximum Mechanical Advantage and Efficiency Some Lifting Machines Simple Wheel and Axle Wheel and Differential Axle Pulleys Weston s Differential Pulley Block Worm and Worm Wheel Single Purchase Crab Winch Double Purchase Crab Winch Simple Screw Jack Differential Screw Jack Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples

10 (ix) 11. CIRCULAR AND CURVILINEAR MOTION Introduction and Definitions Equations of Angular Motion Equations of Linear Motion and Angular Motion Relation between Linear and Angular Motion Centrifugal and Centripetal Force Motion of a Cyclist Round a Curve Motion of a Vehicle on a Level Curved Path Motion of a Vehicle on a Banked Circular Track Super Elevation for Railways Highlights Objective Type Questions Exercises Theoretical Questions Unsolved Examples SIMPLE STRESSES AND STRAINS Classification of Loads Stress Simple Stress Strain Hooke s Law Mechanical Properties of Metals Tensile Test Strain Hardening (or Work Hardening) Poisson s Ratio Relations between the Elastic Modulii Stresses Induced in Compound Ties or Struts Thermal Stresses and Strains Highlights Objective Type Questions Theoretical Questions Unsolved Examples Part II EXPERIMENTS Experiment No Experiment No Experiment No Experiment No Experiment No Experiment No Experiment No Experiment No Experiment No Experiment No

11 A Textbook of Applied Mechanics By R.K. Rajput 40% OFF Publisher : Laxmi Publications ISBN : Author : R.K. Rajput Type the URL : Get this ebook

ENGINEERING MECHANICS

ENGINEERING MECHANICS ENGINEERING MECHANICS (In SI Units) For BE/B.Tech. Ist YEAR Strictly as per the latest syllabus prescribed by Mahamaya Technical University, Noida By Dr. R.K. BANSAL B.Sc. Engg.