Lecture on Engineering Mechanics

ME 101: Engineering Mechanics

A. Narayana Reddy

Department of Mechanical Engineering,Indian Institute of Technology Guwahati,

Guwahati - 781039, India.

Class time table and venue

CourseME 101: Engineering Mechanics (3 1 0 8)3 lecture hours, 1 tutorial hour and 8 credits.

VenueDivision-I: L1, Division-II: L2, Division-III: L1, Division-IV: L2

Day Division - I & II III & IVMONDAY 2:00 PM to 2:55 PM 11:00 AM to 11:55 AMTHURSDAY 4:00 PM to 4:55 PM 9:00 AM to 9:55 AMFRIDAY 3:00 PM to 3:55 PM 10:00 AM to 10:55 AM

Tutorial schedule for all the groupsWednesday: 8:00 AM to 8:55 AM (T1 at L1, T2 at L2, T3 at L3, T4 at L4, T5at 1006, T6 at 1G1, T7 at 1G2, T8 at 1207, T9 at 2101, T10 at 2102, T11 at3202, T12 at 4001, T13 at 4G3, T14 at 4G4)

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Syllabus

StaticsBasic principles: Equivalent force system, equations of equilibrium, freebody diagram, static indeterminacy.Structures: Difference between trusses, frames and beams, 2D truss, methodof joints, method of section, simple beam, types of loading and supports,shear force and bending moment diagram in beams.Friction: Dry friction, description and applications of friction in wedges,thrust bearing (disk friction), belt, screw, journal bearing (axle friction),rolling resistance.Virtual work and energy method: Principle of virtual work (PVW),applications of PVW, mechanical efficiency, work of a force/couple (springsetc.), potential energy and equilibrium, stability.Center of gravity and moment of inertia: First and second moment of area,radius of gyration, parallel axis theorem, product of inertia, rotation of axesand principal moment of inertia, mass moment of inertia.

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Syllabus

DynamicsKinematics of particles: Rectilinear motion, curvilinear motion, use ofCartesian, polar and spherical coordinate system, relative and constrainedmotion, space curvilinear motion.Kinetics of particles: Force, mass and acceleration, work and energy,impulse and momentum, impact problems, system of particles.Kinematics and kinetics of rigid bodies: Translation, fixed axis rotational,General plane motion, Coriolis acceleration, work energy, power, potentialenergy, impulse-momentum and associated conservation principles, Eulerequations of motion and its application.

You can also find the syllabus on the following Dept. of MechanicalEngineering, IITG website.http://www.iitg.ernet.in/mech/files/courses/ME101.pdf

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Text/Reference Books

I. H. Shames, Engineering Mechanics: Statics and dynamics, 4th Ed, PHI,2002.

F. P. Beer and E. R. Johnston, Vector Mechanics for Engineers, Vol I - Statics,Vol II Dynamics, 9th Ed, Tata McGraw Hill, 2011.

J. L. Meriam and L. G. Kraige, Engineering Mechanics, Vol I Statics, Vol IIDynamics, 6th Ed, John Wiley, 2008.

R. C. Hibbeler, Engineering Mechanics: Principles of Statics and Dynamics,Pearson Press, 2006.

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Marks distribution:

End semester 40%Mid semester 20%

Quiz 10%Tutorial 20%

Class participation 10%

75% attendance is mandatory

Tutorial problems should be solved and submitted to the respective tutor onevery Wednesday from 8:00 to 8:55 AM.

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Mechanics is the oldest branch of physical sciences.

Principle of lever and Buoyancy were discovered by Archimedes (287 -212 BCE).

Mechanics deals with action of forces on a body with state of rest ormotion.

Branches of mechanicsRigid-body mechanics

Deformable-body mechanics or solid mechanics

Fluid mechanics

Rigid-body mechanicsStatics

Dynamics

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Why to study mechanics?

Mechanics is a basic requirement for deformable-body mechanics and fluidmechanics. It is also a foundation of most other engineering sciences.

Few motivating examples:

Example - 1: Rotating top

(a) (b)

Why inclined axis of rotating top becomes vertical?Lecture 1 A Narayana Reddy Indian Institute of Technology Guwahati 8 / 18

Example - 2: cyclone rotation

The image is taken from http://thewatchers.adorraeli.com/2014/10/10/very-severe-tropical-cyclone-hudhud-targets-india/

Why large cyclone is always counterclockwise direction in NorthernHemisphere?Example - 3: Foucaults pendulum (67 m long wire with suspended weight of28 Kg) was developed by a French physicist Leon Foucault in 1851.Does oscillation of Foucaults pendulum affected by the spin of earth?

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Rigid bodyRigid body does not deform under action of forces!

Fundamental conceptsLength (Space): needed to locate position of a point with reference pointor origin. Also useful in describing the geometric properties of physicalsystems such as rigid body, deformable body, fluid.

Time: measure of succession of events. Essential quantity for dynamics.

Mass: measure of quantity of matter in a body. Also measure of inertiaof body, i.e., the resistance offer to the change in velocity.

Force: represents action of one body on another by physical contact orwithout physical contact. It is characterized by its magnitude, directionand point of application.Examples of forces: A body can apply force on another body throughphysical contact, gravitational force, electromagnetic forces.

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Fundamental Principles

Simon Stevin (1548-1620) developed theory about the parallelogram law offorces

A Q

RP

Parallelogram Law

P QR

R

Experimental Verification of the Parallelogram LawP R Q

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Fundamental principles

Principle of transmissibility:

F

= F

Principle of Transmissibility

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Fundamental principles

Newtons First Law: Every particle continues in its state of rest oruniform motion in a straight line unless compelled by an unbalancedexternal force.

Newtons Second Law: A particle will have an acceleration proportionalto a nonzero resultant applied force. Mathematically, F = ma.Newtons Third Law: The forces of action and reaction between twoparticles have the same magnitude and line of action with opposite sense.

Newtons Law of Gravitation: Two particles are attracted with equaland opposite forces,

F = GMmr2, W = mg, g =

GMr2

. (1)

Significance of Newtons first law and inertial frame of reference.

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Newtonian Mechanics

Absolute conceptsSpace, time and mass are absolute concepts and also independent of eachother.

Rest mass and inertial mass of a body are same. In other words, the restmass of a body is equal to moving mass with respect to every observer.(Not true in theory of relativity!)

Difference between mass and weightMass is the property of matter containing in a body and it does notchange with location in a space.

Weight refers to the gravitational attraction between a body and theearth. Therefore, the magnitude of attraction force depends on theelevation at which the body is placed (i.e., the spatial location of thebody with respect to the earth).Weight of a body is the gravitational force acting on it.

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Engineering Mechanics: Statics and Dynamics

EquilibriumThe body is said to be in equilibrium if the body is either at rest or movingwith a constant velocity.

StaticsStatics deals with the equilibrium ofbodies under action of forces.

DynamicsDynamics deals with motion of bodies(accelerated motion).

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Idealizations

ParticleA particle consists of mass with negligible dimensions.

SunEarth

OrbitExample: Size of the earth isinsignificant compared to thedimensions of orbit. So, the earth canbe considered as particle in modellingof orbital motion.

Rigid bodyA combination of large number of particles is said to be rigid body if thedistance between any two particles remain constant before and afterapplication of forces.

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Idealizations

Concentrated forceA concentrated force represents the effect of a loading which is assumed toact at a point on a body. This idealization is applicable when area over whichload is acting is very small compared to the overall size of the body.

Example: Contactforce between wheeland ground.

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Units of some quantities and prefixes

Quantity Dimensional symbol SI unit SI unit symbolMass M Kilogram kgLength L Meter mTime T Second sForce F Newton N (= kg.m/s2)

Exponential form Prefix SI symbol1 000 000 000 109 giga G

Multiple 1 000 000 106 mega M1 000 103 kilo k0.001 10-3 milli m

Submultiple 0.000 001 10-6 micro 0.000 000 001 10-9 nano n

Usually, capital letter K is used to represent Kelvin scale of temperature. So,avoid using capital letter K for prefix kilo. In fact, kilo symbol in Kilogramis the lower case letter k.

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