ENGINEERING MECHANICS (Credit Hours: 3+1=4) Specific Objectives of course:

• To enable students to understand relationships of physical processes, kinetics and kinematics.

• To develop skills to use the basic principles of mechanics in engineering applications

Course Outline:

Basic Concepts: Concepts of space, time, mass, velocity, acceleration and force. Scalar and vector quantities, Newton'slaws of motion, Law of gravitation.

System of Forces: Resultant and resolution of co-planer forces using parallelogram, triangle & polygon law and funicularpolygon. Simple cases of resultant and resolution of forces in space, Conditions of equilibrium of co-planar forces,analytical and graphical formulations.

Equilibrium of Rigid Bodies: Free body concept, conditions of support and attachment to other bodies, Support Reactionsunder different types of loading, Introduction to shear force and bending moment diagrams. Degree of restraint and staticdeterminacy. Statically determinate problems especially of civil engineering importance, Equilibrium of two-force andthree-force bodies.

Kinematics: Work, energy and power. Virtual work formulation of equilibrium of coplanar force. Potential energy, energycriterion for equilibrium, stability of equilibrium, application to simple cases.

Rigid Bodies: Geometrical properties of plane areas, first moment of area, centroid, second moment of area, principal axes,polar second moment of area and radius of gyration.

Friction: Coulomb's theory of friction. Problems involving friction on flat and curved surfaces.

Application of Principles of Dynamics: Rectilinear and curvilinear motion, Newton’s equation of motion, Dynamicequilibrium

Introduction to practical use of the above principles and properties.

Lab Outline:

The Design work and/or experiments related to above mentioned outline shall be covered in theLaboratory/Design class.

(PEC)Recommended Books:

1. Hibbeler, R. C. Engineering Mechanics- Statics and Dynamics, Prentice Hall. (14th Edition), 2016.

2. Ferdinand P. Beer and E. Russel Johnston Jr. “Vector Mechanics for Engineers”, 11th Edition, 2016.

3. F. L. Singer, Engineering Mechanics, 4th ed, Harper and Row Publisher, 1987.

4. J. L. Mariam & L. G. Kraige; Engineering Mechanics Statics and Dynamics; John Wiley & Sons, 8thEdition, 2016.

Reference books.

1.Engineering Mechanics by Timoshenko , McGraw - Hill (Revised Fourth Edition 2008).

2. Engineering Mechanics Statics By Pytel and Kissulaas Third Edition SI (Indian Edition).

Basic Concepts:

The following concepts and definitions are basic to the study of mechanics, and they should be understood at theoutset.

Space is the geometric region occupied by bodies whose positions are described by linear and angular measurementsrelative to a coordinate system. For three-dimensional problems, three independent coordinates are needed. For two-dimensional problems, only two coordinates are required.

Time is the measure of the succession of events and is a basic quantity in dynamics. Time is not directly involved inthe analysis of statics problems.

Mass is a measure of the inertia of a body, which is its resistance to a change of velocity. Mass can also be thought ofas the quantity of matter in a body. The mass of a body affects the gravitational attraction force between it and otherbodies. This force appears in many applications in statics.

Force is the action of one body on another. A force tends to move a body in the direction of its action. The action of aforce is characterized by its magnitude, by the direction of its action, and by its point of application. Thus force is avector quantity. The SI units of force is Newton.

A particle is a body of negligible dimensions. In the mathematical sense, a particle is a body whose dimensions areconsidered to be near zero so that we may analyze it as a mass concentrated at a point. We often choose a particle as adifferential element of a body. We may treat a body as a particle when its dimensions are irrelevant to the descriptionof its position or the action of forces applied to it.

Rigid body. A rigid body can be considered as a combination of a large number of particles in which all the particlesremain at a fixed distance from one another, both before and after applying a load. This model is important becausethe body’s shape does not change when a load is applied, and so we do not have to consider the type of material fromwhich the body is made. In most cases the actual deformations occurring in structures, machines, mechanisms, andthe like are relatively small, and the rigid-body assumption is suitable for analysis.

Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value(magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric)system as meters per second (m/s) or as the SI base unit of (m⋅s−1).

Acceleration is defined as the rate of change of velocity. Acceleration is inherently a vector quantity, and an objectwill have non-zero acceleration if its speed and/or direction is changing. The average acceleration is given by

Velocity

Acceleration

Deceleration

Time

v(t)

y V(t+𝛥t)

𝛥v

a =𝛥𝑣

𝛥𝑡

x

Scalar is the measurement of a medium strictly in magnitude.

Vector is a measurement that refers to both the magnitude of the medium as well as the direction of the movement themedium has taken.

Scalar Quantities

Length, area, volume, speed, mass,density, pressure, temperature, energy,

entropy, work, power

Vector Quantities

Displacement, velocity, acceleration, momentum, force, lift, drag, thrust, weight, torque, acceleration due to gravity.

Velocity

Volume

Newton’s Three Laws of Motion. Engineering mechanics is formulated on the basis of Newton’s three laws ofmotion, the validity of which is based on experimental observation. These laws apply to the motion of a particle asmeasured from a nonaccelerating reference frame. They may be briefly stated as follows.

First Law. A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this stateprovided the particle is not subjected to an unbalanced force. Fig. a

Second Law. A particle acted upon by an unbalanced force F experiences an acceleration a that has the same directionas the force and a magnitude that is directly proportional to the force. Fig. b

If F is applied to a particle of mass m, this law may be expressed mathematically as

F = ma

Third Law. The mutual forces of action and reaction between two particles are equal, opposite, and collinear. Fig. c

Newton’s Law of Gravitational Attraction. This law states that a body attracts every other body in

the universe with a force which is directly proportional to the product of their masses but

also inversely proportional to the square of the distance between their centers. Mathematically ,

𝐹 α 𝑚1𝑚2

𝐹 α1

𝑟2

Combining above two equations,

𝐹α𝑚1𝑚2

𝑟2

𝐹 = 𝐺𝑚1𝑚2

𝑟2

where:

•F is the force between the masses;

•G is the gravitational constant (6.674×10−11 N · (m/kg)2

•m1 is the first mass;

•m2 is the second mass;

•r is the distance between the centers of the masses.

Units: In mechanics we use four fundamental quantities called dimensions. These are length,mass, force, and time. The units used to measure these quantities cannot all be chosenindependently because they must be consistent with Newton’s second law of motion. The fourfundamental dimensions and their units and symbols in the two systems are summarized in thefollowing table.

Prob#1. Determine the weight in newtons of a car whose mass is 1400 kg. Convert the mass of thecar to slugs and then determine its weight in pounds.

Soln.

Step#1W = mg = 1400(9.81) = 13 730 N

Step#2

Since 1 slug is equal to 14.594 kg, therefore the mass of the car in slugs is

m = 1400 kg1 𝑠𝑙𝑢𝑔

14.594 𝑘𝑔= 95.9 𝑠𝑙𝑢𝑔𝑠

Step#3

Finally, its weight in pounds is,1 𝑠𝑙𝑢𝑔 = 32.2 𝑙𝑏

W = mg (95.9)(32.2) = 3090 lb

Alternatively,1 𝑘𝑔 = 2.204 𝑙𝑏

𝑊 = 1400 ⨯ 2.204 = 3090 𝑙𝑏

Prob#2: Use Newton’s law of universal gravitation to calculate the weight of a 70-kg personstanding on the surface of the earth. Then repeat the calculation by using W = mg and compareyour two results.

Soln.

Step#1: By the law of gravitation

𝐹 = 𝐺𝑚1𝑚2

𝑟2

𝐹 =(6.673 1011)(5.976 1024)(70)

[6371 ⨯ 103]2

F = 688 N

Step#2:W = mg = 70(9.81) = 687 N

Prob#3: Compute the magnitude F of the force which the earth exerts on the moon. Perform thecalculation first in newtons and then convert your result to pounds.

Soln. Step#3

Step#1

Step#2

Step#4.

Prob#4 A simply supported beam weighs 1000lb, find this mass in kilogram and slugs.

Soln.

Prob#5 From the gravitational law calculate the weight W(gravitational force with respect to theearth) of a 80-kg man in a spacecraft traveling in a circular orbit 250 km above the earth’s surface.Express W in both newtons and pounds.

Soln.

Prob#6 The mass of Sun is 33300 times the mass of the earth. The mass of earth is4.095⨯1023𝑙𝑏𝑓. 𝑠2/𝑓𝑡.The distance between sun and the earth is 92.96⨯106𝑚𝑖𝑙𝑒𝑠. Compute themagnitude F of the force which the sun exerts on the earth. Perform the calculation first in poundsand then convert your result to newtons.

Soln.

Prob#7 Determine the weight in newtons of a woman whose weight in pounds is 130. Also, findher mass in slugs and in kilograms. Determine your own weight in newtons.

Soln.

Step#1 Step#3

Step#2 Step#4

Prob#8 What is the mass in both slugs and kilograms of a 3000-lb car?

Soln.

Step#1

Step#3

Step#2