Lecture 01 BY

Engr Muhammad UsmanMechanical Engineering

DepartmentCECOS University

Basic Mechanical Engineering

TextbookEngineering

Mechanics– Statics (6th Edition)by

J.L Meriam and L.G Kraige

CREDIT HOURS: THEORY = 3 HOURSCONTACT HOURS: THEORY = 3 HOURS

Course Structure

• Lectures will cover concepts and principles, not detailed problem solving

• 06 homework assignments• 06 quizzes• Mid Term Exam• Final Examination

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STUDENT PERFORMANCE EVALUATION / GRADING

• Class participation, Assignments, Quizzes and the Final examination will evaluate student progress.

 FINAL GRADE The final grade will be determined by averaging each section and

assigning them the following weights: 

Quizzes ............................12.5%Assignments………………12.5%Mid Term Exam……………25%Final Examination .............50%

---------------------------------------------------------Total ............................. 100%

COURSE OUTLINE• Fundamental concept and principle of

mechanics, important vector quantity• Force system i.e concurrent• Non concurrent and parallel force system• Resultant of forces• Moment and couple• Equilibrium of forces (law & type) concept of

free body diagram

• Principle of friction , types of friction normal reaction, co-efficient of friction, laws of friction

• Simple lifting machine• Types of machines, simple pulley, first, second

and third system of pulley• Fundamental of dynamics, application of

newton’s 2nd law of motion

• Projectile motion, circular motion, analysis of motion in 2D & 3D Spaces

• Simple harmonic motion, types of energy, momentum

• Work power and energy• Strength of material, types of stress strain• Hook’s law, modulus of elasticity, linear strain

lateral strain, poission ratio volumetric• Fluid mechanics, chain, design of fly wheel,

bearings, mechanical power transmission.

BRANCHES OF MECHANICS

S ta tics D yn a m ics

R ig id B o d ies(T h in g s th a t do no t ch a ng e sh ap e)

D e form a b le B o d ies(T h in g s th a t d o ch an g e sh ap e)

In co m p ress ib le C o m p re ss ib le

F lu id s

M e ch a n ics

What is Mechanics?Mechanics is the branch of physical science which deals with the state

of rest or motion of bodies that are subjected to the action of forces.

Mechanics is the study of forces that act on bodies and the resultant motion that those bodies experience.

With roots in physics and mathematics, Engineering Mechanics is the basis of all the mechanical sciences.

Physical science is the study of the physical world around you. Any of several branches of science, such as physics, chemistry, and astronomy, that study the nature and properties of energy and nonliving matter.

Introduction Basic mechanics involves the study of two principal areas – statics anddynamics.

Statics is the study of forces on objects or bodies which are at rest ormoving at a constant velocity, and the forces are in balance, or in staticequilibrium. A ball at rest may have several forces acting on it, such as gravitationalforce (weight) and a force opposing that gravity (reaction). The ball is atrest or static, has forces in balance or EQUILIBRIUM

Dynamics is the study of forces on moving bodies, and the forces are indynamic equilibrium.

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Basic Concept

• Space• Time• Mass• Force• Particle• Rigid body

Space

• Space is the boundless three-dimensional extent in which objects and events have relative position and direction.

Time

• Time is a dimension and measure in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them.

Mass

• Quantity of matter in a body. Used to characterize and compare bodies, e.g., response to earth’s gravitational attraction and resistance to changes in translational motion. Mass is a measure of inertia of a body. (Inertia: the tendency of a body to maintain its state of rest or uniform motion unless acted upon by external force). Its unit is kg.

Force

• 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 a force is characterized by its magnitude, by the direction of its action, and by its point of application. Force is a vector quantity.

Particle

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

Continue

It is an object that has mass, but a size that can be neglected. For example, the size of earth is insignificant compared to the size of its orbit, and therefore the earth can be modeled as a particle when studying its orbital motion.

Rigid Body

The term "rigid body" refers to a system with any number of particles, but which are constrained not to move relative to each other. That is, a rigid body does not deform. All particles in a rigid body remain at a fixed distance from one another even after applying forces. A rigid body is nothing but a solid body of finite size in which change in original shape (deformation in other words) is not allowed.

Scalar & Vector Quantity

Vector Classification

• Vector can be classified as

Free Vector Sliding Vector Fixed Vector

Free Vector• A free vector is one whose action is not

confined to or associated with a unique line in space. For example if a body is in translational motion, velocity of any point in the body may be taken as a vector and this vector will describe equally well the velocity of every point in the body. Hence, we may represent the velocity of such a body by a free vector. In statics, couple moment is a free vector.

Sliding Vector

• A sliding vector has a unique line of action in space but not a unique point of application. For example, when an external force acts ona rigid body, the force can be applied at any point along its line of action without changing its effect on the body as a whole,* and thus it is a sliding vector.

Fixed Vector

• A fixed vector is one for which a unique point of application is specified. The action of a force on a deformable or non rigid body must be specified by a fixed vector at the point of application of the force. In this instance the forces and deformations within the body depend on the point of application of the force, as well as on its magnitude and line of action.

Negative of a Vector

• The negative vector of a vector as a vector having the same magnitude as the original vector but the opposite direction. The negative of a vector A is denoted as –A.

Unit vector

• A vector whose magnitude is equal to one is called unit vector.

• It is used to represent the direction of a vector.

Up = + Down = - Right = + Left = -

y

x

+

+

-

-

Quadrant IQuadrant II

Quadrant III Quadrant IV

0 o East

90 o North

West 180 o

270 o South

360 o

Rectangular Coordinates

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0O East

90O North

West 180O

270O South

360O

+x

+y

- x

- y

120O

-240O

30O West of North30O Left of +y

60O North of West60O Above - x

MEASURING THESAME DIRECTION

IN DIFFERENT WAYS

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315O or (7/4) RADIANS

0O East

90O North

West 180O

270O South

360O

+x

+y

- x

- y

+10

-10

-45O or45O SOUTH OF EAST

VECTOR NOTATIONS

•RRECTANGULAR COORDINATES10, -10 (X = +10, Y = -10)

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A

B

C

Sin = A / C

Cos = B / C

Tan = A / B

AC

B

A

BA RIGHT TRIANGLE

C

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X

Y

A

Ax

Ay

Bx

By

B

Ax A = COS

A= SIN Ay

Bx B = COS

B= SINBy

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y

x

+

+

-

- 0 radians radians

3/2 radians

2 radians

Quadrant III

Quadrant IV

Quadrant I

Quadrant II

Sin Cos Tan

+ + +

+ - -

- - +

- + -

/2 radians

90 o

0 o

180 o

270 o

360 o

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Sine And Cosine Rules

For triangles that are not right-angle, the following two laws are important in vector algebra introduced in chapter two later:

Cosine Rule a2 = b2 + c2 – 2bc cos (1.8) b2 = a2 + c2 – 2ac cos c2 = a2 + b2 – 2ab cos

Sine Rule a = b = c sin sin sin

Fundamental Principles

1 - 37

• Newton’s First Law: If the resultant force on a particle is zero, the particle will remain at rest or continue to move in a straight line.

• Newton’s Third Law: The forces of action and reaction between two particles have the same magnitude and line of action with opposite sense.

• Newton’s Second Law: A particle will have an acceleration proportional to a nonzero resultant applied force.

amF

Law of gravitation• Two particles are attracted with equal and

opposite forces,

• F= the mutual force of attraction between the particle.

• M1 ,M2 = Mass of two particle• r= the distance between the center of particle.• G= A universal constant known as constant of

gravitational

22 ,R

GMgmgWr

MmGF

Unit Conversion Factors

39

40

41

42

43

44

Prefixes for power of 10

45

Examples

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Accuracy

• The quality or state of being correct or precise.• The degree to which the result of a

measurement, calculation, or specification conforms to the correct value or a standard.

Limit & Approximation

• Limit is the point or level beyond which something does not or may not extend or pass.

• Approximation is a guess or estimate. Ninety-three million miles is an approximation of the distance of the earth from the sun.

Home Practice

• Sample Problem ½ and 1/3.

Problem 1.1 Determine the angles made by the vector V = - 36i +15j with the positive x- and y-axes. Write the unit vector n in the direction of V.

Problem 1.2Determine the magnitude of the vector sum V= V1 + V2 and the angle x which V makes with the positive x-axis. Complete both graphical and algebraic solutions.

Problem 1.3For the given vectors V1 and V2 of Prob. 1/2, determine the magnitude of the vector difference V =V2+ V1 and the angle x which V makes with the positive x-axis. Complete both graphical and algebraic solutions.

Problem 1.4A force is specified by the vector F= 160i +80j - 120k N. Calculate the angles made by F with the positive x-, y-, and z-axes.

Problem 1.5What is the mass in both slugs and kilograms of a 1000-lb beam?