Applied Mechanics - Introduction to Mechanics and Dynamics PDF

Key Points

Covers the concepts of statics and dynamics in applied mechanics
Explains the resolution of forces and their applications in engineering
Includes practical examples and problem-solving techniques
Discusses the importance and necessity of applied mechanics in various fields

Ekemini Tom

229 pages

Language:English

Type:Textbook

Linguistics

Ekemini Tom

229 pages

Language:English

Type:Textbook

Linguistics

329

Self-Instructional Material

 Concept of Mechanics and Applied Mechanics

 Importance and Necessity of Applied Mechanics

 Branches of Mechanics

 Concept of Rigid Body

 Definitions of Terms Used in Mechanics

 System of Units Used in Mechanics

 Resolution of a Force

 Laws of Mechanics

Mechanics is that branch of science which deals with the behaviour

of a body when the body is at rest or in motion. The mechanics may be

divided into Statics and Dynamics. The branch of science, which deals with

the study of a body when the body is at rest, is known as Statics while the

branch of science which deals with the study of a body when the body is in

motion, is known as Dynamics. Dynamics is further divided into kinematics

and kinetics. The study of a body in motion, when the forces which cause

the motion are not considered, is called kinematics and if the forces are also

considered for the body in motion, that branch of science is called kinetics.

The classification of Applied Mechanics are shown in Fig. 1.1 below.

APPLIED MECHANICS

INTRODUCTION

LEARNING OBJECTIVES

1.1 CONCEPT OF MECHANICS AND APPLIED

MECHANICS

1. Static

(body is at rest)

2. Dynamics

(body is in motion)

(i) kinematics

(body is in motion. The forces which

cause motion, are not considered)

(i) kinematics

(body is in motion. Forces which

cause motion, are considered)

Fig. 1.1

Applied Mechanics

Self-Instructional Material

Applied mechanics deals with the application of principles and laws

of mechanics to the practical engineering problems.

Actually mechanics is a science which is based on a systematic

understanding and gathering of the facts, laws and principles governing

natural phenomenon. Applied mechanics is an art of utilisation of the

established facts, laws and principles to create certain desired

phenomenon,.

Note. Statics deals with equilibrium of bodies at rest, whereas dynamics

deals with the motion of bodies and the forces that cause them.

These days, the young engineers should have sound knowledge of

fundamental subjects such as mechanics. They must have sound

understanding of the fundamental principles that apply and be familiar with

various general methods of solution of engineering problems rather than

proficient in the use of any one. The study of applied mechanics makes the

young engineers to build a strong foundation, to acquaint them with as

many general methods of solution as possible and to illustrate the

application of these methods to practical engineering problems.

Applied mechanics deals with the application of principles and laws

of mechanics to the practical engineering problems.

The mechanics is the branch of science which deals with the physical

state of rest or motion of bodies under the action of forces. Depending upon

the nature of the body involved, the mechanics can be divided into:

(i) Mechanics of rigid bodies (known as Applied Mechanics)

(ii) Mechanics of deformable bodies (known as Mechanics of solids or

strength of materials)

(iii) Mechanics of fluids.

BRANCHES OF MECHANICS

1.2 IMPORTANCE AND NECESSITY OF APPLIED

MECHANICS

1.3 BRANCHES OF MECHANICS

Applied Mechanics

(Mechanics of Rigid bodies)

Mechanics of Fluids

Mechanics

of Solids

Fig. 1.1(a) shows the branches of mechanics

Applied Mechanics

Self-Instructional Material

Rigid bodies are those bodies which do not deform under the action

of applied forces. The distance between any two points remains constant,

when body is subjected to external forces.

Under the action of loads or external forces the physical bodies

deform, although slightly. But in many situation this deformation is

negligibly small to affect the results. So, the assumption of a rigid body shall

mean that the body does not deform or the distances between any two points

of the body does not change under the action of applied forces. Applied

mechanics is the mechanics of rigid body.

1.5.1. Vector Quantity. A quantity which is completely specified by

magnitude and direction, is known as a vector quantity. Some examples of

vector quantities are: velocity, acceleration, force and momentum. A vector

quantity is represented by means of a straight line with an arrow as shown

in Fig. 1.2. The length of the straight line (i.e., AB) represents the magnitude

and arrow represents the direction of the vector. The symbol 

󰇍



also

represents this vector, which means it is acting from A to B.

1.5.2. Scalar Quantity. A quantity, which is completely specified by

magnitude only, is known as a scalar quantity. Some examples of scalar

quantity are : mase,length, time and temperature.

1.5.3. A Particle. A particle is a body of infinitely small volume (or a

particle is a body of negligible dimensions) and the mass of the particle is

considered to be concentrated at a point. Hence a particle is assumed to a

point and the mass of the particle is concentrated at this point.

1.5.4. Law of Parallelogram of Forces. The law of parallelogram of

forces is used to determine the resultant* of two forces acting at a point in

a plane. It states, “If two forces, acting at a point be represented in

magnitude and direction by the two adjacent sides of a parallelogram, then

their resultant is represented in magnitude and direction by the diagonal of

the parallelogram passing through that point."

Let two forces P and Q act at a point O as shown in Fig. 1.3. The force

P is represented in magnitude and direction by OA whereas the force Q is

presented in magnitude and direction by OB. Let the angle between the two

forces be 'a'. The resultant of these two forces will be obtained in magnitude

1.4 CONCEPT OF RIGID BODY

1.5 DEFINITIONS OF TERMS USED IN MECHANICS

Fig. 1.2 Vector Quantity

Overview

Applied Mechanics - Introduction to Mechanics and Dynamics

Applied Mechanics explores the fundamental principles of mechanics, focusing on the behavior of bodies at rest and in motion. It covers essential topics such as the concepts of statics and dynamics, the resolution of forces, and the laws governing mechanical systems. This resource is ideal for engineering students and professionals seeking to understand the applications of mechanics in real-world scenarios. The material includes practical examples and problem-solving techniques relevant to various engineering fields. Key Points Covers the concepts of statics and dynamics in applied mechanics Explains the resolution of forces and their applications in engineering Includes practical examples and problem-solving techniques Discusses the importance and necessity of applied mechanics in…

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Figures

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 1.3

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 1.9

The resultant component along Y-axis is given by equation (1.7) as

is acting along OY as shown in Fig. 1.15.

Then according to the law of gravitational attraction

When two forces are equal, opposite and collinear they are in

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 2.6

Measure length ad. This gives the resultant.

Forces P and Q form two sides of a parallelogram and according to

(i) Choose a convenient scale to represent the forces

A small block of weight 100 N is placed on an inclined

Hence component of the weight perpendicular to the inclined plane

(a) Analytical Method. Resolve each force along horizontal and vertical

Hence the algebraic sum of horizontal component should be zero and

The ball is supported by a string AB and is resting against a vertical

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 2.31

In S.I. system, moment is expressed in Nm (Newton metre).

Hence their moments about A will be zero. The moment of the force at

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 3.4

Triangle OBC is a right-angled triangle. And anle

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 3.7

In order to find the point At which the resultant is acting, Varignon's

Let the resultant R is acting at C as shown in Fig. 3.10.

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 3.11

The resultant R of three like forces is given by,

This force is to be replaced at the point B. Introduce two equal and

(i) Single force system. The single force system will consist only

Forces at A, B, C, D and E and 4 N, 8 N, 8 N, 16 N and 12 N

Since all the forces are vertical and parallel, hence their resultant is

If the two forces acting on a body are equal and opposite but are

(a) When three forces are concurrent. The three con- current forces

-axis as shown in Fig. 3.23, then determine the magnitude and

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 3.24

Three like parallel forces 20 N, 40 N and 60 N are acting at points A, B

Four parallel forces of magnitudes 100 N, 200 N, 50 N and 400 N are

Five forces are acting on a body as shown in Fig. 3.37. Determine the

Determine the resultant of the parallel forces shown in Fig. 3.38.

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 3.39

Three forces of magnitude 40 kN, 15 kN and 20 kN are acting at a point

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 3.42

If in the above problem, the sides of the groove makes an angle of 45°

Applied Mechanics - Introduction to Mechanics and Dynamics — Fig 4.2

FAQs

What is the concept of mechanics in applied mechanics?

Mechanics is the branch of science that deals with the behavior of a body when it is at rest or in motion. It is divided into two main branches: Statics, which studies bodies at rest, and Dynamics, which studies bodies in motion. Dynamics is further divided into Kinematics, which focuses on motion without considering forces, and Kinetics, which involves the forces that cause motion.

What are the laws of mechanics discussed in the document?

The document outlines several fundamental laws of mechanics. These include Newton's first and second laws of motion, which describe the relationship between force, mass, and acceleration. Additionally, the gravitational law of attraction is mentioned, stating that two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The principle of transmissibility of forces is also highlighted, indicating that a force can be applied at any point along its line of action without changing the effect on the body.

How is the resultant of two forces calculated in applied mechanics?

The resultant of two forces acting at a point can be calculated using the law of parallelogram of forces. If two forces, P and Q, are acting at an angle α to each other, the magnitude of the resultant R is given by the equation R = √(P² + Q² + 2PQ cos α. The direction of the resultant can be determined using the tangent function, where tan θ = (Q sin α) / (P + Q cos α), with θ being the angle made by the resultant with one of the forces.

What is the significance of the angle of friction in applied mechanics?

The angle of friction is defined as the angle made by the resultant of the normal reaction and the limiting force of friction with the normal reaction. It is denoted by φ and is significant because it determines the conditions under which a body remains at rest or begins to slide on an inclined plane. The relationship between the angle of friction and the coefficient of friction is expressed as tan φ = μ, where μ is the coefficient of friction, indicating that the angle of friction is equal to the angle of an inclined plane at which a body begins to slide.

What are the types of friction mentioned in the document?

The document distinguishes between two main types of friction: static friction and dynamic friction. Static friction occurs when two surfaces are at rest relative to each other, while dynamic friction occurs when one surface slides over another. The laws of solid friction are also discussed, highlighting that the force of friction acts in the opposite direction to the motion and that the limiting frictional force is proportional to the normal reaction between the two surfaces.

How is the efficiency of a machine calculated in applied mechanics?

The efficiency of a machine is calculated as the ratio of the output work to the input work, expressed mathematically as η = Output / Input. In the context of lifting machines, the output is the product of the load lifted and the distance through which the load is lifted, while the input is the product of the effort applied and the distance moved by the effort. The efficiency can also be expressed in terms of mechanical advantage (M.A.) and velocity ratio (V.R.) as η = M.A. / V.R.

What is the principle of moments in applied mechanics?

The principle of moments states that the moment of the resultant of a number of forces about any point is equal to the algebraic sum of the moments of all the forces of the system about the same point. This principle is crucial for analyzing systems where multiple forces are acting, as it allows for the determination of the resultant moment by considering the individual moments of each force acting on the body.