Engineering Mechanics 3(2+1)

LESSON 1. BASIC CONCEPTS

1.2 SOME BASIC TERMS USED IN MECHANICS

The followings are the basic terms which are used in mechanics:

Mass: The quantity of the matter possessed by a body is called mass. The mass of a body can not change unless the body is damaged and part of it is physically separated.

Length: It is a concept to measure linear distances.

Time: Time is the measure of succession of events. The successive event selected is the rotation of earth about its own axis and this is called a day.

Space: Any geometric region in which the study of a body has been done is called space.

Displacement: It is defined as the distance moved by a body/particle in the specified direction.

Velocity: The rate of change of displacement with respect to time is defined as velocity.

Acceleration: It is the rate of change of velocity with respect to time.

Momentum: The product of mass and velocity is called momentum. Thus

Momentum = Mass × Velocity

Particle: It can be defined as an object which has only mass and no size.

• Such a body cannot exist theoretically.

• When we deal with the problems involving distances considerably larger compared to the size of the body, the body may be treated as particle.

1.3 LAWS OF MECHANICS

The following are the fundamental laws of mechanics:

(i) Newton’s first law

(ii) Newton’s second law

(iii) Newton’s third law

(iv) Newton’s law of gravitation

(v) Law of transmissibility of forces

(vi) Parallelogram law of forces

Law of transmissibility of forces and law of parallelogram of forces will be discussed in coming lessons. Let us discuss the remaining laws:

(i) Newton’s first law: It states that everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by an external agency acting on it.

(ii) Newton’s second law: It states that the rate of change of momentum of a body is directly proportional to the impressed force and it takes place in the direction of the force acting on it.               

          According to this law,

                  Force = rate of change of momentum. But momentum = mass × velocity

                  As mass do not change,

                  Force = mass × rate of change of velocity

                  i.e., Force = mass × acceleration

                  F = m × a

(iii) Newton’s third law: It states that for every action there is an equal and opposite reaction.

1.4 UNITS AND DIMENSIONS OF QUANTITIES

1.4.1 Units

Measurements are always made in comparison with certain standards. For example, when we say that cloth piece is 2.5 metres long, the measurement of length is with respect to a scale on which graduations are marked. In turn, the graduation of the scale must have been made according to a national or an international standard. The standard so chosen for the measurement of length is called the unit of length. In this example, ‘metre’ is the unit of length.

Similarly, for the measurement of time, weight, current, speed etc, different units are used.

Each physical quantity is measured for the purpose of analysis, study, comparison, experimentation/results, design etc. with the help of measuring units by comparison.

There are four systems of units used for the measurement of physical quantities. viz. FPS (Foot – Pound – Second) system, CGS (Centimetre – Gram – Second) system, MKS (Meter - Kilogram – Second) system and SI (System international dꞌunits – the French name)

The SI system of units is said to be an absolute system.

S.I Units (International System of Units)

The fundamental units of the system are metre (m) for length, kilogram (kg) for mass and second (s) for time.

 The unit for force is newton (N). One newton is the amount of force required to induce an acceleration of 1 m/sec² on one kg mass. Weight of a body (in N) = Mass of the body (in kg ) × Acceleration due to gravity (in m/sec²).

1.4.2 Dimensions

The branch of mathematics dealing with dimensions of quantities is called dimensional analysis. There are two systems of dimensional analysis viz. absolute system and gravitational system.

Absolute system (MLT system)

• A system of units defined on the basis of length, time and mass is referred to as an absolute system.

• According to SI system of units, three basic units metre, second and kilogram can be used. In MLT system, M refers to Mass, L refers to Length and T refers to Time.

Gravitational system (FLT system)

• A system of units defined on the basis of length, time and force is referred to as a gravitational system.

• In this system, force is measured in a gravitational field. Thus, its magnitude depends upon the location where the measurement is made. FLT system refers to the Force-Length-Time system.

The dimensions of basic quantities in MLT and FLT systems are shown in Table 1.1.

Table 1.1 Dimensions of quantities in MLT and FLT systems

Quantity	MLT-System	FLT-system
Length	L	L
Mass	M	FL-1T2
Area	L2	L2
Volume	L3	L3
Velocity	LT-1	LT-1
Acceleration	LT-2	LT-2
Momentum	MLT–1	FT
Stress	ML-1T-2	FL-2
Weight	MLT-2	F
Force	MLT-2	F
Power	ML2T-3	FLT-1
Density	ML-3	FL-4T3

 

1.5 VECTORS:

Various quantities used in engineering mechanics may be grouped into scalars and vectors.

Scalar Quantity: A quantity is said to be scalar if it is completely defined by its magnitude alone. Examples of scalar quantities are:

Area, length, Mass, Moment of inertia, Energy, Power, Volume and Work etc.

Vector Quantity: A quantity is said to be vector if it is completely defined only when its magnitude as well as direction are specified. Examples of vector quantities include:

Force, Moment, Momentum, Displacement, Velocity and Acceleration.