Engineering Mechanics Basics

Mechanics

Mechanics is the physical science which deals with the effects of forces on objects. No other subject plays a greater role in engineering analysis than mechanics. Although the principles of mechanics are few, they have wide application in engineering.

BASIC CONCEPTS

1.     Space

The geometric region in which study of a body is involved is called space. A point in the space may be referred with respect to a predetermined point by a set of linear and angular measurements. The reference point is called the origin and set of measurements as “coordinates”. If coordinates involve only mutually perpendicular directions, they are known as Cartesian / Rectangular Coordinates. If the coordinates involve angle and distances, it is termed as Polar / Angular Coordinate system.

2.     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. The unit of time is taken as second which is defined as the duration of 9192631770 period of radiation of the cesium-133 atom.

3.     Mass

The quantity of the matter possessed by a body is called mass. The mass of a body will not change unless the body is damaged or part of it is physically separated. When a body is taken out in a spacecraft, the mass will not change but its weight may change due to the change in gravitational force. Even the body may become weightless when gravitational force vanishes but the mass remains the same.

4.     Velocity

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

v = ds/dt

5.     Acceleration

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

a = dv/dt

Where “v” is velocity.

6.     Force

It 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 can also be defined as product of mass and acceleration. It is expressed in lbs. and KN.

F = ma

7.     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.

8.     Rigid Body

                                                                    

A body is considered rigid when the change in distance between any two of its points is negligible. For instance, the calculation of the tension in the cable which supports the boom of a mobile crane under load is essentially unaffected by the small internal deformations in the structural members of the boom. For the purpose, then, of determining the external forces which act on the boom, we may treat it as a rigid body. Statics deals primarily with the calculation of external forces which act on rigid bodies in equilibrium. Determination of the internal deformations belongs to the study of the mechanics of deformable bodies.

9.     Scalar Quantities

A quantity is said to be scalar if it is completely defined by its magnitude alone. Examples of scalars are length, area, time, volume, density, speed, energy, and mass.

10.             Vector Quantities

A quantity is said to be vector if it is completely defined only when its magnitude as well as direction are specified. Vector quantities, on the other hand, possess direction as well as magnitude, and must obey the parallelogram law of addition. Examples of vector quantities are displacement, velocity, acceleration, force, moment, and momentum.

11.             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 moves without rotation, then the movement or displacement of any point in the body may be taken as a vector. This vector describes equally well the direction and magnitude of the displacement of every point in the body. Thus, we may represent the displacement of such a body by a free vector.

12.             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 on a 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.

13.             Fixed Vector

A fixed vector is one for which a unique point of application is specified. The action of a force on a deform able 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.

FUNDAMENTAL PRINCIPLES

The Parallelogram Law for the Addition of Forces

This states that two forces acting on a particle may be replaced by a single force, called their resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces

The Principle of Transmissibility

This states that the conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point, provided that the two forces have the same line of action

NEWTON’S THREE FUNDAMENTAL LAWS

First Law

If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion)

Second Law

If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force.

F = ma

Where F, m, and a represent, respectively, the resultant force acting on the particle, the mass of the particle, and the acceleration of the particle.

Third Law

The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense

Newton’s Law of Gravitation

Everybody attracts the other body. The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to the square of the distance between them.

F = G m₁m₂/d²

Whereas G is known as constant of gravitation