Engineering Mechanics Problems and Solutions

Introduction

Previous chapters were concerned with the forces and reactions under which a body was held stationary; that branch of mechanics is called Statics. However, if the forces remained unbalanced, the body moves; this branch of mechanics is called Dynamics. It is further divided into two branches:

A body under motion can be idealized as a particle which is concentrated about its centre of gravity. It is assumed that a particle does not have rotational movement. However, if rotational movement of the body cannot be neglected then such body cannot be treated as particle.

Displacement, Velocity and Acceleration

Displacement is the minimum distance or smallest route travelled by a body from a starting point to the destination point along a straight line. It is a vector quantity as it is concerned with both magnitude and direction of motion.

Consider a particle moves from origin point A to destination point B via different paths A-1-2-B, A-B and A-3-4-B as shown in Fig. 10.1. Here the smallest route A-B travelled along a straight line will be displacement. However the other route traversed by the body will be called distance which depends upon magnitude only and called a scalar quantity. Being vector quantity, the displacement can have positive or negative value but distance always has a positive quantity.

Velocity of a body is described as the rate of change of displacement with respect to time. Velocity can be average velocity, instantaneous velocity and uniform velocity depending upon the variation of displacement and time.

Average velocity: In the previous example if body travels displacement Δs during time interval Δt via path A-B then the average velocity is given by

Instantaneous velocity: At a particular instant, the velocity of a body is known as Instantaneous velocity.