LAWS OF MECHANICS

1. Principle of Transmissibility

It states that the state of the rigid body (either at rest or in motion with constant velocity) willremain unchanged if a force at a point in the body is replaced by a force of the same magnitudeand same direction but acting at a different point on a body, keeping ‘line of action’ of the forceunchanged.

2. The Parallelogram Law of Forces

The law states that ‘two forces acting on rigid body or on particle can be replaced by a singleequivalent force (known as ‘resultant’), obtained by drawing the diagonal of the parallelogramhaving length of sides proportionate to the given forces, through that point’.

RESOLUTION AND COMPOSITION OF FORCES

This is an analytical method of finding the resultant of a given system of many coplanar forcesacting at a point. In this method we first resolve all forces in two mutually directions, sayhorizontal and vertical directions; or in the x- and y-directions. Then we find the algebraic sumof these components and find the required resultant, as illustrated in the next example.

Example:

Find the resultant of the force system shown.

Solution:

x-component:

22

oox

32

3kN360coskN460coskN2R

kN49.3R x

y-component:

22

ooy

32

2kN360sinkN460sinkN2R

kN53.3R y

Resultant Force:

22kN53.3kN49.3R

R = 4.96 kN

Direction:

kN49.3kN53.3tan 1

θ = 45.66o

Equivalent force system:

Example:

Two wires are attached to a bolt in a foundation as shown. Determine the pull exerted by thebolt on the foundation.

Solution:x-component: oo

x 25cosN360015cosN6650R

N7.3160R x

y-component: ooy 25sinN360015sinN6650R

N572.3242R y

Resultant Force:

22N572.3242N7.3160R

R = 4528.167 N

Direction:

N7.3160N572.3242tan 1

θ = 45.73o

Equivalent force system:

Reference:

Engineering Mechanics by SP NItsure © 2006 Technical Publications Pune

Engineering Mechanics by Dr. IS Gujral © 2008 Published by Laxmi Publications (P) LTD