This document discusses the concept of virtual work. It defines virtual work as the imaginary work done by actual forces on a system due to an infinitesimally small imaginary displacement from equilibrium. The principle of virtual work states that the algebraic sum of virtual works done by all forces must be equal to zero for a system in equilibrium. The document also provides examples of using the concept of virtual work to solve mechanics problems involving forces on linkages, springs, friction, and other systems.

2. CONTENTS
1. INTRODUCTION
2. CONCEPT OF VIRTUAL WORK
3. PRINCIPLE OF VIRTUAL WORK
4. PROCESS OF ANALYSIS
5. WORK ENERGY PRINCIPLE

3. INTRODUCTION
Whenever a force acts on a body , and the body undergoes some
displacements, then work is said to be done .
Eg : if a force P acting on a body, causes it to move through a
distance s as shown . Then work done by the force P
W = Force * Displacement
=F * S

4. CONCEPT OF VIRTUAL WORK
If we assume that the body, in equilibrium, undergoes an
infinite small imaginary displacement known as virtual
displacement .
The imaginary work done due to imaginary displacement and
actual force is called as virtual work.
The term ‘virtual’ is used to stress its purely hypothetical
nature, as we do not actually displace the system. we only
imagine, as to what would happen, if the system is displaced.

5. PRINCIPLE OF VIRTUAL WORK
If a system of forces or system of body s in equilibrium undergoes
a small ,imaginary displacement condition with the geometry
condition .
The Algebraic sum of virtual work done by all the forces much be
equal to zero.
In general, the virtual work done by external active forces on an
ideal mechanism system in equilibrium is zero.

6. PROCESS OF ANALYSIS
Draw free body diagram (F B D ) of mechanism showing all the forces.
Select co ordinate axis at some fixed point such that the point does
not displace during displacement of system .
Select or fix a variable defining equilibrium of system .
Give a small imaginary displacement to the system (d0)
In given system identify the active forces which do some work when
system is given a small virtual displacement.
 Find x coordinate of the point where horizontal active force is acting
and find y coordinate of the point where vertical active force is acting .
Find the coordinates in terms of “𝜃”
Differentiate the coordinates wrt “𝜃” to get virtual displacement in
terms of d𝜃 𝑎𝑛𝑑 𝛿𝜃

7. WORK ENERGY PRINCIPLE
The work energy principle for a particle can be stated as if a
particle of mass “m” subjected to unbalanced force system ,the
total work done by all forces during the displacement is equal
to the kinetic energy during that displacement .
U2-1=KE1-KE2
Work done by external force =WD =F*Displacement
Work done by frictional force =WD =Fr *Displacement , where
Fr=Frictional force , Fr =𝜇. 𝑅
Work done by Gravitiational force = mgh
Work done by spring force = ½ k(x1^2-x2^2), where k is
spring constant (N/m).

8. QUESTIONS
Q1.The mechanism shown in Fig. Ex. 17.5.1 is acted upon by the force P, derive an expression for
the magnitude of Q required for equilibrium.

9. SOLUTION:
NOTE:- VIRTUAL WORK DONE BY RA IS ZERO AS THIS FORCE IS
PERPENDICULAR TO VIRTUAL DISPLACEMENT OF A ROLLER A WHICH IS
HORIZONTAL.

10. Q2. As the bracket ABC is slowly rotated, the 6 kg block starts to slide towards the spring when =
20°. The maximum deflection of spring is observed to be 50 mm. Find coefficients of static and
kinetic friction. Refer fig.
SOLUTION:-

12. Q3. A trolley is moving towards the bumper spring and has K.E. = 11.25 kN.m. The constant of
main spring is 180 N/mm. The two secondary springs are 300 mm behind main shield a - a.
These springs having constants 90 N/mm. Determine maximum movement of shield a-a. Refer
Fig.
SOLUTION:-
Given:- K.E=11.25N.m
Kmain =180 N/mm=180*10^3 N/m ; Ksec=90N/mm=90*10^3N/m ; 300mm=0.3m

13. Q4. The boxes are transported by a conveyor belt with a velocity V to a fixed inclined plane at A.
From A they slide and finally fall off at B. If = 0.4. Determine the velocity of conveyor belt if boxes
are to have zero velocity at 'B'. Refer Fig.
SOLUTION:-

14. Q5. Two rods each of length 2L are hinged at B and supported as shown in Fig. Ex. 17.5.13. Find
magnitude of P to maintain equilibrium when 0 = 30°.
SOLUTION:-