This lecture discusses the equilibrium of particles and free-body diagrams. It defines particle equilibrium as being at rest if originally at rest or having constant velocity if in motion. The condition for particle equilibrium is that the sum of all forces acting on the particle is zero. Examples of connections involving springs and cables/pulleys are provided. The procedure for drawing free-body diagrams involves outlining the particle, showing all known and unknown forces, and labeling the forces. Example problems are solved to demonstrate applications of these concepts.

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A particle is said to be in equilibrium:
1. provided it is at rest if originally at rest, or
2. particle has constant velocity if originally in
motion

5. CCOONNDDIITTIIOONNSS FFOORR EEQQUUIILLIIBBRRIIUUMM OOFF AA
PPAARRTTIICCLLEE
According to the Newton’s First Law, which
states that “a particle originally at rest will
remain in rest condition if resultant force acting
on the particle is zero”, the condition for
equilibrium can be obtained by summing up all
the forces algebraically and equating the sum to
zero, as follows: ΣF = 0

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(i) Springs
When a force (F) is applied to a linear elastic spring
having stiffness k (also called spring constant), there
will be change in the length of spring (s) in direct
proportion to the applied force, as follows: F = ks
For example, the force required to stretch or
compress the spring, as shown in the following figure,
is given as: F = ks = 500 × 0.2 = 100 N

7. CCOONNNNEECCTTIIOONNSS OOFFTTEENN
EENNCCOOUUNNTTEERREEDD IINN PPAARRTTIICCLLEE
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(ii) Cables and Pulleys
Let us consider a cable subjected to tension T and
passing over a pulley, as shown in the following
figure:
For the cable and pulley system, as shown in the
above figure, the following points may be noted:
• Cable is assumed to have negligible weight and
they cannot stretch
• A cable may support only a tensile force, T, and
this force always acts in the direction of the cable
• For any θ value, the cable is subjected to a
constant tensile force T throughout its length.

8. PPRROOCCEEDDUURREE FFOORR
DDRRAAWWIINNGG AA FFRREEEE--BBOODDYY
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Free-body diagram of a given system is required to apply
the equilibrium conditions for analysis of the system.
Following steps are adopted for drawing free-body
diagrams:
• Draw outlined shape of the given system
• Isolate or cut “free” the particle from its surroundings and
the sketch of the particle
Show all known and unknown forces
• Indicat
e
all the forces acting on the particle, on the sketch
each force

9. • Label the magnitudes and the directions of all the known
and unknown forces acting on the particle

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13. Multiple Choice Problems
1. A 0.7 m long spring having stiffness k = 400 N/m
is subjected to tensile force of 200 N. The length
of the spring after applying load will be
(a) 0.2 m (b) 0.5 m
(c) 0.7 m (d) 1.2 m
Ans: (d)
Feedback:
For a spring, we have:
F = ks
⇒ s =
F
k =
200
400 = 0.5 m
The length of the spring after applying load
= 0.7 + 0.5 = 1.2 m

14. Multiple Choice Problems
2. If angle θ is 30° for the cable passing over a pulley,
as shown in the figure below, the tension T in the
cable will be
(a) 0 (b) 600 N
(c) 693 N (d) 1200N
Ans: (b)
Feedback:
Since the same cable is passing over a pulley, the
tension at any location of the cable will remain
same irrespective of the orientation of the cable.