Short Notes: Equilibrium of Forces | Short Notes for Mechanical Engineering PDF Download

 Page 1


Equilibrium of Forces 
Basic concept
• Mechanics can be defined as the branch of physics concerned with the state 
of rest or motion of bodies that subjected to the action of forces. OR It may 
be defined as the study of forces acting on body when it is at rest or in motion 
is called mechanics.
• Mechanics can be divided into two branches.
o Statics It is the branch of mechanics that deals with the study of forces 
acting on a body in equilibrium. Either the body at rest or in uniform 
motion is called statics
° Dynamics: It is the branch of mechanics that deals with the study of 
forces on body in motion is called dynamics. It is further divided into two 
branches.
¦ Kinetics It is the branch of the dynamics which deals the study of 
body in motion under the influence of force i.e. is the relationship 
between force and motion are considered or the effect of the force 
are studied
¦ Kinematics: It is the branch of the dynamics that deals with the 
study of body in motion without considering the force.
Force
• Force In general force is a Push or Pull, which creates motion or tends to 
create motion, destroy or tends to destroys motion.
• In engineering mechanics force is the action of one body on another.
Page 2


Equilibrium of Forces 
Basic concept
• Mechanics can be defined as the branch of physics concerned with the state 
of rest or motion of bodies that subjected to the action of forces. OR It may 
be defined as the study of forces acting on body when it is at rest or in motion 
is called mechanics.
• Mechanics can be divided into two branches.
o Statics It is the branch of mechanics that deals with the study of forces 
acting on a body in equilibrium. Either the body at rest or in uniform 
motion is called statics
° Dynamics: It is the branch of mechanics that deals with the study of 
forces on body in motion is called dynamics. It is further divided into two 
branches.
¦ Kinetics It is the branch of the dynamics which deals the study of 
body in motion under the influence of force i.e. is the relationship 
between force and motion are considered or the effect of the force 
are studied
¦ Kinematics: It is the branch of the dynamics that deals with the 
study of body in motion without considering the force.
Force
• Force In general force is a Push or Pull, which creates motion or tends to 
create motion, destroy or tends to destroys motion.
• In engineering mechanics force is the action of one body on another.
• A force tends to move a body in the direction of its action, A force is 
characterized by its point of application, magnitude, and direction, i.e. a force 
is a vector quantity.
Units of force
The following force units are frequently used.
• Newton
° The S.l unit of force is Newton and denoted by N. which may be defined 
as 1N = 1 kg. 1 m/s2
• Dynes
° Dyne is the C.G.S unit of force. 1 Dyne = 1 g. 1 cm/s2 One Newton force 
= 105 dyne
• Pounds
° The FPS unit of force is the pound. 1 Ibf = 1 Ibm. 1ft/s2 One pound force 
= 4.448 N One dyne force = 2.248 x 10"6 lbs
Principle of transmissibility of forces
• The state of rest of motion of a rigid body is unaltered if a force acting in the 
body is replaced by another force of the same magnitude and direction but 
acting anywhere on the body along the line of action of the replaced force.
• For example the force F acting on a rigid body at point A. According to the 
principle of transmissibility of forces, this force has the same effect on the 
body as a force F applied at point B .
Free-Body Diagram:
• A diagram or sketch of the body in which the body under consideration is 
freed from the contact surface (surrounding) and all the forces acting on it 
(including reactions at contact surface) are drawn is called free body diagram. 
Free body diagram for few cases are shown in below
Steps to draw a free-body diagram:
Page 3


Equilibrium of Forces 
Basic concept
• Mechanics can be defined as the branch of physics concerned with the state 
of rest or motion of bodies that subjected to the action of forces. OR It may 
be defined as the study of forces acting on body when it is at rest or in motion 
is called mechanics.
• Mechanics can be divided into two branches.
o Statics It is the branch of mechanics that deals with the study of forces 
acting on a body in equilibrium. Either the body at rest or in uniform 
motion is called statics
° Dynamics: It is the branch of mechanics that deals with the study of 
forces on body in motion is called dynamics. It is further divided into two 
branches.
¦ Kinetics It is the branch of the dynamics which deals the study of 
body in motion under the influence of force i.e. is the relationship 
between force and motion are considered or the effect of the force 
are studied
¦ Kinematics: It is the branch of the dynamics that deals with the 
study of body in motion without considering the force.
Force
• Force In general force is a Push or Pull, which creates motion or tends to 
create motion, destroy or tends to destroys motion.
• In engineering mechanics force is the action of one body on another.
• A force tends to move a body in the direction of its action, A force is 
characterized by its point of application, magnitude, and direction, i.e. a force 
is a vector quantity.
Units of force
The following force units are frequently used.
• Newton
° The S.l unit of force is Newton and denoted by N. which may be defined 
as 1N = 1 kg. 1 m/s2
• Dynes
° Dyne is the C.G.S unit of force. 1 Dyne = 1 g. 1 cm/s2 One Newton force 
= 105 dyne
• Pounds
° The FPS unit of force is the pound. 1 Ibf = 1 Ibm. 1ft/s2 One pound force 
= 4.448 N One dyne force = 2.248 x 10"6 lbs
Principle of transmissibility of forces
• The state of rest of motion of a rigid body is unaltered if a force acting in the 
body is replaced by another force of the same magnitude and direction but 
acting anywhere on the body along the line of action of the replaced force.
• For example the force F acting on a rigid body at point A. According to the 
principle of transmissibility of forces, this force has the same effect on the 
body as a force F applied at point B .
Free-Body Diagram:
• A diagram or sketch of the body in which the body under consideration is 
freed from the contact surface (surrounding) and all the forces acting on it 
(including reactions at contact surface) are drawn is called free body diagram. 
Free body diagram for few cases are shown in below
Steps to draw a free-body diagram:
1. Select the body (or part of a body) that you want to analyze, and draw it.
o
2. Identify all the forces and couples that are applied onto the body and draw 
them on the body. Place each force and couple at the point that it is applied.
3. Label all the forces and couples with unique labels for use during the solution 
process.
4. Add any relevant dimensions onto your picture.
Equilibrium: The concept of equilibrium Is introduced to describe a body which Is 
stationary or which is moving with a constant velocity. In statics, the concept of 
equilibrium is usually used in the analysis of a body which is stationary, or is said 
to be in the state of static equilibrium.
Particles: A particle is a body whose size does not have any effect on the results of 
mechanical analyses on it and, therefore, its dimensions can be neglected.
Rigid body: A body is formed by a group of particles. The size of a body affects the 
results of any mechanical analysis on it. A body is said to be rigid when the relative 
positions of its particles are always fixed and do not change when the body is 
acted upon by any load (whether a force or a couple).
Force System:
• When a member of forces simultaneously acting on the body, it is known as 
force system. A force system is a collection of forces acting at specified 
locations. Thus, the set of forces can be shown on any free body diagram 
makes-up a force system.
Types of system of forces
• Collinear forces:
° In this system, line of action of forces act along the same line is called 
collinear forces. For example consider a rope is being pulled by two 
players as shown in figure * •
*
F a
• Coplanar forces
° When all forces acting on the body are in the same plane the forces are 
coplanar
• Coplanar Concurrent force system
° A concurrent force system contains forces whose lines of action meet at 
same one point. Forces may be tensile (pulling) or Forces may be 
compressive (pushing)
Tvro fijQpcring % load
..Concurrent 
pom\A
1 0 I)
force* acting or rirq
1 r u n | o i n t Forces act < n g on font
• Non-Concurrent Co-Planar Forces
o A system of forces acting on the same plane but whose line of action 
does not pass through the same point is known as non concurrent
Page 4


Equilibrium of Forces 
Basic concept
• Mechanics can be defined as the branch of physics concerned with the state 
of rest or motion of bodies that subjected to the action of forces. OR It may 
be defined as the study of forces acting on body when it is at rest or in motion 
is called mechanics.
• Mechanics can be divided into two branches.
o Statics It is the branch of mechanics that deals with the study of forces 
acting on a body in equilibrium. Either the body at rest or in uniform 
motion is called statics
° Dynamics: It is the branch of mechanics that deals with the study of 
forces on body in motion is called dynamics. It is further divided into two 
branches.
¦ Kinetics It is the branch of the dynamics which deals the study of 
body in motion under the influence of force i.e. is the relationship 
between force and motion are considered or the effect of the force 
are studied
¦ Kinematics: It is the branch of the dynamics that deals with the 
study of body in motion without considering the force.
Force
• Force In general force is a Push or Pull, which creates motion or tends to 
create motion, destroy or tends to destroys motion.
• In engineering mechanics force is the action of one body on another.
• A force tends to move a body in the direction of its action, A force is 
characterized by its point of application, magnitude, and direction, i.e. a force 
is a vector quantity.
Units of force
The following force units are frequently used.
• Newton
° The S.l unit of force is Newton and denoted by N. which may be defined 
as 1N = 1 kg. 1 m/s2
• Dynes
° Dyne is the C.G.S unit of force. 1 Dyne = 1 g. 1 cm/s2 One Newton force 
= 105 dyne
• Pounds
° The FPS unit of force is the pound. 1 Ibf = 1 Ibm. 1ft/s2 One pound force 
= 4.448 N One dyne force = 2.248 x 10"6 lbs
Principle of transmissibility of forces
• The state of rest of motion of a rigid body is unaltered if a force acting in the 
body is replaced by another force of the same magnitude and direction but 
acting anywhere on the body along the line of action of the replaced force.
• For example the force F acting on a rigid body at point A. According to the 
principle of transmissibility of forces, this force has the same effect on the 
body as a force F applied at point B .
Free-Body Diagram:
• A diagram or sketch of the body in which the body under consideration is 
freed from the contact surface (surrounding) and all the forces acting on it 
(including reactions at contact surface) are drawn is called free body diagram. 
Free body diagram for few cases are shown in below
Steps to draw a free-body diagram:
1. Select the body (or part of a body) that you want to analyze, and draw it.
o
2. Identify all the forces and couples that are applied onto the body and draw 
them on the body. Place each force and couple at the point that it is applied.
3. Label all the forces and couples with unique labels for use during the solution 
process.
4. Add any relevant dimensions onto your picture.
Equilibrium: The concept of equilibrium Is introduced to describe a body which Is 
stationary or which is moving with a constant velocity. In statics, the concept of 
equilibrium is usually used in the analysis of a body which is stationary, or is said 
to be in the state of static equilibrium.
Particles: A particle is a body whose size does not have any effect on the results of 
mechanical analyses on it and, therefore, its dimensions can be neglected.
Rigid body: A body is formed by a group of particles. The size of a body affects the 
results of any mechanical analysis on it. A body is said to be rigid when the relative 
positions of its particles are always fixed and do not change when the body is 
acted upon by any load (whether a force or a couple).
Force System:
• When a member of forces simultaneously acting on the body, it is known as 
force system. A force system is a collection of forces acting at specified 
locations. Thus, the set of forces can be shown on any free body diagram 
makes-up a force system.
Types of system of forces
• Collinear forces:
° In this system, line of action of forces act along the same line is called 
collinear forces. For example consider a rope is being pulled by two 
players as shown in figure * •
*
F a
• Coplanar forces
° When all forces acting on the body are in the same plane the forces are 
coplanar
• Coplanar Concurrent force system
° A concurrent force system contains forces whose lines of action meet at 
same one point. Forces may be tensile (pulling) or Forces may be 
compressive (pushing)
Tvro fijQpcring % load
..Concurrent 
pom\A
1 0 I)
force* acting or rirq
1 r u n | o i n t Forces act < n g on font
• Non-Concurrent Co-Planar Forces
o A system of forces acting on the same plane but whose line of action 
does not pass through the same point is known as non concurrent
coplanar forces or system, for example, a ladder resting against a wall 
and a man is standing on the rung but not on the center of gravity.
• Coplanar parallel forces
o When the forces acting on the body are in the same plane but their line 
of actions are parallel to each other known as coplanar parallel forces 
for example forces acting on the beams and two boys are sitting on the 
sea saw.
• Non-coplanar parallel forces
o In this case all the forces are parallel to each other but not in the same 
plane, for example the force acting on the table when a book Is kept on
it.
ADDITION OF FORCES
• ADDITION OF (FORCES) BY HEAD TO TAIL RULE
o To add two or more than two vectors (forces), join the head of the first 
vector with the tail of the second vector, and join the head of the second 
vector with the tail of the third vector and so on.
° Then the resultant vector is obtained by joining the tail of the first vector 
with the head of the last vector. The magnitude and the direction of the 
resultant vector (Force) are found graphically and analytically.
• RESULTANT FORCE
° A resultant force is a single force, which produces same effect so that of 
number of forces can produce is called resultant force
COMPOSITION OF FORCES
• The process of finding out the resultant Force of given forces (components 
vector) is called composition of forces. A resultant force may be determined 
by following methods
O PARALLELOGRAM METHOD
¦ According to parallelogram method 'If two forces (vectors) are 
acting simultaneously on a particle be represented (in magnitude 
and direction) by two adjacent sides of a parallelogram, their 
resultant may represent (in magnitude and direction) by the 
diagonal of the parallelogram passing through the point.
¦ The magnitude and the direction of the resultant can be determined 
either graphically or analytically as explained below.
¦ Graphical method Let us suppose that two forces FI and F2 acting 
simultaneously on a particle as shown In the figure (a) the force F2 
makes an angle 0 with force FI
• First of all we will draw a side OA of the parallelogram In magnitude and 
direction equal to force FI with some suitable scale. Similarly draw the side 
OB of parallelogram of same scale equal to force F2, which makes an angle 6 
with force F I. Now draw sides BC and AC parallel to the sides OA and BC. 
Connect the point 0 to Point C which is the diagonal of the parallelogram
O Fi
Page 5


Equilibrium of Forces 
Basic concept
• Mechanics can be defined as the branch of physics concerned with the state 
of rest or motion of bodies that subjected to the action of forces. OR It may 
be defined as the study of forces acting on body when it is at rest or in motion 
is called mechanics.
• Mechanics can be divided into two branches.
o Statics It is the branch of mechanics that deals with the study of forces 
acting on a body in equilibrium. Either the body at rest or in uniform 
motion is called statics
° Dynamics: It is the branch of mechanics that deals with the study of 
forces on body in motion is called dynamics. It is further divided into two 
branches.
¦ Kinetics It is the branch of the dynamics which deals the study of 
body in motion under the influence of force i.e. is the relationship 
between force and motion are considered or the effect of the force 
are studied
¦ Kinematics: It is the branch of the dynamics that deals with the 
study of body in motion without considering the force.
Force
• Force In general force is a Push or Pull, which creates motion or tends to 
create motion, destroy or tends to destroys motion.
• In engineering mechanics force is the action of one body on another.
• A force tends to move a body in the direction of its action, A force is 
characterized by its point of application, magnitude, and direction, i.e. a force 
is a vector quantity.
Units of force
The following force units are frequently used.
• Newton
° The S.l unit of force is Newton and denoted by N. which may be defined 
as 1N = 1 kg. 1 m/s2
• Dynes
° Dyne is the C.G.S unit of force. 1 Dyne = 1 g. 1 cm/s2 One Newton force 
= 105 dyne
• Pounds
° The FPS unit of force is the pound. 1 Ibf = 1 Ibm. 1ft/s2 One pound force 
= 4.448 N One dyne force = 2.248 x 10"6 lbs
Principle of transmissibility of forces
• The state of rest of motion of a rigid body is unaltered if a force acting in the 
body is replaced by another force of the same magnitude and direction but 
acting anywhere on the body along the line of action of the replaced force.
• For example the force F acting on a rigid body at point A. According to the 
principle of transmissibility of forces, this force has the same effect on the 
body as a force F applied at point B .
Free-Body Diagram:
• A diagram or sketch of the body in which the body under consideration is 
freed from the contact surface (surrounding) and all the forces acting on it 
(including reactions at contact surface) are drawn is called free body diagram. 
Free body diagram for few cases are shown in below
Steps to draw a free-body diagram:
1. Select the body (or part of a body) that you want to analyze, and draw it.
o
2. Identify all the forces and couples that are applied onto the body and draw 
them on the body. Place each force and couple at the point that it is applied.
3. Label all the forces and couples with unique labels for use during the solution 
process.
4. Add any relevant dimensions onto your picture.
Equilibrium: The concept of equilibrium Is introduced to describe a body which Is 
stationary or which is moving with a constant velocity. In statics, the concept of 
equilibrium is usually used in the analysis of a body which is stationary, or is said 
to be in the state of static equilibrium.
Particles: A particle is a body whose size does not have any effect on the results of 
mechanical analyses on it and, therefore, its dimensions can be neglected.
Rigid body: A body is formed by a group of particles. The size of a body affects the 
results of any mechanical analysis on it. A body is said to be rigid when the relative 
positions of its particles are always fixed and do not change when the body is 
acted upon by any load (whether a force or a couple).
Force System:
• When a member of forces simultaneously acting on the body, it is known as 
force system. A force system is a collection of forces acting at specified 
locations. Thus, the set of forces can be shown on any free body diagram 
makes-up a force system.
Types of system of forces
• Collinear forces:
° In this system, line of action of forces act along the same line is called 
collinear forces. For example consider a rope is being pulled by two 
players as shown in figure * •
*
F a
• Coplanar forces
° When all forces acting on the body are in the same plane the forces are 
coplanar
• Coplanar Concurrent force system
° A concurrent force system contains forces whose lines of action meet at 
same one point. Forces may be tensile (pulling) or Forces may be 
compressive (pushing)
Tvro fijQpcring % load
..Concurrent 
pom\A
1 0 I)
force* acting or rirq
1 r u n | o i n t Forces act < n g on font
• Non-Concurrent Co-Planar Forces
o A system of forces acting on the same plane but whose line of action 
does not pass through the same point is known as non concurrent
coplanar forces or system, for example, a ladder resting against a wall 
and a man is standing on the rung but not on the center of gravity.
• Coplanar parallel forces
o When the forces acting on the body are in the same plane but their line 
of actions are parallel to each other known as coplanar parallel forces 
for example forces acting on the beams and two boys are sitting on the 
sea saw.
• Non-coplanar parallel forces
o In this case all the forces are parallel to each other but not in the same 
plane, for example the force acting on the table when a book Is kept on
it.
ADDITION OF FORCES
• ADDITION OF (FORCES) BY HEAD TO TAIL RULE
o To add two or more than two vectors (forces), join the head of the first 
vector with the tail of the second vector, and join the head of the second 
vector with the tail of the third vector and so on.
° Then the resultant vector is obtained by joining the tail of the first vector 
with the head of the last vector. The magnitude and the direction of the 
resultant vector (Force) are found graphically and analytically.
• RESULTANT FORCE
° A resultant force is a single force, which produces same effect so that of 
number of forces can produce is called resultant force
COMPOSITION OF FORCES
• The process of finding out the resultant Force of given forces (components 
vector) is called composition of forces. A resultant force may be determined 
by following methods
O PARALLELOGRAM METHOD
¦ According to parallelogram method 'If two forces (vectors) are 
acting simultaneously on a particle be represented (in magnitude 
and direction) by two adjacent sides of a parallelogram, their 
resultant may represent (in magnitude and direction) by the 
diagonal of the parallelogram passing through the point.
¦ The magnitude and the direction of the resultant can be determined 
either graphically or analytically as explained below.
¦ Graphical method Let us suppose that two forces FI and F2 acting 
simultaneously on a particle as shown In the figure (a) the force F2 
makes an angle 0 with force FI
• First of all we will draw a side OA of the parallelogram In magnitude and 
direction equal to force FI with some suitable scale. Similarly draw the side 
OB of parallelogram of same scale equal to force F2, which makes an angle 6 
with force F I. Now draw sides BC and AC parallel to the sides OA and BC. 
Connect the point 0 to Point C which is the diagonal of the parallelogram
O Fi
passes through the same point 0 and hence it is the resultant of the given tw | 
forces. By measurement the length of diagonal gives the magnitude of 
resultant and angle a gives the direction of the resultant as shown in fig (A)
Analytical method
• In the paralleogram OABC, from point C drop a perpendicular CD to meet OA 
at D as shown in fig (B)
• In parallelogram OABC, OA = F1 OB = F2 Angle AOB = 6
• Now consider the ACAD in which Angle CAD = 0 AC = F2
• By resolving the vector F2 we have, ,CD = F2 Sin 0 and AD = F2 Cosine 0
• Now consider AOCD .Angle DOC = a. Angle ODC = 90°
According to Pythagoras theorem ,(Hyp)2 = (per)2 + (base)2
• OC2 = DC2 + OD2 , OC2 = DC2 + (OA + AD) 2
• FR 2 = F2 Sin2 0 + (FI + F2 Cosine 0 )2
• FR 2 = F2 2 Sin2 0 + F21 + F2 2 Cos2 0 + 2 FI F2 Cosine 0.
• FR 2 = F2 2 Sin2 0 + F2 2 Cos2 0 +F21 + 2 FI F2 Cosine 0.
• FR 2 = F2 2 (Sin2 0 + Cos2 0) + F21+ 2 FI F2 Cosine 0.
• FR 2 = F2 2 (1) + F21+ 2 FI F2 Cosine 0.
• FR 2 = F2 2 + F21+ 2 FI F2 Cosine 0.
• FR 2 = F21+F2 2 + 2 FI F2 Cosine 0
• FR =V F21+F2 2 + 2 FI F2 Cosine 0.
TRIANGLE METHOD OR TRIANGLE LAW OF FORCES
• According to triangle law or method" If two forces acting simultaneously on a 
particle by represented (in magnitude and direction) by the two sides of a 
triangle taken in order their resultant is represented (in magnitude and 
direction) by the third side of the triangle taken in opposite order. OR If two 
forces are acting on a body such that they can be represented by the two 
adjacent sides of a triangle taken in the same order, then their resultant will 
be equal to the third side (enclosing side) of that triangle taken in the 
opposite order. The resultant force (vector) can be obtained graphically and 
analytically or trigonometry.
• Graphically, Now draw lines OA and AB to some convenient scale in 
magnitude equal to FI and F2.
• Join point 0 to point B the line OB will be the third side of triangle, passes 
through the same point 0 and hence it is the resultant of the given two forces.
• By measuring the length of OB gives the magnitude of resultant and angle a 
gives the direction of the resultant as shown in fig (B).