7. Mechanics of Rigid Bodies
It is a branch of science which deals with the study of bodies that do not undergo
any deformation under the application of forces.
It can be further classified into two types:
Statics: It deals with the study of the behavior of bodies or particles in the
state of rest.
Dynamics: It deals with the study of the behavior of bodies or particles in the
state of motion.
Kinematics: The forces causing the motion are not considered
Example: Train moving, moving water in a river.
Kinetics: The forces causing the motion are mainly considered.
Example: A little boy switches on the button of the toy, and the toy starts
rotating around the bar.
8. Statics
Deals with forces and its effects
when the body is at rest
Dynamics
Deals with forces and its effects when
the body is in moving condition
TrussBridge Engine
9. BASIC IDEALISATIONS
A number of ideal conditions are assumed to exist while applying the
principles of mechanics to practical problems.
Particle : A body of infinitely small volume whose
mass can be neglected.
Body: assemblage of a number of particles is known
as a body.
Rigid body: A rigid body is one in which the positions
of the constituents particles do not change under the
application of external forces.
10. Deformable body
Displacement: total linear movement made by a body to change its position from initial
position to final position moving along a particular direction.
Distance travelled: total movement made by a body to change its position from initial position
to final position.
Speed: The time rate of distance travelled is called speed (m/s).
Velocity: The time rate of displacement is called VELOCITY (m/s).
Acceleration: The time rate of change of velocity is called acceleration(M/S²).
11. Mass: The total amount of matter present in a body is known
its mass. Denoted by Kg
Weight: A body is attracted towards the earth due to
gravitation. This causes an acceleration directed towards the
centre of earth. It is denoted by g
Scalar quantity: A physical quantity which has only
magnitude is called scalar quantity.
Ex: time, mass ,volume, distance etc.,
Vector quantity: A physical quantity which has both
magnitude and direction is called vector quantity.
Ex: force, velocity, displacement, acceleration.
Continuum: A continuous distribution of molecules in a body
without intermolecular space is called continuum
Point force: A force which is acting at a fixed point known as
the point force.
12. NEWTON’S LAWS OF MOTION
Newton’s first law
Every body continues to remain in it’s state of
rest or of uniform motion along straight line
unless and until compelled by an external
agency to change that state
Force- an external agency which changes or
tends to change the state of rest or of uniform
linear motion of the body
Newton’s second law
The rate of change of momentum is directly
proportional to the applied force and takes
place in the direction of the impressed force.”
F = m . a
13.
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19. For Example: magnitude is 600N
Direction is downwards
point of application is c
Which is 2m from A
Line of action is verticle
20.
21. Types of forces
Concurrent coplanar forces
Collinear forces
Concurrent non-coplanar
Non Concurrent coplanar
(Parallel)
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24.
25.
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31.
32. Types of moment :
If tendency of a force is to rotate the body in the clockwise direction.it is
said to be clockwise moment and is taken as positive
If tendency of a force is to rotate the body in the anti-clockwise direction. it
is said to be anti-clockwise moment and is taken as negative.
33. Moment of F1 about A (MA)= +F1*d1
Moment of F2 about A (MA)= -F2*d2
Note: Moment of F1 about point A= F1*0 = 0
38. Moment of a couple about a point is given by the
algebraic sum of moment of force forming the
couple about that point.
Moment of couple about A,
MA=-Fx+ F(L+x)
= -Fx+FL+Fx
= FL
=Magnitude of force × arm of couple
40. Resolution of forces:
The process of splitting of a force into its two rectangular components(horizontal and
vertical) is known as resolution of forces.
In this figure “F” is the force which makes an angle θ with the horizontal axis, and is
resolved in to two components, namely, Fx and Fy, along x-axis and y- axis respectively.
In triangle CAD ,
Cosθ= Fx/F
Fx= F Cosθ
Sinθ = Fy/F
Fy= F Sinθ
If θ is the angle made by the force F with vertical axis, then
Cosθ= Fy/F
Fy= F Cosθ
Sinθ = Fx/F
Fx= F Sinθ
A
B C
D
θ
Fy
Fx
41. Composition of forces:
It is the process of combining a number of forces into a single force such that the net
effect produced by the single force is equal to the algebraic sum of the effects
produced by the individual forces. The single force in this case is called the resultant
forces which produces the same effect on the body as that produced by the individual
forces acting together.
∑ Fx = F4+F1 Cos θ1 – F3 Sin θ2
∑ Fy = -F2-F1 Sin θ1 – F3 Cos θ2
The magnitude of the resultant,
R = ∑ 𝑭𝒙𝟐 + ∑ 𝑭𝒚𝟐
The direction of the resultant,
Θ = 𝒕𝒂𝒏−𝟏
(
∑𝑭𝒚
∑𝑭𝒙
)
+ve
+ve
-ve
-ve
56. Methods of finding Resultant:
PARALLELOGRAM LAW:
If the two forces are acting simultaneously on a particle and away
from a particle, with the two adjacent sides of the parallelogram
representing both the magnitude and direction of forces, the
magnitude and direction of the resultant can be represented by the
diagonal of the parallelogram starting from the common point of the
two forces.
57.
58. TRIANGLE LAW OF FORCES
If two forces acting simultaneously on a particle can be represented both in magnitude
and direction by the two sides of a triangle taken in order, then the magnitude and
direction of the resultant can be represented by the third side of a triangle, taken in
opposite order.
59. Polygon law of forces
If a number of forces acting on a particle can be represented in both
magnitude and direction by the sides of the polygon taken in order , then the
resultant can be represented in magnitude and direction by the closing side of
the polygon taken in opposite order.
77. A
A barge is pulled by two tug boats. If the resultant forces exerted by the boats 25KN
directed along the axis of the barge determine 1) tension in each rope when α = 45°
2)Value of α such that tension in rope BC is minimum
