Download Coplanar Concurrent Forces

MECHANICS OF SOLIDS
Abishek yadav
130520123001
Types of Quantities
Scalar Quantities:
The Quantities which possess magnitude only are called scalar quantities
Eg: Length, Area, Mass etc.
Vector Quantities:
The Quantities which possess magnitude as well as direction are called
vector quantities
Eg: Force, Velocity , Acceleration
Resolution of vectors
The process of determining the magnitude of a vector is known as vector
resolution
The two methods of vector resolution that we will examine are:
1. Parallelogram Method
2. Trigonometric Method
Units of Measurement
Unit :
The known amount used as a reference in the measurement of a physical quantity
called an Unit
Basic Units :
The units which are used for measurement of basic or fundamental quantities (Mass,
Length, Time)
Derived Units:
All units which are used for measurement of physical quantities other than
fundamental quantities(Area, Volume ,Speed)
System of Units
There are four system of units in use :
1. Foot Pound Second system i.e, FPS system
The system of units is a scheme for measuring dimensional and material
quantities. The fundamental units are the foot for length, the pound for
weight, and the second for time
2. Centrimetre Gram Second system i.e, CGS system
It is a variant of the metric system of physical units based on centimetre as
the unit of length, grams as a unit of mass, and second as a unit of time
3. Metre, Kilogram Second system i.e, MKS system
It is a variant of the metric system of physical units based on metres as the
unit of length, kilograms as a unit of mass, and second as a unit of time
4. System of International i.e, SI system
It is a variant of the metric system of physical units based on ampere as the
unit of electric current, Kelvin as a unit of temperature, candela for luminous
intensity in addition to fundamental units of length, mass and time
Important S.I Units:
S.No
Quantity
Units
1.
Length
m
2.
Area
m2
3.
Density
Kg/m3
4.
Velocity
m/s
5.
Force
N
6.
Acceleration
m/s2
7.
Work
Nm(Joule)
8.
Power
Nm/sec –
(Watt)
9.
Energy
Nm(Joule)
10.
Pressure
N/m2
11.
Mass
Kg
12.
Weight
N
13.
Time
s
Definitions:
Space:
The dimensions of height, depth, and width within which all things exist and
move.
Time:
The indefinite continued progress of existence and events in the past,
present, and future regarded as “Time”.
Particle:
An extremely small piece of matter.
Rigid body:
Non flexible body / fixed body / stiff body
Characteristics of force :
A Force is characterised by
1.Magnitude
2.Lines of action
3.Direction
Magnitude:
Magnitude of a force is denoted by certain number of units. In SI system
of units magnitude of a force is in Newton(N).
Sometimes, magnitude of a force is also denoted by the multiples of
Newton as Kilo Newton (KN) , Mega Newton (MN),Giga Newton (GN).
1KN = 103 N
1MN = 106 N
1GN = 109 N
Line of Action :
An infinite straight line along which the force acts is called line of action
of force.
Direction :
Line of action of force is denoted by an angle with some fixed axis. This
angle with fixed axis and sense of force represents direction of force.
Sense of force (arrow head) indicates whether the force acts outwards
from a particle or towards a particle
Note : Outwards - Tensile
Towards - Compressive
System of Forces:
A body with two or more forces acting simultaneously on it constitute a
system of forces. The force system is classified is classified into subdivisions.
1. Coplanar forces
2. Non – coplanar forces
3. Collinear forces
4. Concurrent forces
5. Parallel forces
6. Like collinear coplanar forces
7. Unlike collinear coplanar forces
8. Coplanar concurrent forces
9. Coplanar non-concurrent forces
10. Non-coplanar concurrent forces
11. Non coplanar non-concurrent forces
Coplanar Forces:
In coplanar force system, all the forces act in one plane. This system is
also called as “forces in plane”.
Non – coplanar Forces:
In Non – coplanar force system, the forces do not act in one plane. This
system is also called as “forces in space”.
Collinear Forces:
The forces which acts on a common line of action are called collinear
forces. If they act in same direction, they are called “Like collinear” and if
they act in opposite direction , they are called “Unlike collinear”
Concurrent Forces :
In concurrent force system , forces intersects at an common point.
Parallel Forces :
In parallel force system ,the line of action of forces are parallel to each
other parallel forces acting in same direction are called “Like parallel
forces” and parallel forces acting in opposite direction are called “Unlike
parallel forces”.
Like collinear coplanar forces :
Forces acting in same direction , lies on a common line of action and acts in
a single plane.
Unlike collinear coplanar forces :
Forces acting in opposite direction , lies on a common line of action and
acts in a single plane.
Coplanar concurrent forces :
Forces intersects at a common point and lies in a single plane.
Coplanar non – concurrent forces :
Forces which do not intersect at a common point , but acts in one plane. They
might be either parallel or non-parallel.
Non – Coplanar concurrent forces :
Forces intersect at one point ,but their lines of action do not lie on the same
plane.
Non – Coplanar non – concurrent forces :
Forces do not intersects at one point and also their lines of action do not lie on
the same plane.
Parallelogram law of forces :
It states that, “If two forces acting simultaneously at a point , be
represented in magnitude and direction by the two adjacent sides of a
parallelogram , then the resultant of these two forces is represented in
magnitude and direction by the diagonal of that parallelogram
originating from that point”
Now to find out the magnitude of the resultant force, we require to draw a
perpendicular from C on OA produced at D. As OB & AC are parallel.
Therefore BOA = CAD = (Corresponding Angles). As OCD is a right
angled triangle therefore by Pythagoras Theorem,
Replacing the sides by their corresponding
forces, [OB = AC = P]
[By Pythagoras Theorem]
Let us take a right angled triangle CDA, and let the hypotenuse CA makes
an angle(θ) with the horizontal i.e.AD. If CA is known, the other two
sides CD & DA can be expressed in terms of CA. DA = CA cos(θ)
& CD = CA sin(θ)
Note: The side which makes an angle (θ) with the hypotenuse will be the
hypotenuse multiplied by cos(θ) and the other side will be hypotenuse
multiplied by sin(θ).
Therefore the Resultant of the two Coplanar Concurrent Forces is R, where
Now we will find the value of (α) i.e. the resultant of the two Coplanar
Concurrent Forces makes an angle(α)with the force P.
,
Now we know that
Triangular law of forces
It states that “If two forces acting at a point area represented by two
sides of a triangle, taken in order , then their resultant force is
represented by the third side taken in opposite order “
Polygon law of forces :
It states that “If number of coplanar concurrent forces are represented
in magnitude and direction by the sides of a polygon taken in an
order , then their resultant force is represented by closing side of
polygon taken in opposite order “
Polygon laws of forces (Con.)
Consider the forces F1, F2, F 3 and F4 are acting at a point O as
shown in Figure. Starting from the point O, the vector OA
represents the force F 1 in magnitude (using suitable scales) and
direction. From the tip A, draw vector AB representing the
force F2. Similarly, vector BC represents the force F3 and vector
CD represents force F4. Join the starting point O to the end point
D giving a vector OD in opposite order. Vector OD represents the
resultant force R = F1 + F2 + F 3 + F4 in magnitude and direction
as shown in Figure
From the triangle law of forces