This document discusses concepts in engineering mechanics including derived laws of forces, units of measurement, and systems of forces. It defines the triangle law and polygon law of forces, which describe the resultant force of multiple concurrent forces. Fundamental and derived units used in mechanics like the MKS and SI systems are also outlined. Finally, different types of force systems are defined, such as collinear, coplanar, and non-coplanar forces that can be concurrent, parallel or non-parallel. Idealizations commonly made in mechanics like treating bodies as rigid or applying point forces are also mentioned.

1. Shaik Nayeem
Engineering Mechanics
Introduction: Derived Laws and System of
forces
1
Shaik Nayeem

2. • Derived Laws
• Triangle Law of Forces
• Polygon law of forces
• Units in Mechanics
• System of Forces
• Idealisations in Mechanics
Contents

3. Derived Laws
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Derived
Laws
Triangle law
of forces
Polygon law
of forces

4. Triangle Law of Forces
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 It is derived from the parallelogram law of forces
 Triangle law of forces is
states that “if two forces
are acting on a body are
represented one after
another by the sides of the
triangle , their resultant is
represented by the closing
side of triangle taken from
first point to the last
point”

5. Polygon law of forces
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 States that “if number of concurrent forces acting
simultaneously on a body are represented in
magnitude and direction by the sides of the
polygon, taken in order, then the resultant is
represented in magnitude and direction by the
closing side of the polygon , taken from first point
to last point”

6. Polygon law of forces(Cont…)
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7. Units in Mechanics
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Fundamental
Units
Length(L)
Mass(M)
Time(S)
Derived Units:
 Sometimes, the units are also expressed in other
units( which are derived from fundamental units)
known as derived units ex: units of area, velocity,
acceleration, pressure etc

8. Units in Mechanics (Cont…)
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SystemofUnits
Meter-Kilogramme-Second (MKS) System
Centimetre- Gramme –Second (CGS) System
Foot- Pound- Second (FPS) System

9. Units in Mechanics (Cont…)
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Some quantities are expressed in MKS units as:

10. Units in Mechanics(Cont…)
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 Another type of system of unit is SI( International
System) units
 SI:- Meter-Kilogramme – Second
 The difference between MKS and SI is mainly in
selecting the unit of force

11. Units in Mechanics(Cont…)
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 Force ∝ 𝑀𝑎𝑠𝑠 𝑋 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
 Force = k X Mass X Acceleration
 In SI units: a=1 m /𝒔𝒆𝒄 𝟐
Force units are: kg-m/𝑠𝑒𝑐2
is called “Newton”
 In MKS units: a=g = 9.81 m /𝒔𝒆𝒄 𝟐
Force in MKS units: kg-wt is called kilogramme
weight
 1kg-wt = 9.81 Newton

12. Units in Mechanics
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Prefixes and Symbols of multiplying factors in SI:

13. System of Forces
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SystemofForces
Collinear Forces
Coplanar Parallel Forces
Coplanar like parallel Forces
Coplanar concurrent Forces
Coplanar non- concurrent Forces
Non-coplanar parallel forces
Non-coplanar concurrent forces
Non-coplanar non-concurrent forces

14. Collinear Forces
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Collinear forces are forces which have
a common line of action, i.e. the line
of action of the forces lie along a
single straight line.

15. Coplanar Parallel Forces
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All forces are
parallel to each
other and lie in
single plane

16. Coplanar like parallel Forces
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All forces are
parallel to each
other, lie in
single plane and
are acting in the
same direction

17. Coplanar concurrent Forces
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Line of action of all
forces pass through
a single point and
forces lie in the
same plane
F1
F3
F2

18. Coplanar non- concurrent Forces
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All forces do not
meet at a point,
but lie in a
single plane

19. Non-coplanar parallel forces
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All the forces are
parallel to each
other, but not in
same plane

20. Non-coplanar concurrent forces
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All forces do not
lie in the same
plane, but their
lines of action
pass through a
single point

21. Non-coplanar non-concurrent forces
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All forces do not
lie in the same
plane and their
lines of action do
not pass through
a single point

22. Idealisations in Mechanics
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Assumptions in
Mechanics
The body is
rigid
The body
can be
treated as
continuum
It may be
treated as a
particleApplied force
can be
treated as
point force
Support
conditions
are idealized

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Thank You
Shaik Nayeem