Chapter one
A. Lecturer Saddam K. Kwais
Introduction to statics
1-1 What Is Mechanics?
Mechanics can be defined as that science which describes and predicts the conditions
of rest or motion of bodies under the action of forces.
Mechanics
Rigid bodies
Statics
Deformable
bodies
Dynamics
Fluid
Compresible
Incompresible
Statics deals with bodies at rest or moving with acceleration equal is zero.
Dynamics deals with bodies at motion where acceleration ≠ 0.
1/2 Fundamental Concepts and Applications
The study of elementary mechanics rests on six fundamental principles based on
experimental evidence.
1. The parallelogram law for the addition of forces: This states that two forces
acting on a particle may be replaced by a single force , called their resultant,
obtained by drawing the diagonal of the parallelogram which has sides equal to
the given forces.
2. The principles of transmissibility: This states that the conditions of equilibrium
or of motion of a rigid body will remain unchanged if a force acting at a given
point of the rigid body is replaced by a force of the same magnitude and same
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Chapter one
A. Lecturer Saddam K. Kwais
Introduction to statics
direction, but acting at different point. Provided that the two forces have the
line of action.
3. Newton's three fundamental laws:
i.
First law
If the resultant force acting on a particle is zero, the particle remain at
rest (if originally at rest) or will move with constant speed in a straight
line (if originally is motion).
ii.
Second law
If the resultant force acting on a particle is not zero, the particle will
have an acceleration proportional to the magnitude of the resultant and
in the direction of this resultant force.
= . (1.1)
= . , = . , = . iii.
Third law
The forces of action and reaction between bodies in contact have the
same magnitude, same line of action, and opposite sense.
4. Newton's law of gravitation:
This states that two particles of mass M and m are mutually attracted with
equal and opposite forces F and –F Fig. (1-1) of magnitude F given by the
formula
= .
. (1.2)
Where
F = the mutual force of attraction between two particles
G = universal constant called the constant of gravitation.
M, m = the masses of the two particles
r = distance between the two particles.
The magnitude W of the weight of a particle of mass m may be expressed
as:
2
Chapter one
A. Lecturer Saddam K. Kwais
Introduction to statics
= . (1.3)
m
r
F
-F
M
Fig. (1-1)
1/3 System of Units
System of Units
International
System of Units
(SI Units)
U.S. Customary
Units
In mechanics we use four fundamental quantities called dimensions. These are length,
mass, force, and time. The four fundamental dimensions and their units and symbols
in the two systems are summarized in the following table.
SI UNITS
U.S. CUSTOMARY
UNITS
Dimensional
Quantity
Symbol
Unit
Symbol
unit
symbol
Length
L
meter
m
foot
ft
Mass
M
Kilogram
kg
slug
-
Time
T
Second
s
second
sec
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Chapter one
Force
A. Lecturer Saddam K. Kwais
F
Newton
N
Introduction to statics
Pound
Ib
International system of unit
The unit of force is a derived unit. It is called the Newton (N) and is defined as the
force which gives an acceleration of 1 m/s2 to a mass 1 kg Fig. (1-2) from Eq. (1.1)
we write:
= (1). (1 ⁄ ) = 1. ⁄ (1.4)
a =1 m/s2
m = 1 kg
F =1 N
Fig. (1.2)
The weight of the body, or the force of gravity exerted on the body, should, like any
other force, be expressed in Newton. From Eq. (1.3) it follows that the weight of a
body of mass 1 kg Fig. (1-3) is
= . = (1). (9.81 ⁄ ) = 9.81(1.5)
m = 1 kg
a =9.81 m/s2
W =9.81 N
Fig. (1.3)
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Chapter one
A. Lecturer Saddam K. Kwais
Introduction to statics
Exponential Form
Prefix
SI Symbol
109
106
103
giga
mega
kilo
G
M
k
10-3
10-6
10-9
milli
micro
nano
m
µ
n
Multiple
1 000 000 000
1 000 000
1 000
Submultiples'
0.001
0.000 001
0.000 000 001
Units of Length
1dm = 0.1 m = 10-1 m
1cm = 0.01 m = 10-2 m
1mm = 0.001 m = 10-3 m
Units of Area
decimeter
centimeter
millimeter
1dm2 = (1dm)2 = (0.1 m)2 = 10-2 m2
1cm2 = (1cm)2 = (0.01 m)2 = 10-4 m2
1mm2 = (1mm)2 = (0.001 m)2= 10-6 m
Units of Volume
square Decimeter
square Centimeter
square Millimeter
1dm3 = (1dm)3 = (0.1 m)3 = 10-3 m3
1cm3 = (1cm)3 = (0.01 m)3 = 10-6 m3
1mm3 = (1mm)3 = (0.001 m)3= 10-9 m3
Cubic Decimeter
Cubic Centimeter
Cubic Millimeter
U.S. Customary unit
The unit of mass is a slug can be derived from the equation F = m.a after substituting
1 Ib and 1 ft/s2 for F and a respectively Fig. (1-4). We write
F = m.a
1 Ib = (1 slug). (1 ft/s2)
And obtain
1 = 1 !
= 1 !. ⁄"# (1.6)
1"#⁄
a =1 ft/s2
m = 1 slug
(=1Ib.s2/ft)
Fig. (1.4)
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F =1 Ib
Chapter one
A. Lecturer Saddam K. Kwais
Introduction to statics
Other U.S. Customary units
mile (mi) = 5280 ft
inch (in) = (1/12) ft
kilopound (kip) = 1000Ib
Note: acceleration of gravity in U.S. Customary unit (g = 32.2 ft/s2)
1/4 Conversion from one system of unit to another
Units of Length
1"# = 0.3048(1.7)
1 mi = 5280 ft = 5280 (0.3048) = 1609 m
1' = 1.609(1.8)
1 in = (1/12) ft = (1/12) (0.3048) = 0.0254 m
1'( = 25.4 = 2.54)(1.9)
Units of Force
1*+(, = 0.4536(1.10)
According to the equation (1.3) W=m.g
1 Ib = (0.4536 kg). (9.81 m/s2) = 4.448 kg. m/s2
1 ! = 4.448(1.11)
Units of Mass
1 slug = 1 Ib . 1 s2/ft = (1 Ib)/(1ft/s2) = (4.448 N)/(0.3048 m/s2) = 14.59 N.s2/m
1 = 14.59(1.12)
Example No.(1) : Converts the moment of force (M = 47 Ib. in) into SI Units.
Solution : we use formulas (1.9) and (1.11) and write:
= 47 !. '( = 47(4.448). (25.4)
= 5310. = 5.31. -(.
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Chapter one
A. Lecturer Saddam K. Kwais
Introduction to statics
Example No.(2) : Converts the moment of force (M = 40 N. m) into U.S. Customary
Units.
Solution : we use formulas (1.7) and (1.11) and write:
= 40. = (40. ).
1 !
1"#
/..
/
4.448
0.3048
= 29.5 !. "#-(.
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