Chapter 1
General Principles
Engineering Mechanics: Statics
Chapter Objectives
To provide an introduction to the basic quantities and
idealizations of mechanics.
To give a statement of Newtons Laws of Motion and
Gravitation.
To review the principles fo
2.7 Position Vectors
x,y,z Coordinates
- Right-handed coordinate system
- Positive z axis points upwards, measuring the
height of an object or the altitude of a point
- Points are measured relative to the origin, O.
2.7 Position Vectors
x,y,z Coordinate
2.5 Cartesian Vectors
Right-Handed Coordinate
System
A rectangular or Cartesian coordinate system is
said to be right-handed provided:
- Thumb of right hand points
in the direction of the positive
z axis when the right-hand
fingers are curled about this
a
2.6 Addition and Subtraction of Cartesian Vectors
Example
Given: A = Axi + Ayj + AZk
and B = Bxi + Byj + BZk
Vector Addition
Resultant R = A + B
= (Ax + Bx)i + (Ay + By )j + (AZ + BZ) k
Vector Substraction
Resultant R = A - B
= (Ax - Bx)i + (Ay - By )j +
2.4 Addition of a System of Coplanar Forces
For resultant of two or more forces:
Find the components of the forces in the specified axes
Add them algebraically
Form the resultant
In this subject, we resolve each force into rectangular
forces along the
2.8 Force Vector Directed along a Line
In 3D problems, direction of F is specified by 2
points, through which its line of action lies
F can be formulated as a Cartesian vector
F = F u = F (r/r)
Note that F has units of
forces (N) unlike r, with
units of
2.9 Dot
Product
Dot product of vectors A and B is written as AB (Read A dot B)
Define the magnitudes of A and B and the angle between their
tails
AB = AB cos
where 0 180
Referred to as scalar
product of vectors as
result is a scalar
2.9 Dot
Product
La