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CE 201 - Statics
Lecture 2
Contents
Vector Operations– Multiplication and Division of Vectors– Addition of Vectors– Subtraction of vectors– Resolution of a Vector
Vector Addition of Forces Analysis of Problems
Vector Operations
Multiplication and Division of a Vector by a Scalar Vector A Scalar a A a = aA Magnitude of aA Direction of A if a is positive (+) Direction of –A (opposite) if a is negative (-)
A
-A
1.5 A
Vector Addition
Vectors are added according to the parallelogram law The resultant R is the diagonal of the parallelogram
If two vectors are co-linear (both have the same line of action), they are added algebraically
A
B
A
B
R = A + BA
B
R = A + B BA
R = A + B
A B
R = A + B
Vector Subtraction
The resultant is the difference between vectors A and B
A
B -B
AR
R
A-B
Resolution of a Vector
If lines of action are known, the resultant R can be resolved into two components acting along those lines (i.e. a and b).
a
b
A
B R
Vector addition of Forces
Force!Is it vector OR scalar? Why?
The two common problems encountered in STATICS are:1. Finding the RESULTANT (by knowing the COMPONENTS).
OR2. Resolving a FORCE into its COMPONENTS (by applying the
parallelogram law).
If more than two forces are to be added!!Apply the same law more than once depending on the number of forces.
3 Forces
F1
F2
F3
R1=F1+F2
R2=R1+F3
Four Forces
F1
F2
F3
R1=F1+F2
R2=R1+F3
F4R3=R2+F4
Analysis of Problems
Two procedures to be followed: Parallelogram law Trigonometry sine and/or cosine laws may be used
Sine Law
A/sin (a) = B/sin (b) = C/sin (c)
a
A B
bC
c
Cosine Law
C = A2+B2-2ABcos (c)
a
A B
bC
c
Examples
2.1 2.2 2.3 2.4 Problem 2-8 Problem 2-25