1. CE Statics
Lecture 1

2. Contents Basic Principles (Chapter 1) Force Vectors (Chapter 2)
Mechanics
Basic Quantities
Newton’s Laws of Motion
Newton’s Law of Gravitational Attraction
Units of Measurement
Force Vectors (Chapter 2)
Scalars and Vectors

3. Mechanics
Mechanics is the branch of the physical sciences concerned with the state of rest or motion of bodies that are subjected to the action of forces.

4. Subdivisions of Mechanics
Deformable Bodies
Rigid Bodies
Fluids
Statics
(At Rest)
Dynamics
(In Motion)

5. Definition of Some Basic Quantities
Length: is needed to locate the position of a point in space and thereby describes the size of a physical system.
Time: is conceived as a succession of events.
Mass: is a property of matter by which we can compare the action of one body with that of another. This property manifests itself as a gravitational attraction between two bodies and provides a quantitative measure of the resistance of matter to a change in velocity.
Force: is considered as a “push” or “pull” exerted by one body on another and it is characterized by its magnitude, direction, and point of application.
Particle: A particle has a mass, but has a size that can be neglected.
Rigid-Body: is a combination of a large number of particles in which all the particles remain at a fixed distance from one another both before and after applying a load.
Concentrated Force: A concentrated force represents the effect of a loading which is assumed to act at a point on a body.

6. Newton’s Three Laws of Motion
First Law
“A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided the particle IS NOT subjected to an unbalanced external force”
Balanced Forces
Particle at Rest Particle in Motion
(v=0, a=0) (v>0, a=0)
Stay at rest Stay in motion

7. Second Law
“A particle acted upon by an unbalanced force (F) experiences an acceleration ( a ) that has the same direction as the force and a magnitude that is directly proportional to the force”. If ( F ) is applied to a particle of mass (m), this law may be expressed mathematically as:
F = ma

8. Third Law
“The mutual forces of action and reaction between two particles are equal in magnitude, opposite in direction and collinear in orientation”.

9. Newton’s Law of Gravitational Attraction
A law governing the gravitational attraction between any two particles is mathematically stated as:
F = G [m1  m2 / r2]
Where F = force of gravitation between the two particles
G = A universal constant of gravitation; (66.73x m3/kg s2)
m1 and m2 = mass of each of the two particles
r = the distance between the two particles

10. Weight
Weight is the gravitational force between the earth and the particle. If we assume that:
W = weight of the particle
m = m1 = is the mass of the particle
m2 = is the mass of the earth
r = is the distance between the earth’s center and the particle
Then:
W = G [m  m2 / r2]
Letting:
g = G  m2 / r2
Therefore, from the second law of motion ( F = ma ):
W = mg
Where
g = the acceleration due to gravity

11. Units of Measurements SI Units
SI is known as the International System of Units where Length is in meters (m), time is in seconds (s), and mass is in kilograms (kg) and force is in Newton (N) (1 Newton is the force required to give 1 kilogram of mass an acceleration of 1 m/s2).

12. US Customary System of Units (FPS)
FPS is the system of units where length is in feet (ft), time is in seconds (s), and force is in pounds (lb). The unit mass is called a slug (1 pound is the force required to give one slug of mass an acceleration of 1 ft/s2).

13. Conversion Factors
Force; 1 lb = N
Mass; slug = kg
Length; ft = m

14. Prefixes
giga = G = 109 = 1,000,000,000
mega = M = 106 = 1,000,000
kilo = k = 103 = 1,000
milli = m = 10-3 = 0.001
micro = μ = 10-6 =
nano = η = 10-9 =

15. FORCE VECTORS Scalars and Vectors Scalar
A quantity identified by positive or negative number.
It is characterized by its magnitude only
Elementary algebra is used when mathematical operations are involved
Examples include mass, length, and volume
Symbolized in Italic Type

16. Vector
A quantity by its magnitude and direction
Examples include force, moment, and displacement
Symbolized in boldface type

17. Graphical Representation of a Vector
Vectors are represented by ARROWS
Magnitude is represented by the length of the arrow
Direction is defined by 
Vector A is written as A
Line of Action 
Head A
Tail