1. Static and Dynamic Chapter 1 : Introduction

2. Introduction to static
Mechanics can be defined as that branch of the physical sciences concern with the state of rest or motion of bodies that are subjected to the action forces.
Basic mechanics is composed of two principal areas:
Static
Deal with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity
Dynamic
Concern with the accelerated motion of bodies.

3. Fundamental concept Basic terms Length Space
needed to locate the position of a point in space and thereby describe the size of a physical system.
once a standard unit of length is defined, one can then quantitatively define distances and geometric properties of a body as multiples of the unit length.
Space
the geometry region occupied by bodies whose positions are described by linear and angular measurement relative to a coordinate system.
for three-dimensional problems three independent coordinates are needed.
for two-dimensional problems only two coordinates will required.

4. Time
the measure of the succession of event and is a basic quantity in dynamics for three-dimensional problems three independent coordinates are needed.
not directly involved in the analysis of static problems
Mass
a measure of the inertia of a body, which is its resistance to a change of velocity.
can be regarded as the quantity of matter in a body.
the property of every body by which it experiences mutual attraction to other bodies.

5. Force Particle the action of one body on another.
tends to move a body in the direction of its action.
the action of a force is characterized by its magnitude, by the direction of its action, and by its points of application.
Particle
has a mass, but a size that can be neglected.
Example: the size of the earth is significant compared to the size of its orbit, therefore the earth can be modeled as a particle when studying its orbital motion.
when the is idealized as a particle, the principles of mechanics reduce to a rather simplified form since the geometry of the body will not involved in the analysis of the problem.

6. Rigid body Conversion factors
can be considered as 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.
as the result, the material properties of any that is assumed to be rigid will not have to considered when analyzing the forces acting on the body.
in most cases the actual deformation occurring in structures, machines, mechanisms, and the like are relatively small, and the rigid-body assumption is suitable for analysis.
Conversion factors

7. Newton’s three laws of motion
First law
A body at rest will remain at rest, and a body in motion will remain at a uniform speed in a straight line, unless it is acted on by an imbalanced force. F2 F1 F3 v

8. Second Law
A particle acted upon by an unbalanced force, F experiences acceleration, a that has the same direction as the force and magnitude that is proportional to the force
If F is applied t a particle of mass, m, this law may be expressed mathematically as
Accelerated motion
F = ma F a

9. Third Law Action - Reaction
For every action, there is an equal but opposite reaction..
Action - Reaction F R
force of A on B
force of B on A

10. Which person in this ring will be harder to move
Which person in this ring will be harder to move? The sumo wrestler or the little boy?

11. Newton’s law of gravitational attraction
Gravitational attraction between any two particles is gover after formulating Law of motion
Where
F = force of gravitation between the two particles
G = universal constant of gravitation; according to experimental evidence,
m1,m2= mass of each of the two particle
r = distance between the two particles

12. Weight
What is the different between Mass and Weight?

13. The relationship between mass and weight can be expressed
develop an approximate expression for finding the weight, W of a particle having a mass m1 = m
Assume the earth to be a non-rotating sphere of constant density and having a mass m2 = Me, then if r is the distance between the earth’s center and the particle, we have
Letting, yields
g = m/s2 so

15. Units of measurement Mechanic deal with four fundamental quantities
Length
Mass
Force
Time
Units and symbols in Two system
SI Units
U.S Customary Units
Quantity
Dimensional Symbol
Unit
Symbol
Mass M
kilogram kg
slug -
Length L
meter m
foot ft
Time T
second s
sec
Force F
newton N
pound lb

16. SI units International system of units Newton (N) 1kg Force?
Force in Newtons(N) is derived from F=ma
Solution
1kg
Force?
(g=9.81m/s2)

17. US Customary The unit of mass, called a slug, is derived from F = ma.
Newton (N)
Force in Newtons(N) is derived from F=ma
Solution
1slug
mass?
(g=32.2 ft/sec2)

18. Conversion factors Terms U.S Customary S.I metric unit Length 1 in.
1 ft
1 mile
= 25.4 mm
= m
= 1609 m
Area
1 in.2
1 ft2
1 sq mile
= 6.45 cm2
= m2
= 2.59 km2
Volume
1 in3
1 ft3
= cm3
= m3
Capacity
1 qt
1 gal
= I
= I
Mass
1 Ib
1 slug
= kg
= 14.6 kg
Velocity
1 in/sec
1 ft/min
I mph
= m/s
= m/s
= m/s = 1.61 km/h
Acceleration
1 in./sec2
1 ft/sec2
= m/s2
= m/s2
Force
1 poundal
= N
= N
Pressure
1 Ib/in.2
1 Ib/ft2
= kPa
= kPa
Energy
1 ft-Ib
1 Btu
1 hp-hr
1 watt-hr
= J
= kJ
= MJ
= 3.6 kJ
Power
1 hp
0.746 kW

19. Example 1.1
Convert 2 km/h to m/s and ft/s
Solution
Since 1 km = 1000 m and 1 h = 3600 s, the factors of conversion are arranged in the following order, so that a cancellation of the units can be applied:

20. Mathematic required Algebraic equations with one unknown
Simultaneous equations with two unknowns
Quadratic equations
Trigonometry functions of a right – angle triangle
Sine law and cosine law as applied to non-right angle triangles.
Geometry

21. Algebraic equations with one unknown
Example 1.2
Solve for x in the equation
Simultaneous equation
Example 1.3
Solve the simultaneous equations.

22. Quadratic equations
Example 1.4
Solve for x in equation

23. Trigonometry functions of a right – angle triangle
Sine law and cosine law as applied to non-right angle triangles
Triangles that are not right – angle triangles  x r y g a b A B C

24. Side divided by the sine of the angle opposite the side
Right – angle triangle where g = 90o g a b A B C g a b A B C

25. Geometry opposite angles are equal when two straight lines intersect
supplementary angles total 1800 d b c a
a = b
c = d b a
a + b = 1800

26. complementary angles total 900
a straight line intersection two parallel lines produces the following equal angles: b a
a + b = 900 d b c a
a = b
c = d or
a = b = c = d

27. the sum of the interior angles of any triangles equals to 180o
similar triangles have the same shape
If AB = 4, AC = 6 and DB = 10, then by proportion b c a
a + b + c = 1800  D A B C E

28. circle equations:
Angle  is defined as one radian when a length of 1 radius is measured on the circumference.