Static and Dynamic Chapter 1 : Introduction

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.

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.

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.

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.

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

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

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

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

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?

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

Weight What is the different between Mass and Weight?

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 = 9.807 m/s2 so

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

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)

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)

Conversion factors Terms U.S Customary S.I metric unit Length 1 in. 1 ft 1 mile = 25.4 mm = 0.3048 m = 1609 m Area 1 in.2 1 ft2 1 sq mile = 6.45 cm2 = 0.093 m2 = 2.59 km2 Volume 1 in3 1 ft3 = 16.39 cm3 = 0.0283 m3 Capacity 1 qt 1 gal = 1.136 I = 4.546 I Mass 1 Ib 1 slug = 0.454 kg = 14.6 kg Velocity 1 in/sec 1 ft/min I mph = 0.0254 m/s = 0.3048 m/s = 0.447 m/s = 1.61 km/h Acceleration 1 in./sec2 1 ft/sec2 =0.0254 m/s2 = 0.3048 m/s2 Force 1 poundal = 4.448 N = 0.138 N Pressure 1 Ib/in.2 1 Ib/ft2 = 6.895 kPa = 47.88 kPa Energy 1 ft-Ib 1 Btu 1 hp-hr 1 watt-hr = 1.356 J = 1.055 kJ = 2.685 MJ = 3.6 kJ Power 1 hp 0.746 kW

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:

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

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

Quadratic equations Example 1.4 Solve for x in equation

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

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

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

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

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

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