Static and Dynamic Chapter 1 Introduction Introduction to

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 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 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 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. F 1 F 2 v F 3

• 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 • F = ma F a Accelerated motion

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

• 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, m 1, m 2= 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 m 1 = m � Assume the earth to be a non-rotating sphere of constant density and having a mass m 2 = Me, then if r is the distance between the earth’s center and the particle, we have • Letting, g = 9. 807 m/s 2 so yields

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

• SI units • International system of units • Newton (N) • Force in Newtons(N) is derived from F=ma 1 kg Force? • Solution (g=9. 81 m/s 2)

• 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 1 slug • Solution mass? (g=32. 2 ft/sec 2)

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 ft 2 1 sq mile = 6. 45 cm 2 = 0. 093 m 2 = 2. 59 km 2 Volume 1 in 3 1 ft 3 = 16. 39 cm 3 = 0. 0283 m 3 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. /sec 2 1 ft/sec 2 =0. 0254 m/s 2 = 0. 3048 m/s 2 Force 1 Ib 1 poundal = 4. 448 N = 0. 138 N Pressure 1 Ib/in. 2 1 Ib/ft 2 = 6. 895 k. Pa = 47. 88 k. Pa Energy 1 ft-Ib 1 Btu 1 hp-hr 1 watt-hr = 1. 356 J = 1. 055 k. J = 2. 685 MJ = 3. 6 k. J Power 1 hp 0. 746 k. W

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 r y x • Sine law and cosine law as applied to non-right angle triangles • Triangles that are not right – angle triangles b A C g a B

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

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

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

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

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