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a home base to excellence Mata Kuliah Kode SKS : Statika : TSP – 106 : 3 SKS Hukum Newton, Vektor Pertemuan - 1 a home base to excellence • TIU : • Mahasiswa dapat menjelaskan tentang prinsip keseimbangan, uraian, dan penjumlahan gaya. • TIK : • Mahasiswa dapat menjelaskan konsep gaya a home base to excellence • Sub Pokok Bahasan : • Definisi • Uraian dan Penjumlahan • Text Book : • Hibbeler, R.C. (2004). Statics and Mechanics of Materials SI Edition. • Hibbeler, R.C. (2010). Structural Analysis. 8th edition. Prentice Hall. ISBN : 978-0-13-257053-4 • Meriam, J.L., Kraige,L.G., (2006), Engineering Mechanics - Statics. 6th edition. John Wiley & Sons, Inc. ISBN : 978-0471739326 Bobot Penilaian : Tugas Ujian Tengah Semester Ujian Akhir Semester : 30 % : 30 % : 40% a home base to excellence Mechanics Mekanika adalah sebuah divisi dari Ilmu Pengetahuan yang mempelajari perilaku sebuah objek akibat beban yang bekerja tehadapnya. Mechanics is the branch of the physical sciences which deals with the state of rest or motion of bodies that are subjected to the action of forces. a home base to excellence Subdivisions of Mechanics Mechanics Deformable Bodies Statics (At Rest) Rigid Bodies Fluids Dynamics (In Motion) a home base to excellence 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 a home base to excellence • 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 a home base to excellence • Third Law “The mutual forces of action and reaction between two particles are equal in magnitude, opposite in direction and collinear in orientation”. F -F a home base to excellence Newton’s Law of Gravitational Attraction A law governing the gravitational attraction between any two particles is mathematically stated as: F = G [m1 Where m2 / r2] F = force of gravitation between the two particles G = A universal constant of gravitation; (66.73x10-12 m3/kg s2) m1 and m2 = mass of each of the two particles r = the distance between the two particles a home base to excellence 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 a home base to excellence 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). a home base to excellence Conversion Factors Force; Mass; Length; 1 lb = 4.4482 N slug = 14.5938 kg ft = 0.304 m a home base to excellence 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 = 0.000 001 nano = η = 10-9 = 0.000 000 001 a home base to excellence 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 a home base to excellence Vector • A quantity by its magnitude and direction • Examples include force, moment, and displacement a home base to excellence 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 Head A Tail Line of Action a home base to excellence 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 1.5 A -A a home base to excellence Vector Addition • Vectors are added according to the parallelogram law • The resultant R is the diagonal of the parallelogram A B A A R =A+ B B R =A+ B R =A+ B B A B • If two vectors are co-linear (both have the same line of action), they are added algebraically R =A+ B A B a home base to excellence Vector Subtraction • The resultant is the difference between vectors A and B A -B R B -B A R A a home base to excellence 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). b B R A a a home base to excellence Analysis of Problems • • • • Two procedures to be followed: Parallelogram law Trigonometry sine and/or cosine laws may be used a home base to excellence Sine Law A B C sin a sin b sin c C b a A c Cosine Law C A 2 B 2 2 AB cos c B a home base to excellence Example 1 • The screw eye in figure is subjected to two forces F1 and F2. Determine the magnitude and direction of the resultant force a home base to excellence Using Parallelogram Law 150 N 65o FR 10o 180o-65o = 115o 100 N 90o-25o = 65o 15o FR 100 2 150 2 2100150 cos 115o 212,6 N sine law : 150 212 ,6 sin sin 115o sin 150 sin 115o 39 ,8o 212 ,6 Direction, f = 15 + = 54,8o from horizontal axis f = 54,8o a home base to excellence Example 2 • Resolve the 1000-N force acting on the pipe, into components in the : (a) x and y direction; (b) x’ and y direction a home base to excellence y y Fy 50o Fy Fy 70o 40o x Fx Fx’ 50o Fy 40o 30o Fx 1000 Fx 884 ,6 N sin 50o sin 60o 40o Fx Fx 1000 cos 40o 766 N Fy 1000 sin 40o 643 N 60o Fx’ x' Fy sin 70 o 1000 Fy 1085 N sin 60o a home base to excellence Example 3 • The ring show in figure is subjected to two forces F1 and F2. If it is required that the resultant force have a magnitude of 1 kN and be directed vertically downward, determine (a) the magnitudes of F1 and F2 provided = 30o, (b) the magnitude of F1 and F2 if F2 is to be minimum a home base to excellence (a) F2 30o 20o F 1 F2 30o 130o 130o F1 20o 30o 20o F1 1000 F1 653 N sin 30o sin 130o F2 1000 F2 446 N sin 20o sin 130o a home base to excellence (b) F2 70o • If is not specified, then by the vector triangle, F2 may be added to F1 in various ways to yield the resultant 1000 N force. • In particular, the minimum length or magnitude of F2 will occur when its line of action is perpendicular to F1. • Hence, when = 90o – 20o = 70o, F2 is minimum F1 1000 sin 70o 940 N F1 F2 1000 cos 70o 342 N 20o