Hukum Newton, Vektor

Transcription

1 Mata Kuliah : Statika Kde : TSP 106 SKS : 3 SKS Hukum Newtn, Vektr Pertemuan - 1

2 TIU : Mahasiswa dapat menjelaskan tentang prinsip keseimbangan, uraian, dan penjumlahan gaya. TIK : Mahasiswa dapat menjelaskan knsep gaya

3 Sub Pkk Bahasan : Definisi Uraian dan Penjumlahan Text Bk : Hibbeler, R.C. (2004). Statics and Mechanics f Materials SI Editin. Hibbeler, R.C. (2010). Structural Analysis. 8th editin. Prentice Hall. ISBN : Meriam, J.L., Kraige,L.G., (2006), Engineering Mechanics - Statics. 6th editin. Jhn Wiley & Sns, Inc. ISBN : Bbt Penilaian : Tugas : 30 % Ujian Tengah Semester : 30 % Ujian Akhir Semester : 40%

4 Mechanics Mekanika adalah sebuah divisi dari Ilmu Pengetahuan yang mempelajari perilaku sebuah bjek akibat beban yang bekerja tehadapnya. Mechanics is the branch f the physical sciences which deals with the state f rest r mtin f bdies that are subjected t the actin f frces.

5 Subdivisins f Mechanics Mechanics Defrmable Bdies Rigid Bdies Fluids Statics (At Rest) Dynamics (In Mtin)

6 First Law a hme base t excellence Newtn s Three Laws f Mtin A particle riginally at rest, r mving in a straight line with cnstant velcity, will remain in this state prvided the particle IS NOT subjected t an unbalanced external frce Balanced Frces Particle at Rest Particle in Mtin (v=0, a=0) (v>0, a=0) Stay at rest Stay in mtin

7 Secnd Law A particle acted upn by an unbalanced frce (F) experiences an acceleratin ( a ) that has the same directin as the frce and a magnitude that is directly prprtinal t the frce. If ( F ) is applied t a particle f mass (m), this law may be expressed mathematically as: F = ma

8 Third Law The mutual frces f actin and reactin between tw particles are equal in magnitude, ppsite in directin and cllinear in rientatin. F -F

9 Newtn s Law f Gravitatinal Attractin A law gverning the gravitatinal attractin between any tw particles is mathematically stated as: F = G [m 1 m 2 / r 2 ] Where F = frce f gravitatin between the tw particles G = A universal cnstant f gravitatin; (66.73x10-12 m 3 /kg s 2 ) m 1 and m 2 = mass f each f the tw particles r = the distance between the tw particles

10 Weight Weight is the gravitatinal frce between the earth and the particle. If we assume that: W = weight f the particle m = m 1 = is the mass f the particle m 2 = is the mass f the earth r = is the distance between the earth s center and the particle Then: W = G [m m 2 / r 2 ] Letting: g = G m 2 / r 2 Therefre, frm the secnd law f mtin ( F = ma ): W = mg Where g = the acceleratin due t gravity

11 Units f Measurements SI Units SI is knwn as the Internatinal System f Units where Length is in meters (m), time is in secnds (s), and mass is in kilgrams (kg) and frce is in Newtn (N) (1 Newtn is the frce required t give 1 kilgram f mass an acceleratin f 1 m/s 2 ).

12 Cnversin Factrs Frce; Mass; Length; 1 lb = N slug = kg ft = m

13 Prefixes giga = G = 10 9 = 1,000,000,000 mega = M = 10 6 = 1,000,000 kil = k = 10 3 = 1,000 milli = m = 10-3 = micr = μ = 10-6 = nan = η = 10-9 =

14 FORCE VECTORS Scalars and Vectrs Scalar A quantity identified by psitive r negative number. It is characterized by its magnitude nly Elementary algebra is used when mathematical peratins are invlved Examples include mass, length, and vlume

15 Vectr A quantity by its magnitude and directin Examples include frce, mment, and displacement

16 Graphical Representatin f a Vectr Vectrs are represented by ARROWS Magnitude is represented by the length f the arrw Directin is defined by Vectr A is written as A A Head Line f Actin Tail

17 Vectr Operatins Multiplicatin and Divisin f a Vectr by a Scalar Vectr A Scalar a A a = aa Magnitude f aa Directin f A if a is psitive (+) Directin f A (ppsite) if a is negative (-) A 1.5 A -A

18 Vectr Additin Vectrs are added accrding t the parallelgram law The resultant R is the diagnal f the parallelgram A A R = A + B B A B R = A + B R = A + B B A B If tw vectrs are c-linear (bth have the same line f actin), they are added algebraically A R = A + B B

19 Vectr Subtractin The resultant is the difference between vectrs A and B A -B B -B R A R A

20 Reslutin f a Vectr If lines f actin are knwn, the resultant R can be reslved int tw cmpnents acting alng thse lines (i.e. a and b). b B R A a

21 Analysis f Prblems Tw prcedures t be fllwed: Parallelgram law Trignmetry sine and/r csine laws may be used

22 Sine Law A sin a B sinb C sin c b C a Csine Law A c B 2 C A B 2AB cs c 2

23 Example 1 The screw eye in figure is subjected t tw frces F 1 and F 2. Determine the magnitude and directin f the resultant frce

24 Using Parallelgram Law 150 N F R = = N F 150 cs , N 2 2 R sine law : 150 sin 212, 6 sin , 6 sin sin115, 39 8 f = 54,8 Directin, f = 15 + = 54,8 frm hrizntal axis

25 Example 2 Reslve the 1000-N frce acting n the pipe, int cmpnents in the : (a) x and y directin; (b) x and y directin

26 y F y y F y F x x F x 60 F y 40 F x 40 F x 1000cs 40 F y 766N 30 F x x' Fx sin50 F y sin sin sin 60 F F x y 884, 6N 1085N F y 1000 sin N

27 Example 3 The ring shw in figure is subjected t tw frces F 1 and F 2. If it is required that the resultant frce have a magnitude f 1 kn and be directed vertically dwnward, determine (a) the magnitudes f F 1 and F 2 prvided = 30, (b) the magnitude f F 1 and F 2 if F 2 is t be minimum a hme base t excellence

28 (a) F F F F1 sin30 F2 sin sin sin130 F 1 F 2 653N 446N F

29 (b) F 2 70 If is nt specified, then by the vectr triangle, F 2 may be added t F 1 in varius ways t yield the resultant 1000 N frce. In particular, the minimum length r magnitude f F 2 will ccur when its line f actin is perpendicular t F 1. Hence, when = = 70, F 2 is minimum F 1 F F sin cs N 342N 20