9/22/2015 Mekanika 1 Mekanika Mekanika Kinematika Cabang dari ilmu fisika yang mengkaji tentang materi, gaya, dan gerakannya Terfokus pada gerakannya saja Dinamika Gerakan dan penyebabnya 2i 1 9/22/2015 Gerak satu dimensi Gerak 1 dimensi Gerakan pada lintasan garis lurus Menganggap yang bergerak adalah partikle bebas mengabaikan bentuk dan ukuran Setiap geraknya dapat direpresentasikan secara vektor 3 Perpindahan, Waktu, Kecepatan 4 2 9/22/2015 Posisi dan perpindahan Bergeraknya benda adalah murni translasional, tanpa melibatkan gerak rotasi Perpindahan adalah sebuah vektor jarak dari satu titik acuan ke titik tujuan yang masing-masing merupakan koordinat dari partikel. 5 6 3 9/22/2015 Perpindahan x x2 x1 Vektor 7 Jarak Tempuh Skalar 8 4 9/22/2015 Posisi dan perpindahan Dikatakan bergerak bila Perubahan posisi dan waktu Terjadi perpindahan bila Perubahan posisi koordinat sistem 9 Kecepatan rata-rata Kecepatan rata-rata selama interval waktu adalah kuantitas vektor yang mengalami perubahan komponen koordinat x dibagi interval waktunya x x2 x1 t t 2 t1 vav x x2 x1 x t 2 t1 t 10 5 9/22/2015 Average Velocity Average velocity is positive when during the time interval coordinate x increased and particle moved in the positive direction If particle moves in negative x-direction during time interval, average velocity is negative x x2 x1 19 m 277 m 258 m t t 2 t1 25.0 s 16.0 s 9.0 s vav x x 258 m 29 m / s t 9.0s 11 X-t Graph Kecepatan rata-rata hanya bergantung pada perubahan jarak terhadap interval waktu, tidak mengkaji secara detail pada setiap perubahan waktunya 12 6 9/22/2015 Beberapa kuantitas kecepatan rata-rata Mobil tercepat 341 m/s Pejalan cepat 2 m/s Gerakan random molekul2 udara 500 m/s Kecepatan orbit satelit komunikasi siput 10-3 3000 m/s m/s Kecepatan cahaya di ruang hampa 3 x 108 m/s Pesawat tercepat 1000 m/s Kecepatan orbit elektron dalam atom hidrogen 2 x 108 m/s 13 Kecepatan sesaat Kecepatan sesaat sebuah vektor yang menyatakan kecepatan rata-rata yang dibatasi waktu yang sangat singkat (mendekati 0) x dx v x lim t 0 t dt 14 7 9/22/2015 Kecepatan sesaat 15 Kecepatan sesaat 16 8 9/22/2015 Kecepatan sesaat Concept Question The graph shows position versus time for a particle undergoing 1-D motion. At which point(s) is the velocity vx positive? At which point(s) is the velocity negative? At which point(s) is the velocity zero? At which point is speed the greatest? 17 Acceleration 18 9 9/22/2015 Acceleration If the velocity of an object is changing with time, then the object is undergoing an acceleration. Acceleration is a measure of the rate of change of velocity with respect to time. Acceleration is a vector quantity. In straight-line motion its only non-zero component is along the axis along which the motion takes place. 19 Average Acceleration Average Acceleration over a given time interval is defined as the change in velocity divided by the change in time. In SI units acceleration has units of m/s2. aav x v2 x v1x vx t2 t1 t 20 10 9/22/2015 Instantaneous Acceleration Instantaneous acceleration of an object is obtained by letting the time interval in the above definition of average acceleration become very small. Specifically, the instantaneous acceleration is the limit of the average acceleration as the time interval approaches zero: v x dvx t 0 t dt a x lim 21 Acceleration of Graphs 22 11 9/22/2015 Arah Percepatan vs Kecepatan 23 Acceleration of Graphs 24 12 9/22/2015 25 aav x ax vxf vxi t 2 t1 vx t v xf v xi t 0 vxf vxi axt 26 13 9/22/2015 Constant Acceleration Motion Position of a particle moving with constant acceleration vav x v0 x vx 2 vx v0 x axt vav x x x x0 t t 0 vav x v0 x v0 x a x t v0 x a x t 1 2 x x0 1 v0 x a x t 2 t 1 2 1 x x0 v0 x t a x t 2 2 27 Constant Acceleration Motion Relationship between position of a particle moving with constant acceleration, and velocity and acceleration itself: vx v0 x axt t vx v0 x ax v v 1 v v 1 x x0 v0 x t a x t 2 x x0 v0 x x 0 x a x x 0 x 2 ax 2 ax 2 vx2 v02x 2ax ( x x0 ) 28 14 9/22/2015 Gerak Jatuh Bebas 29 Gerak Jatuh Bebas Example of motion with constant acceleration is acceleration of a body falling under influence of the earth’s gravitation All bodies at a particular location fall with the same downward acceleration, regardless of their size and weight Aristotle 384 - 322 B.C.E. Idealized motion free fall: we neglect earth rotation, decrease of acceleration with decreasing altitude, air effects Galileo Galilei 1564 - 1642 30 15 9/22/2015 Freely Falling Bodies The constant acceleration of a freely falling body is called acceleration due to gravity, g Approximate value near earth’s surface g = 9.8 m/s2 = 980 cm/s2 = 32 ft/s2 g is the magnitude of a vector, it is always positive number Exact g value varies with location 31 Motion in 2 or 3 Dimensions 32 16 9/22/2015 Projectile Motion A projectile is any object that is given an initial velocity and then follows a path (trajectory) determined solely by gravity and air resistance. The motion of a projectile will take place in a plane (so, it is 2D motion). For projectile motion we can analyze the x- and y-components of the motion separately. The horizontal motion (along the x-axis) will have zero acceleration and thus have constant velocity. The vertical motion (along the y-axis) will have constant downward acceleration of magnitude g = 9.80 m/s2. The initial velocity components, vox and voy, can be expressed in terms of the magnitude vo and direction ao of the initial velocity. 33 Kita kombinasikan gerak dalam 2 arah Projectile Motion Arah Horisontal a x 0 vx v0 x x x0 v0 xt Arah Vertikal ay g v y v0 y gt y y0 v0 y t 1 2 gt 2 Kecepatan arah x dan y pada posisi pusat koordinat : v0 x v0 cosa 0 v0 y v0 sin a 0 34 17 9/22/2015 Projectile Motion Lintasan (koord.) benda pada suatu titik x (v0 cosa 0 )t y (v0 sin a 0 )t 1 2 gt 2 vx v0 cosa 0 v y v0 sin a 0 gt 35 Koordinat horisontal max Koord. Pada titik R (horisontal maximum) Untuk arah gerak ke atas y y0 v0 y t 1 2 at 2 nilai y=0 dan y0 = 0 t 2v0 y g 0 0 v0 y t 1 2 gt 2 R v0 xt v0 x g 2v 20 sin a cosa g 2v 0 sin 2a 2 2v0 y g v0 x v0 cosa 0 v0 y v0 sin a 0 36 18
