1 / 35

Fisika Dasar I WAHIDIN ABBAS FT Mesin UNY abbas@uny.ac.id

Fisika Dasar I WAHIDIN ABBAS FT Mesin UNY abbas@uny.ac.id. Pengukuran dan Satuan Satuan dasar Sistem Satuan Konversi Sistem Satuan Analisis Dimensional Kinematika Partikel Kecepatan dan percepatan rata-rata & sesaat Gerak dengan percepatan konstan. Mekanika Klasik (Newton) :

driscoll-roman
Download Presentation

Fisika Dasar I WAHIDIN ABBAS FT Mesin UNY abbas@uny.ac.id

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FisikaDasarIWAHIDIN ABBASFT Mesin UNYabbas@uny.ac.id • Pengukuran dan Satuan • Satuan dasar • Sistem Satuan • Konversi Sistem Satuan • Analisis Dimensional • Kinematika Partikel • Kecepatan dan percepatan rata-rata & sesaat • Gerak dengan percepatan konstan

  2. Mekanika Klasik (Newton): • Mekanika: Bagaimana dan mengapa benda-benda dapat bergerak • Klasik: • Kecepatan tidak terlalu cepat (v << c) • Ukuran tidak terlalu kecil (d >> atom) • Pengalaman sehari-hari banyak yang terjadi berdasarkan aturan-aturan mekanika klasik. • Lintasan bola kasti • Orbit planet-planet • dll...

  3. Units • Bagaimana mengukur dimensi? • Semua ukuran di dalam mekanika klasik dapat dinyatakan dengan satuan dasar: • Length L Panjang • Mass M Massa • Time T Waktu • Contoh: • Kecepatan mempunyai satuanL / T (kilometer per jam). • Gaya mempunyai satuanML/ T2.

  4. Panjang: Jarak Panjang (m) Jari-jari alam semesta1 x 1026 Ke galaksi Andromeda2 x 1022 Ke bintang terdekat4 x 1016 Bumi - matahari 1.5 x 1011 Jari-jari bumi 6.4 x 106 Sears Tower 4.5 x 102 Lapangan sepak bola 1.0 x 102 Tinggi manusia 2 x 100 Ketebalan kertas 1 x 10-4 Panjang gelombang sinar biru 4 x 10-7 Diameter atom Hidrogen 1 x 10-10 Diameter proton1 x 10-15

  5. Waktu: IntervalTime (s) Umur alam semesta 5 x 1017 Umur Grand Canyon 3 x 1014 32 tahun 1 x 109 1 tahun 3.2 x 107 1 jam 3.6 x 103 Perjalanan cahaya dari mh ke bumi 1.3 x 100 Satu kali putaran senar gitar 2 x 10-3 Satu putaran gel. Radio FM 6 x 10-8 Umur meson pi netral 1 x 10-16 Umur quark top 4 x 10-25

  6. Massa: ObjectMass (kg) Galaksi Bima Sakti 4 x 1041 Matahari 2 x 1030 Bumi 6 x 1024 Pesawat Boeing 747 4 x 105 Mobil 1 x 103 Mahasiswa 7 x 101 Partikel debu 1 x 10-9 Quark top 3 x 10-25 Proton 2 x 10-27 Electron 9 x 10-31 Neutrino 1 x 10-38

  7. Satuan ... • Satuan Internasional, SI (Système International) : • mks: L = meters (m), M = kilograms (kg), T = seconds (s) • cgs: L = centimeters (cm), M = grams (gm), T = seconds (s) • Satuan Inggris: • Inci (Inches, In), kaki (feet, ft), mil (miles, mi), pon (pounds) • Pada umumnya kita menggunakan SI, tetapi dalam masalah tertentu dapat dijumpai satuan Inggris. Mahasiswa harus dapat melakukan konversi dari SI ke Satuan Inggris, atau sebaliknya.

  8. Converting between different systems of units • Useful Conversion factors: • 1 inch = 2.54 cm • 1 m = 3.28 ft • 1 mile = 5280 ft • 1 mile = 1.61 km • Example: convert miles per hour to meters per second:

  9. Analisis Dimensional • Analisis dimensional merupakan perangkat yang sangat berguna untuk memeriksa hasil perhitungan dalam sebuah soal. • Sangat mudah dilakukan! • Contoh: Dalam menghitung suatu jarak yang ditanayakan di dalam sebuah soal, diperoleh jawaban d = vt2(kecepatan x waktu2) Satuan untuk besaran pada ruas kiri= L Ruas kanan = L / T x T2 = L x T • Dimensi ruas kiri tidak sama dengan dimensi ruas kanan, dengan demikian, jawaban di atas pasti salah!!

  10. Lecture 1, Act 1Dimensional Analysis • The periodPof a swinging pendulum depends only on the length of the pendulumdand the acceleration of gravityg. • Which of the following formulas forPcouldbe correct ? P = 2 (dg)2 (a) (b) (c) Given: dhas units of length(L)andghas units of(L / T 2).

  11. Lecture 1, Act 1Solution • Realize that the left hand sidePhas units of time (T) • Try the first equation (a) Not Right !! (a) (b) (c)

  12. Lecture 1, Act 1Solution • Try the second equation (b) Not Right !! (a) (b) (c)

  13. Lecture 1, Act 1Solution • Try the third equation (c) This has the correct units!! This must be the answer!! (a) (b) (c)

  14. Motion in 1 dimension • In 1-D, we usually write position as x(t1 ). • Since it’s in 1-D, all we need to indicate direction is + or . • Displacement in a time t = t2 - t1isx = x(t2) - x(t1) = x2 - x1 x some particle’s trajectoryin 1-D x2 x x1 t1 t2 t t

  15. 1-D kinematics • Velocity v is the “rate of change of position” • Average velocity vav in the time t = t2 - t1is: x trajectory x2 x Vav = slope of line connecting x1 and x2. x1 t1 t2 t t

  16. 1-D kinematics... • Considerlimit t1 t2 • Instantaneous velocity v is definedas: x sov(t2) = slope of line tangent to path at t2. x2 x x1 t1 t2 t t

  17. 1-D kinematics... • Acceleration a is the “rate of change of velocity” • Average acceleration aavin the time t = t2 - t1is: • Andinstantaneous acceleration a is definedas: using

  18. Recap • If the position x is known as a function of time, then we can find both velocity vand acceleration a as a function of time! x t v t a t

  19. More 1-D kinematics • We saw that v = dx / dt • In “calculus” language we would write dx = v dt, which we can integrate to obtain: • Graphically, this is adding up lots of small rectangles: v(t) + +...+ = displacement t

  20. 1-D Motion with constant acceleration • High-school calculus: • Also recall that • Since a is constant, we can integrate this using the above rule to find: • Similarly, since we can integrate again to get:

  21. Recap Plane w/ lights • So for constant acceleration we find: x t v t a t

  22. Lecture 1, Act 2Motion in One Dimension • When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? (a)Bothv = 0anda = 0. (b)v  0, but a = 0. (c) v = 0, but a  0. y

  23. Lecture 1, Act 2Solution • Going up the ball has positive velocity, while coming down it has negative velocity. At the top the velocity is momentarily zero. • Since the velocity is continually changing there must be some acceleration. • In fact the acceleration is caused by gravity (g = 9.81 m/s2). • (more on gravity in a few lectures) • The answer is (c) v = 0, but a  0. x t v t a t

  24. Solving for t: Derivation: • Plugging in for t:

  25. Average Velocity • Remember that v v vav v0 t t

  26. Recap: Washers • For constant acceleration: • From which we know:

  27. vo ab x = 0, t = 0 Problem 1 • A car is traveling with an initial velocity v0. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab

  28. Problem 1... • A car is traveling with an initial velocity v0. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab. At what time tf does the car stop, and how much farther xf does it travel? v0 ab x = 0, t = 0 v = 0 x = xf , t = tf

  29. Problem 1... • Above, we derived: v = v0 + at • Realize thata = -ab • Also realizing that v = 0at t = tf : find 0 = v0 - ab tfor tf = v0 /ab

  30. Problem 1... • To find stopping distance we use: • In this case v = vf = 0, x0 = 0 and x = xf

  31. Problem 1... • So we found that • Suppose that vo = 65 mi/hr = 29 m/s • Suppose also thatab = g = 9.81 m/s2 • Find that tf = 3 s and xf = 43 m

  32. Tips: • Read ! • Before you start work on a problem, read the problem statement thoroughly. Make sure you understand what information is given, what is asked for, and the meaning of all the terms used in stating the problem. • Watch your units ! • Always check the units of your answer, and carry the units along with your numbers during the calculation. • Understand the limits ! • Many equations we use are special cases of more general laws. Understanding how they are derived will help you recognize their limitations (for example, constant acceleration).

  33. Recap of today’s lecture • Scope of this course • Measurement and Units (Chapter 1) • Systems of units (Text: 1-1) • Converting between systems of units (Text: 1-2) • Dimensional Analysis (Text: 1-3) • 1-D Kinematics (Chapter 2) • Average & instantaneous velocity and acceleration (Text: 2-1,2-2) • Motion with constant acceleration (Text: 2-3) • Example car problem (Ex. 2-7) • Look at Text problems Chapter 2: # 6, 12, 56, 119

More Related