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Physics 111: Lecture 1, Pg 1 Fisika Dasar I l Pengukuran dan Satuan çSatuan dasar çSistem Satuan çKonversi Sistem Satuan çAnalisis Dimensional l Kinematika.

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Presentasi berjudul: "Physics 111: Lecture 1, Pg 1 Fisika Dasar I l Pengukuran dan Satuan çSatuan dasar çSistem Satuan çKonversi Sistem Satuan çAnalisis Dimensional l Kinematika."— Transcript presentasi:

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2 Physics 111: Lecture 1, Pg 1 Fisika Dasar I l Pengukuran dan Satuan çSatuan dasar çSistem Satuan çKonversi Sistem Satuan çAnalisis Dimensional l Kinematika Partikel çKecepatan dan percepatan rata-rata & sesaat çGerak dengan percepatan konstan

3 Physics 111: Lecture 1, Pg 2

4 Physics 111: Lecture 1, Pg 3

5 Physics 111: Lecture 1, Pg 4 l Mekanika Klasik (Newton): çMekanika: Bagaimana dan mengapa benda-benda dapat bergerak çKlasik: »Kecepatan tidak terlalu cepat(v << c) »Ukuran tidak terlalu kecil(d >> atom) l Pengalaman sehari-hari banyak yang terjadi berdasarkan aturan-aturan mekanika klasik. çLintasan bola kasti çOrbit planet-planet çdll...

6 Physics 111: Lecture 1, Pg 5 l Bagaimana mengukur dimensi? l Semua ukuran di dalam mekanika klasik dapat dinyatakan dengan satuan dasar: çLength LPanjang çMass MMassa çTime TWaktu l Contoh: çKecepatan mempunyai satuan L / T (kilometer per jam). çGaya mempunyai satuan ML / T 2. Units

7 Physics 111: Lecture 1, Pg 6 Panjang: Jarak (m) JarakPanjang (m) Jari-jari alam semesta 1 x Ke galaksi Andromeda2 x Ke bintang terdekat4 x Bumi - matahari1.5 x Jari-jari bumi6.4 x 10 6 Sears Tower 4.5 x 10 2 Lapangan sepak bola1.0 x 10 2 Tinggi manusia 2 x 10 0 Ketebalan kertas 1 x Panjang gelombang sinar biru 4 x Diameter atom Hidrogen 1 x Diameter proton 1 x

8 Physics 111: Lecture 1, Pg 7 Waktu: IntervalTime (s) Umur alam semesta 5 x Umur Grand Canyon 3 x tahun 1 x tahun3.2 x jam3.6 x 10 3 Perjalanan cahaya dari mh ke bumi1.3 x 10 0 Satu kali putaran senar gitar 2 x Satu putaran gel. Radio FM 6 x Umur meson pi netral 1 x Umur quark top 4 x

9 Physics 111: Lecture 1, Pg 8 Massa: ObjectMass (kg) Galaksi Bima Sakti 4 x Matahari 2 x Bumi 6 x Pesawat Boeing x 10 5 Mobil 1 x 10 3 Mahasiswa 7 x 10 1 Partikel debu 1 x Quark top 3 x Proton 2 x Electron 9 x Neutrino 1 x

10 Physics 111: Lecture 1, Pg 9 Satuan... l Satuan Internasional, SI (Système International) : çmks: L = meters (m), M = kilograms (kg), T = seconds (s) çcgs: L = centimeters (cm), M = grams (gm), T = seconds (s) l Satuan Inggris: çInci (Inches, In), kaki (feet, ft), mil (miles, mi), pon (pounds) l 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.

11 Physics 111: Lecture 1, Pg 10 Converting between different systems of units l Useful Conversion factors: ç1 inch= 2.54 cm ç1 m = 3.28 ft ç1 mile= 5280 ft ç1 mile = 1.61 km l Example: convert miles per hour to meters per second:

12 Physics 111: Lecture 1, Pg 11 l Analisis dimensional merupakan perangkat yang sangat berguna untuk memeriksa hasil perhitungan dalam sebuah soal. çSangat mudah dilakukan! l Contoh: Dalam menghitung suatu jarak yang ditanayakan di dalam sebuah soal, diperoleh jawaban d = vt 2 (kecepatan x waktu 2 ) Satuan untuk besaran pada ruas kiri= L Ruas kanan = L / T x T 2 = L x T l Dimensi ruas kiri tidak sama dengan dimensi ruas kanan, dengan demikian, jawaban di atas pasti salah!! Analisis Dimensional

13 Physics 111: Lecture 1, Pg 12 Lecture 1, Act 1 Dimensional Analysis l The period P of a swinging pendulum depends only on the length of the pendulum d and the acceleration of gravity g. çWhich of the following formulas for P could be correct ? (a)(b)(c) Given: d has units of length (L) and g has units of (L / T 2 ). P = 2  (dg) 2

14 Physics 111: Lecture 1, Pg 13 Lecture 1, Act 1 Solution T l Realize that the left hand side P has units of time (T ) l Try the first equation (a)(b)(c) (a) Not Right !!

15 Physics 111: Lecture 1, Pg 14 (a)(b)(c) (b) Not Right !! l Try the second equation Lecture 1, Act 1 Solution

16 Physics 111: Lecture 1, Pg 15 (a)(b)(c) (c) This has the correct units!! This must be the answer!! l Try the third equation Lecture 1, Act 1 Solution

17 Physics 111: Lecture 1, Pg 16 Motion in 1 dimension l In 1-D, we usually write position as x(t 1 ). Since it’s in 1-D, all we need to indicate direction is + or .  Displacement in a time  t = t 2 - t 1 is  x = x(t 2 ) - x(t 1 ) = x 2 - x 1 t x t1t1 t2t2  x  t x1x1 x2x2 some particle’s trajectory in 1-D

18 Physics 111: Lecture 1, Pg 17 1-D kinematics t x t1t1 t2t2  x x1x1 x2x2 trajectory l Velocity v is the “rate of change of position” Average velocity v av in the time  t = t 2 - t 1 is:  t V av = slope of line connecting x 1 and x 2.

19 Physics 111: Lecture 1, Pg 18 l Consider limit t 1 t 2 l Instantaneous velocity v is defined as: 1-D kinematics... t x t1t1 t2t2  x x1x1 x2x2  t so v(t 2 ) = slope of line tangent to path at t 2.

20 Physics 111: Lecture 1, Pg 19 1-D kinematics... l Acceleration a is the “rate of change of velocity” Average acceleration a av in the time  t = t 2 - t 1 is: l And instantaneous acceleration a is defined as: using

21 Physics 111: Lecture 1, Pg 20 Recap l If the position x is known as a function of time, then we can find both velocity v and acceleration a as a function of time! x a v t t t

22 Physics 111: Lecture 1, Pg 21 More 1-D kinematics l We saw that v = dx / dt l In “calculus” language we would write dx = v dt, which we can integrate to obtain: l Graphically, this is adding up lots of small rectangles: v(t) t = displacement

23 Physics 111: Lecture 1, Pg 22 l High-school calculus: l Also recall that l Since a is constant, we can integrate this using the above rule to find: l Similarly, since we can integrate again to get: 1-D Motion with constant acceleration

24 Physics 111: Lecture 1, Pg 23 Recap l So for constant acceleration we find: x a v t t t Plane w/ lights

25 Physics 111: Lecture 1, Pg 24 Lecture 1, Act 2 Motion in One Dimension l 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) Both v = 0 and a = 0. (b) v  0, but a = 0. (c) v = 0, but a  0. y

26 Physics 111: Lecture 1, Pg 25 Lecture 1, Act 2 Solution x a v t t t l Going up the ball has positive velocity, while coming down it has negative velocity. At the top the velocity is momentarily zero. l Since the velocity is continually changing there must continually changing there must be some acceleration. be some acceleration. çIn fact the acceleration is caused by gravity (g = 9.81 m/s 2 ). ç(more on gravity in a few lectures) l The answer is (c) v = 0, but a  0.

27 Physics 111: Lecture 1, Pg 26 Derivation: l Plugging in for t: l Solving for t:

28 Physics 111: Lecture 1, Pg 27 Average Velocity l Remember that v t t v v av v0v0

29 Physics 111: Lecture 1, Pg 28 Recap: l For constant acceleration: l From which we know: Washers

30 Physics 111: Lecture 1, Pg 29 Problem 1 l A car is traveling with an initial velocity v 0. At t = 0, the driver puts on the brakes, which slows the car at a rate of a b x = 0, t = 0 abab vovo

31 Physics 111: Lecture 1, Pg 30 Problem 1... l A car is traveling with an initial velocity v 0. At t = 0, the driver puts on the brakes, which slows the car at a rate of a b. At what time t f does the car stop, and how much farther x f does it travel? x = x f, t = t f v = 0 x = 0, t = 0 abab v0v0

32 Physics 111: Lecture 1, Pg 31 Problem 1... l Above, we derived: v = v 0 + at l Realize that a = -a b l Also realizing that v = 0 at t = t f : find 0 = v 0 - a b t f or t f = v 0 /a b

33 Physics 111: Lecture 1, Pg 32 Problem 1... l To find stopping distance we use: l In this case v = v f = 0, x 0 = 0 and x = x f

34 Physics 111: Lecture 1, Pg 33 Problem 1... l So we found that l Suppose that v o = 65 mi/hr = 29 m/s l Suppose also that a b = g = 9.81 m/s 2 ç Find that t f = 3 s and x f = 43 m

35 Physics 111: Lecture 1, Pg 34 Tips: l Read ! çBefore 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. l Watch your units ! çAlways check the units of your answer, and carry the units along with your numbers during the calculation. l Understand the limits ! çMany 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).

36 Physics 111: Lecture 1, Pg 35 Recap of today’s lecture l Scope of this course l Measurement and Units (Chapter 1) çSystems of units(Text: 1-1) çConverting between systems of units(Text: 1-2) çDimensional Analysis(Text: 1-3) l 1-D Kinematics l 1-D Kinematics (Chapter 2) çAverage & instantaneous velocity and acceleration (Text: 2-1, 2-2) çMotion with constant acceleration (Text: 2-3) l Example car problem(Ex. 2-7) l Example car problem(Ex. 2-7) Chapter 2: # 6, 12, 56, 119 l Look at Text problems Chapter 2: # 6, 12, 56, 119


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