kuliah 1 introduction and measurement

Geological Engineering DepartmentFaculty of Engineering

Physics for Scientists and Engineers

Introduction

and

Chapter 1

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1.1 PENDAHULUAN

Fisika :Fisika :

Ilmu pengetahuan yang mempelajari benda-benda dialam, gejala-gejala, kejadian-kejadian alam serta interaksi dari benda-benda dialam .

Fisika merupakan ilmu pengetahuan dasar yang mempelajari sifat-sifat dan interaksi antar materi dan radiasi.

Fisika merupakan ilmu pengetahuan yang didasarkan pada pengamatan eksperimental dan pengukuran kuantitatif (Metode Ilmiah).

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Physics

• Fundamental Science– Concerned with the fundamental principles of the Universe– Foundation of other physical sciences– Has simplicity of fundamental concepts

• Divided into five major areas– Classical Mechanics– Relativity– Thermodynamics– Electromagnetism– Optics– Quantum Mechanics

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Fisika

Klasik Kuantum(sebelum 1920) (setelah 1920)

Posisi dan Momentum partikel dapat ditetapkan secara tepat ruang dan waktu merupakan dua hal yang terpisah

Ketidak pastian Posisi dan Momentum partikel ruang dan waktu merupakan satu kesatuan

Hukum Newton Dualisme Gelombang-Partikel

Teori Relativitas Einsten1.3

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Classical Physics

• Mechanics and electromagnetism are basic to all other branches of classical and modern physics

• Classical physics– Developed before 1900– Our study will start with Classical Mechanics

• Also called Newtonian Mechanics or Mechanics

• Modern physics– From about 1900 to the present

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Objectives of Physics

• To find the limited number of fundamental laws that govern natural phenomena

• To use these laws to develop theories that can predict the results of future experiments

• Express the laws in the language of mathematics– Mathematics provides the bridge between theory and

experiment

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Theory and Experiments

• Should complement each other• When a discrepancy occurs, theory may be

modified– Theory may apply to limited conditions

• Example: Newtonian Mechanics is confined to objects traveling slowly with respect to the speed of light

– Try to develop a more general theory

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Classical Physics Overview

• Classical physics includes principles in many branches developed before 1900

• Mechanics– Major developments by Newton, and continuing through

the 18th century

• Thermodynamics, optics and electromagnetism– Developed in the latter part of the 19th century

– Apparatus for controlled experiments became available

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Modern Physics

• Began near the end of the 19th century• Phenomena that could not be explained by

classical physics• Includes theories of relativity and quantum

mechanics

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Special Relativity

• Correctly describes motion of objects moving near the speed of light

• Modifies the traditional concepts of space, time, and energy

• Shows the speed of light is the upper limit for the speed of an object

• Shows mass and energy are related

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Quantum Mechanics

• Formulated to describe physical phenomena at the atomic level

• Led to the development of many practical devices

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Measurements

• Used to describe natural phenomena• Needs defined standards• Characteristics of standards for measurements

– Readily accessible – Possess some property that can be measured reliably– Must yield the same results when used by anyone

anywhere– Cannot change with time


Fact:The earth has a circumference of approximately 40 million meters (4. X 107 m). How fast must one move on average to travel around the world in 80 days?


Measurement is the quantitative comparison of a physical parameter to a standard unit. Therefore we need standards.

Accuracy is the difference of a measurement from the (unknown) true value. All measurement contain experimental error.

Precision is the “fineness” of the division of the scale used to compare to the standard unit. Precision limits our knowledge.


Why did we observe a variety of values in our measurement?

Measurement is the quantitative comparison of a physical parameter to a standard unit. Therefore we need standards. a standard unit.

A “hand” is not a standard unit.

Our measurement is subject to error.

Our measurement is coarse.

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Precision is the fineness of a measurement.

Accuracy is the correspondence of a measurement to an (unknown) true value.

Less Less preciseprecise

Less Less accurateaccurate

StandardStandard

MeasuremeMeasurementnt

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Uncertainty in Measurements

• There is uncertainty in every measurement – this uncertainty carries over through the calculations– May be due to the apparatus, the experimenter,

and/or the number of measurements made– Need a technique to account for this uncertainty

• We will use rules for significant figures to approximate the uncertainty in results of calculations


What numbers one writes down reveals one’s knowledge (and ignorance) of the actual true (but unknown) value.

Example:2. 2.0 2.01 2.0085 2.00852 represent the values of a measurement at various levels of precision.

Significant figures:

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Significant Figures

• A significant figure is one that is reliably known

• Zeros may or may not be significant– Those used to position the decimal point are not significant

– To remove ambiguity, use scientific notation

• In a measurement, the significant figures include the first estimated digit

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Significant Figures, examples

• 0.0075 m has 2 significant figures– The leading zeros are placeholders only– Can write in scientific notation to show more clearly:

7.5 x 10-3 m for 2 significant figures

• 10.0 m has 3 significant figures– The decimal point gives information about the reliability of

the measurement

• 1500 m is ambiguous– Use 1.5 x 103 m for 2 significant figures– Use 1.50 x 103 m for 3 significant figures– Use 1.500 x 103 m for 4 significant figures

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Operations with Significant Figures – Multiplying or Dividing• When multiplying or dividing, the number of

significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures.

• Example: 25.57 m x 2.45 m = 62.6 m2

– The 2.45 m limits your result to 3 significant figures

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Operations with Significant Figures – Adding or Subtracting

• When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum.

• Example: 135 cm + 3.25 cm = 138 cm– The 135 cm limits your answer to the units decimal

value

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Operations With Significant Figures – Summary

• The rule for addition and subtraction are different than the rule for multiplication and division

• For adding and subtracting, the number of decimal places is the important consideration

• For multiplying and dividing, the number of significant figures is the important consideration

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Rounding

• Last retained digit is increased by 1 if the last digit dropped is greater than 5

• Last retained digit remains as it is if the last digit dropped is less than 5

• If the last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number

• Saving rounding until the final result will help eliminate accumulation of errors

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Standards of Fundamental Quantities

• Standardized systems– Agreed upon by some authority, usually a

governmental body

• SI – Systéme International– Agreed to in 1960 by an international committee– Main system used in this text

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1770 1780 1790 1800 1810

Fundamental UnitsFundamental Units

• Système International de Metrique (SI)— “Metric System”

• First introduced in France in 1799—(on Napoleon’s coup)

La La $$

American Rev

US Constitution

French Rev

Napoleon

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Fundamental Quantities and Their Units

Quantity SI Unit

Length meter

Mass kilogram

Time second

Temperature Kelvin

Electric Current Ampere

Luminous Intensity Candela

Amount of Substance mole

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Quantities Used in Mechanics

• In mechanics, three basic quantities are used– Length– Mass– Time

• Will also use derived quantities– These are other quantities that can be expressed in

terms of the basic quantities• Example: Area is the product of two lengths

– Area is a derived quantity– Length is the fundamental quantity

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Length

• Length is the distance between two points in space

• Units– SI – meter, m

• Defined in terms of a meter – the distance traveled by light in a vacuum during a given time

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Mass

• Units– SI – kilogram, kg

• Defined in terms of a kilogram, based on a specific cylinder kept at the International Bureau of Standards

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Standard Kilogram

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Time

• Units– seconds, s

• Defined in terms of the oscillation of radiation from a cesium atom

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US Customary System

• Still used in the US, but text will use SI

Quantity Unit

Length foot

Mass slug

Time second

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Prefixes

• Prefixes correspond to powers of 10• Each prefix has a specific name• Each prefix has a specific abbreviation

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Prefixes, cont.

• The prefixes can be used with any basic units• They are multipliers of the basic unit• Examples:

– 1 mm = 10-3 m– 1 mg = 10-3 g

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Dimensions and Units

• Each dimension can have many actual units

• Table 1.5 for the dimensions and units of some derived quantities

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Dimensional Analysis

• Technique to check the correctness of an equation or to assist in deriving an equation

• Dimensions (length, mass, time, combinations) can be treated as algebraic quantities – add, subtract, multiply, divide

• Both sides of equation must have the same dimensions

• Any relationship can be correct only if the dimensions on both sides of the equation are the same

• Cannot give numerical factors: this is its limitation

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Dimensional Analysis, example

• Given the equation: x = ½ at 2

• Check dimensions on each side:

• The T2’s cancel, leaving L for the dimensions of each side– The equation is dimensionally correct– There are no dimensions for the constant

LTTL

L 2

2

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Dimensional Analysis to Determine a Power Law• Determine powers in a proportionality

– Example: find the exponents in the expression• You must have lengths on both sides• Acceleration has dimensions of L/T2

• Time has dimensions of T• Analysis gives

m nx a t

2x at

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Symbols

• The symbol used in an equation is not necessarily the symbol used for its dimension

• Some quantities have one symbol used consistently– For example, time is t virtually all the time

• Some quantities have many symbols used, depending upon the specific situation– For example, lengths may be x, y, z, r, d, h, etc.

• The dimensions will be given with a capitalized, nonitalicized letter

• The algebraic symbol will be italicized

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Conversion

• Always include units for every quantity, you can carry the units through the entire calculation

• Multiply original value by a ratio equal to one

• Example

– Note the value inside the parentheses is equal to 1 since 1 in. is defined as 2.54 cm

15.0 ?

2.5415.0 38.1

1

in cm

cmin cm

in

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Order of Magnitude

• Approximation based on a number of assumptions– may need to modify assumptions if more precise

results are needed

• Order of magnitude is the power of 10 that applies

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KESIMPULAN

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1.2 BESARAN DAN SATUAN1.2 BESARAN DAN SATUAN

Besaran :

Sesuatu yang dapat diukur dinyatakan dengan angka (kuantitatif) Contoh : panjang, massa, waktu, suhu, dll.

Mengukur :

Membandingkan sesuatu dengan sesuatu yang lain yang sejenis yang ditetapkan sebagai satuan.

contoh : panjang jalan 10 km

Besaran Fisika baru terdefenisi jika : ada nilainya (besarnya) ada satuannya

nilai

satuan

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Satuan : Ukuran dari suatu besaran ditetapkan sebagai satuan. Contoh :

Sistem satuan : ada 2 macam 1. Sistem Metrik : a. mks (meter, kilogram, sekon)

b. cgs (centimeter, gram, sekon)2. Sistem Non metrik (sistem British)

Sistem Internasional (SI) Sistem satuan mks yang telah disempurnakan yang paling banyak

dipakai sekarang ini. Dalam SI :Ada 7 besaran pokok berdimensi dan 2 besaran pokok tak berdimensi

meter, kilometer satuan panjang detik, menit, jam satuan waktu gram, kilogram satuan massa dll.

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NO Besaran Pokok Satuan Singkatan Dimensi

1 Panjang Meter m L

2 Massa Kilogram kg M

3 Waktu Sekon s T

4 Arus Listrik Ampere A I

5 Suhu Kelvin K θ

6 Intensitas Cahaya Candela cd j

7 Jumlah Zat Mole mol N

7 Besaran Pokok dalam Sistem internasional (SI)7 Besaran Pokok dalam Sistem internasional (SI)

NO Besaran Pokok Satuan Singkatan Dimensi

1 Sudut Datar Radian rad -

2 Sudut Ruang Steradian sr -

Besaran Pokok Tak Berdimensi

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Dimensi Cara besaran itu tersusun oleh besaran pokok.

Besaran TurunanBesaran yang diturunkan dari besaran pokok.

1. Untuk menurunkan satuan dari suatu besaran2. Untuk meneliti kebenaran suatu rumus atau persamaan

- Metode penjabaran dimensi :

1. Dimensi ruas kanan = dimensi ruas kiri2. Setiap suku berdimensi sama

- Guna Dimensi :

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Contoh :

a. Tidak menggunakan nama khusus

NO Besaran Satuan

1 Kecepatan meter/detik

2 Luas meter 2

b. Mempunyai nama khusus

NO Besaran Satuan Lambang

1 Gaya Newton N

2 Energi Joule J

3 Daya Watt W

4 Frekuensi Hertz Hz

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Geological Engineering DepartmentFaculty of EngineeringBesaran Turunan dan Dimensi

NO Besaran Pokok Rumus Dimensi

1 Luas panjang x lebar [L]2

2 Volume panjang x lebar x tinggi [L]3

3 Massa Jenis [m] [L]-3

4 Kecepatan

[L] [T]-1

5 Percepatan [L] [T]-2

6 Gaya massa x percepatan [M] [L] [T]-2

7 Usaha dan Energi gaya x perpindahan [M] [L]2 [T]-2

8 Impuls dan Momentum gaya x waktu [M] [L] [T]-1

massa volume

perpindahan waktu

kecepatan waktu

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Faktor Penggali dalam SI

NO Faktor Nama Simbol

1 10 -18 atto a

2 10 -15 femto f

3 10 -12 piko p

4 10 -9 nano n

5 10 -6 mikro μ

6 10 -3 mili m

7 10 3 kilo K

8 10 6 mega M

9 10 9 giga G

10 10 12 tera T

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1. Tentukan dimensi dan satuannya dalam SI untuk besaran turunan berikut :

a. Gaya

b. Berat Jenis

c. Tekanan

d. Usaha

e. Daya

Jawab :

b. Berat Jenis = = =

= MLT-2 (L-3) = ML-2T-2 satuan kgm-2

berat

volume

Gaya

Volume

MLT -2

L3a. Gaya = massa x

percepatan

= M x LT -2

= MLT -2 satuan kgms-2

c. Tekanan = = = MLT -2 satuan kgm-1s-1

gaya

luas

MLT -2

L2

d. Usaha = gaya x jarak = MLT -2 x L = ML 2 T -2 satuan kgm-2s-2

e. Daya = = = ML 2 T -1 satuan kgm-2s-1 usaha

waktu

ML 2 T -2

T

Contoh SoalContoh Soal

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2. Buktikan besaran-besaran berikut adalah identik :

a. Energi Potensial dan Energi Kinetik

b. Usaha/Energi dan Kalor

Jawab :

a. Energi Potensial : Ep = mgh

Energi potensial = massa x gravitasi x tinggi

= M x LT-2 x L = ML2T-2

Energi Kinetik : Ek = ½ mv2

Energi Kinetik = ½ x massa x kecepatan2

= M x (LT-1) 2

= ML2T-2

Keduanya (Ep dan Ek) mempunyai dimensi yang sama keduanya identik

b. Usaha = ML2T-2

Energi = ML2T-2

Kalor = 0.24 x energi = ML2T-2

Ketiganya memiliki dimensi yang sama identik1.12

kuliah 1 introduction and measurement

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