kuliah 1 introduction and measurement
DESCRIPTION
kuliah pertama fisika di semester 2TRANSCRIPT
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Geological Engineering DepartmentFaculty of Engineering
Physics for Scientists and Engineers
Introduction
and
Chapter 1
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Geological Engineering DepartmentFaculty of Engineering
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).
1.2
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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
Quantum Mechanics
• Formulated to describe physical phenomena at the atomic level
• Led to the development of many practical devices
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Geological Engineering DepartmentFaculty of Engineering
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
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Geological Engineering DepartmentFaculty of Engineering
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?
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Geological Engineering DepartmentFaculty of Engineering
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.
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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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
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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
Standard Kilogram
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Geological Engineering DepartmentFaculty of Engineering
Time
• Units– seconds, s
• Defined in terms of the oscillation of radiation from a cesium atom
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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
Prefixes
• Prefixes correspond to powers of 10• Each prefix has a specific name• Each prefix has a specific abbreviation
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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
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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Geological Engineering DepartmentFaculty of Engineering
KESIMPULAN
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Geological Engineering DepartmentFaculty of Engineering
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
1.4
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Geological Engineering DepartmentFaculty of Engineering
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.
1.5
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Geological Engineering DepartmentFaculty of Engineering
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
1.6
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Geological Engineering DepartmentFaculty of Engineering
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 :
1.7
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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
1.8
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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
1.9
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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
1.10
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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
1.11
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Geological Engineering DepartmentFaculty of Engineering
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