general physics national taichung university tsung-wen yeh
TRANSCRIPT
General Physics
National Taichung UniversityTsung-Wen Yeh
Content 1. Physics, Mathematics, and the Real World 2. One Dimensional Kinematics 3. Two Dimensional Kinematics 4. Particle Dynamics I 5. Particle Dynamics II 6. Work and Energy 7. Conservation of Mechanical Energy 8. Linear Momentum 9. System of Particles 10. Rotational Motion
Content 11. Gravitation 12. Solids and Fluids 13. Oscillations 14. Mechanical Waves 15. Sound 16. Temperature, Thermal Expansion, and Ideal Gas
Law 17. First Law of Thermodynamics 18. Kinetic Theory 19. Entropy and The Second Law of Thermodynamics 20. Electrostatics 21 The Electric Fields
Content 22. Quantitative Treatment of Current and Circuit
Elements 23. Quantitative Circuit Reasoning 24. Magnetism and Magnetic Fields 25. Electromagnetic Induction 26. As the Twentieth Century Opens: The Unanswered
Questions 27. Relativity 28. Inroad into the Micro-Universe of Atoms 29. The Concept of Quantization 30. The Nucleus and Energy Technologies 31. The Elementary Particles 32. The Standard Model and 21st Century Physics
Text Books
Main text book: Introductory Physics, building understand
ing, Jerold Touger Reference books:
University Physics, Harris Benson Principles of Physics, Serway & Jewett Fundamentals of Physic, Halliday, Resnick, &
Walker
Scores
100 Excercises : 40 % Final exam : 20 % 4 tests : 40 %
What Is Physics ?
Physics is the activity of trying to find the rules by which nature plays.
We Believe that “There are rules, that nature is in
some sense orderly”
What Is Physics ?
Physics is the activity of trying to find the rules by which nature plays.
We Believe that “There are rules, that nature is in
some sense orderly”
What Is Physics ?
Physics is the activity of trying to find the rules by which nature plays.
We Believe that “There are rules, that nature is in
some sense orderly”
What Is Physics ?
Physics is the activity of trying to find the rules by which nature plays.
We Believe that “There are rules, that nature is in
some sense orderly”
Rules : Our Brain Can Imagine
What Is Physics ?
Physics is the activity of trying to find the rules by which nature plays.
We Believe that “There are rules, that nature is in
some sense orderly”
Order : In Lit., Soc., Math, Eco., Bio., etc. forms
In Words
Physics is a fundamentally human activity.
The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. --Albert Einstein
In Words
Science and the arts are somewhat alike.
There is no science without fancy, No art without facts. --Vladimir Nabokov
In Words
Physics, like all true science, require collective understanding—not just how I understand something but reaching agreement on how we understand it.
Art is I.Science is we. --Claude Bernard
緒論 為何要學習科學?1. 科學提供一種有力的工具使我們能瞭解周遭的世界是如何運作,及我們又是如何與環境產生互動。
2. 科學知識與日常生活息息相關。
科學方法 科學方法由四個步驟所組成:1. 觀察:瞭解大自然最直接的方法就是觀察它是如何運作,及運作的原因。
2. 自眾多現象中尋找規律及規則性。3. 設定假設及建立理論。4. 預測及測試。
科學方法 -四步驟循環
找出規律
假設
預測
觀察實驗數據
偏見
科學信條:
任何新實驗,都可能改變一已成立的理論或定律。
科學定律
科學定律的形成:1. 假設:一種出於富有經驗的嘗試性猜測。2. 理論:一種對物理世界的描述能同時涵蓋自然現象及通過實驗的驗證。
3. 定律:當理論已經過相當多的驗證且此理論應當在宇宙的任何一處皆成立。
科學的運作方法
1. 科學必須忠於實驗(觀察)所呈現的事實。2. 由四步驟循環之任一步驟開始均應得到相同的結論。
3. 科學結果必須是可複製的。4. 四步驟循環是持續且沒有終點。5. 科學與藝術或文學一樣,均是人類創造性活動的結果,因此新發現常是充滿驚奇且沒有脈絡可尋。
分辨偽科學
可以利用以下方法來檢驗某一學說是否屬於偽科學:
1. 支持此學說的”事實”是否是事實?2. 是否存在另一種解釋?3. 其主張是否可證明為偽?4. 其主張是否已經過嚴格檢驗?5. 其主張是否與一些已被廣為接受的觀念之間存在不合理的矛盾?
Chapter I Introduction What is Physics ?① Who investigates the physics ? - Physic
ists② A physicist is a Scientist③ A Scientist retains childlike curiosity and
wonder about Nature④ Physics deals with the behavior and com
position of matter and its interactions.
Classical Physics
Physics developed in 1600~1900 are called classical physics
① Classical Mechanics② Thermodynamics③ Electromagnetism
Modern Physics
After 1905, the lately developed physics are called modern physics
① Special Relativity② Quantum Mechanics③ General Relativity
The Goal of Physicists
To Explain physical phenomena in simplest and most economical terms, i.e., elegant form
Classifications of physics Concept: a physical quantity can be used to analy
ze natural phenomena Laws & Principles: math’s relationships - laws ;
general statements - principles Models: a convenient representation of a physica
l system Theories: a theory uses a combination of priciple
s, a model, and initial assumptions to deduce specific consequences or laws
Category of Physics
The Goal of Physicists Matter Hierarchy:
matter
atomsnuclei
electrons
protons
neutrons
2U quarks1 D quark
1 U quark2 D quarks
The Goal of PhysicistsForces
Strong EM Weak GravityFour Basic Interactions:
ElectroWeak
Grand-Unified
Unified
Measurement and Units
Distance Measurements Very Large distance Tiny distance
Very Large Objects 10^21 meter 10^42 Kilogram
Tiny Objects Each pits has
4x10^-7 meter
Systeme Internationale (SI Units)
Mass Units
SI – kilogram, kg Defined in terms of kilogram,
based on a specific cylinder kept at the International Bureau of Weights and Measures
See table 1.2 for masses of various objects
Time Units
Seconds, s Historically defined in terms of a solar
day, as well as others Now defined in terms of the
oscillation of radiation from a cesium atom
See table 1.3 for some approximate time intervals
Length Units
SI – meter, m Historically length has had many definitions Length is now defined in terms of a
meter – the distance traveled by light in a vacuum during a given time
See table 1.1 for some examples of lengths
Systems of Measurements, SI Summary
SI System Most often used in the text
Almost universally used in science and industry
Length is measured in meters (m) Time is measured in seconds (s) Mass is measured in kilograms (kg)
Number Notation
When writing out numbers with many digits, spacing in groups of three will be used No commas
Examples: 25 100 5.123 456 789 12
Reasonableness of Results
When solving problem, you need to check your answer to see if it seems reasonable
Reviewing the tables of approximate values for length, mass, and time will help you test for reasonableness
Significant Figures No mearsurement is completely precise. Ex, you cannot read distance much smale
r than 0.001 m (1 mm) on a meter stick. The number of places that you can legi
timately read with your measuring instrument is called the number of significant figures.
Significant Figures (cont.)
A numerical value should always be written to show the number of significant figures.
When you use your measured values to calculate a result, you cannot claim greater accuracy (more significant figures) for your results than for the measurements from which is came.
Example 1-2Suppose A=2.000 m znd B=3.000 m are the measured lengths of the two legs of a right triangle. You wish to calculate the length of hypotenuse using
the Pythagorean theorem: Rules:
2 2 2A B C
Prefixes
Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation
Prefixes, cont. The prefixes can
be used with any base units
They are multipliers of the base unit
Examples: 1 mm = 10-3 m 1 mg = 10-3 g
Fundamental and Derived Quantities In mechanics, three fundamental quantities
are used Length Mass Time
Will also use derived quantities These are other quantities that can be expressed
as a mathematical combination of fundamental quantities
Density
Density is an example of a derived quantity
It is defined as mass per unit volume
Units are kg/m3
Vm
Dimensional Analysis
The basic quantities involved in the definition of a derived quantity are called its dimensions.
Mass [M], Length [L], Time [T] Energy has a dimenion [MLT-2]
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
Basic Quantities and Their Dimension Dimension has a specific meaning – it
denotes the physical nature of a quantity
Dimensions are denoted with square brackets Length – L Mass – M Time – T
Dimensional Analysis, cont. Cannot give numerical factors: this is its limitation Dimensions of some common quantities are given
below
Dimensional Analysis, example Given the equation: x = 1/2 a t2
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
LTT
LL 2
2
Conversion of Units
When units are not consistent, you may need to convert to appropriate ones
Units can be treated like algebraic quantities that can cancel each other out
See Appendix A for an extensive list of conversion factors
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 The ratio is called a conversion factor
Example
cm1.38in1cm54.2
in0.15
cm?in0.15
Converting Units
Different units are used in life Convert units into our favorite ones—
SI units Examples
1 min = 60 s, 1 s = 1/60 min 1 km = 1000 m 1 kg = 1000 g
Example 1-1A bus travels 110 km/h on open highway. What is this speed in stand SI units ?
Step 1: Choose SI units for answer Step 2: Write 110 km/h=110 km/1hr Step 3: Write the conversion relations:
1 km = 1000 m, 1 h = 60 min, 1 min =60s
Step 4: In fractions
1km 1h 1min1, 1, 1
1000m 60min 60s
Example 1-1A bus travels 110 km/h on open highway. What is this speed in stand SI units ?
Step 4: Multiply by 1 as many as necessary
1km 1000 1h 1min 110 000110 30.6 m/s
1h 1km 60min 60s 3600 s
m m
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 In order of magnitude calculations, the
results are reliable to within about a factor of 10
Uncertainty in Measurements
There is uncertainty in every measurement, this uncertainty carries over through the calculations Need a technique to account for this
uncertainty We will use rules for significant figures
to approximate the uncertainty in results of calculations
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
Significant Figures, examples 0.0075 m has 2 significant figures
The leading zeroes 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
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
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
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
Rounding Last retained digit is increased by 1 if the
last digit dropped is 5 or above Last retained digit is remains as it is if the
last digit dropped is less than 5 If the last digit dropped is equal to 5, the
retained should be rounded to the nearest even number
Saving rounding until the final result will help eliminate accumulation of errors
More examples Addition/Subtraction
Multiplication/Division
Powers/Roots
6 5 6 6 63.75 10 5.2 10 3.75 10 0.52 10 4.27 10
8 10 8 ( 10) 2(3.0 10 / )(2.1 10 ) (3.0)(2.1) 10 6.3 10m s s m m
4 3 3 (3)(4) 12 1/ 2
(12)(1/ 2) 6
(3.61 10 ) 3.61 10 (47.04 10 )
47.02 10 6.86 10
More examples Addition/Subtraction
The answer should have the same number of digits to the right of the decimal point as the term in the sum or difference that has the smallest number of digits to right of the decimal points.
Multiplication/Division The answer should have the same number of
significant figures as the least accurate of the quantity entering the calculation.
Powers/Roots Raise the digits to the given power and multiply
the exponent by the power.
Exercises5 3
3 2
2 3 4
193
1. (3.6 10 ) (2.1 10 ) ( )
2. (4.2 10 / ) (0.57 ) ( / )
3.[(5.1 10 ) (6.8 10 )] (1.8 10 )
4. (6.4 10 )
5. (1.46 ) (2.3 )
6. A 3.6-cm-long radio antenna is added to the front of an airplane
41 m lo
m km m
m s ms m s
cm m N
m cm
ng. What is the overall length ?
7. Repeat the Exercise 6 given that the airplane's length is 41.05 m.