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.