Chapter one: Doing Physics class website: hsiaoscu.pbworks.com

In this chapter you’ll learn: The different realms of physics, and their applications in both natural and technological systems物理有哪些領域？應用？ 物理量（有單位有大小） The SI unit system 單位系統 How to express and manipulate numbers in physics calculations數字 Scientific notation科學表示法 Accuracy and significant figures準確度‘ 有效位數‘ Making quick estimates 估算 A universal strategy for solving physics problems如何解物理問題？ 如何做計算？ 數 字

Realms of Physics Physics provides a unified description of basic principles that govern physical reality.物理敘述自然遵循之基本原理 It’s convenient to divide physics into a number of different but related realms.分成6個互聯之主要成分 Here we consider six distinct realms:

The SI Unit System 表準國際單位系統 Provides precise definitions of seven fundamental physical quantities 7個基本物理量 Length: the meter長度 Time: the second時間 Mass: the kilogram質量 Electric current: the ampere電流 Temperature: the kelvin溫度 Amount of a substance: the mole摩爾數 Luminous intensity: the candela 流明 Supplementary units describe angles角度單位 Plane angle: the radian徑, 3.14159…徑(rad.)= 180度(degree) Solid angle: the steradian 立體角(ster.)

Operational Definitions 操作型的定義 Of the three most basic units— length, time, and mass — two are defined operationally, so their definitions can be implemented in any laboratory.長度時間質量其中的兩個才有這樣的定義才可以在任何實驗室裡操作 The meanings of both these definitions will become clearer as you advance in your study of physics:於此 日後會更明瞭 The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.1公尺=光在真空裡…………….秒行進的距離 The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.銫原子能階躍遷發的光其週期的………………..倍 The standard of mass is less satisfactory:質量的標準只依靠一個公斤原型 The kilogram is defined by the international prototype kilogram kept at the International Bureau of Weights and Measures at Sèvres, France.

Scientific Notation 科學表示法 The vast range of quantities that occur in physics are best expressed with ordinary-sized numbers multiplied by powers of 10: 31416.5 = 3.14165104 0.002718 = 2.71810–3 SI prefixes describe powers of 10: 10的倍數有縮寫 Every three powers of 10 gets a different prefix. Examples: 3.0109 W = 3.0 GW (3 gigawatts) 1.610–8 m = 16 nm (16 nanometers) 1012 kg = 1 Pg (1 petagram) GB(gigabyte) PB(petabyte)

Converting Units 單位轉換 Units matter! Measures of physical quantities must always have the correct units.單位是很重要的 物理量要有對的單位 Conversion tables (Appendix C of the textbook) give relations between physical quantities in different unit systems:不同單位系統之間的轉換 Convert units by multiplying or dividing so that the units you don’t want cancel, leaving only the units you do want.除掉不要的單位 留下要的單位 Example: Since 1 ft = 0.3048 m, a 5280-foot race (1 mile) is equal to Example: 1 kilowatt-hour (kWh, a unit of energy) is equivalent to 3.6 megajoules (MJ, another energy unit). Therefore a monthly electric consumption of 343 kWh amounts to

Significant Figures有效位數 The answer to the last example in the preceding slide is 1.23 GJ—not 1234.8 MJ or 1.2348 GJ as your calculator would show. That’s because the given quantity, 343 kWh, has only three significant figures. That means we know that the actual value is closer to 343 kWh than to 342 kWh or 344 kWh. If we had been given 343.2 kWh, we would know that the value is closer to 343.2 kWh than to 343.1 kWh or 343.3 kWh. In that case, the number given has four significant figures Significant figures tell how accurately we know the values of physical quantities.有效位數與準確度有關數字的計算不能增加有效位數 Calculations can’t increase that accuracy, so it’s important to report the results of calculations with the correct number of significant figures.

Rules for Significant Figures有效位數的規則 In multiplication and division, the answer should have the same number of significant figures as the least accurate of the quantities entering the calculation.乘除法 同最少有效位數者 Example: (3.1416 N)(2.1 m) = 6.6 N·m Note the centered dot, normally used when units are multiplied (the kWh is an exception). In addition and 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 the right of the decimal point.加減法時 要看小數點後的位數 最少者 Example: 3.2492 m – 3.241 = 0.008 m Note the loss of accuracy, with the answer having only one significant figure.

Estimation 估算 It’s often sufficient to estimate the answer to a physical calculation, giving the result to within an order of magnitude or perhaps one significant figure. 能估算出對的數量級！！ Estimation can provide substantial insight into a problem or physical situation. 快速掌握問題的核心 Example: What’s the United States’ yearly gasoline consumption?石油的年耗量？ There are about 300 million people in the U.S., so perhaps about 100 million cars (108 cars). A typical car goes about 10,000 miles per year (104 miles). A typical car gets about 20 miles per gallon. So in a year, a typical car uses (104 miles)/(20 miles/gallon) = 500 gal. So the United States’ yearly gasoline consumption is about (500 gal/car)(108 cars) = 51010 gallons. That’s about 201010 L or 200 GL.

A Strategy for Problem Solving 解方 The IDEA strategy consists of four broad steps.策略IDEA IDEA is not a “cookbook” but rather a general framework to organizing your path to the solution of a problem. IDEA是流程 The four IDEA steps are INTERPRET 了解問題 DEVELOP 設想解決的方法 EVALUATE 計算並解題 ASSESS 檢查結果

INTERPRET 了解問題： 找出有用的理論 主角 配角

DEVELOP 設想解決的方法： 畫圖 要用的數學方程式 需要的資料

EVALUATE 計算並解題： 先用符號進行計算 有需要再帶入數字

ASSESS 檢查結果： 單位對不對 數字的大小合不合理 特殊情形下對不對

Summary Together, the different realms of physics provide a unified description of basic principles that govern physical reality. The SI unit system provides precise definitions of fundamental physical quantities. Those with operational definitions can be reproduced anywhere. Handling the numbers that represent physical quantities involves Using scientific notation and SI prefixes Understanding significant figures Estimation The IDEA strategy provides a general framework for problem solving in physics.