2053 College Physics. Chapter 1 Introduction

Transcription

1 2053 College Physics Chapter 1 Introduction 1

2 Fundamental Quantities and Their Dimension Length [L] Mass [M] Time [T] other physical quantities can be constructed from these three 2

3 Systems of Measurement SI -- Systéme International agreed to in 1960 by an international committee main system used in this text also called mks for the first letters in the units of the fundamental quantities (meter, kilogram, second) 3

4 Systems of Measurements, cont cgs Gaussian system named for the first letters of the units it uses for fundamental quantities (centimeter, gram, second) US Customary everyday units often uses weight, in pounds, instead of mass as a fundamental quantity 4

5 Length Units SI meter, m cgs centimeter, cm US Customary foot, ft meter the distance traveled by light in a vacuum during a given time 5

6 Mass Units SI kilogram, kg cgs gram, g USC slug, slug kilogram, mass of a cylinder kept at the International Bureau of Weights and Measures, a standard of mass 6

7 Standard Kilogram 7

8 Time Units seconds, s in all three systems Certain number of oscillations of radiation from a cesium atom 8

9 US Official Atomic Clock 9

10 Table 1-1, 10 p3.

11 Table 1-2, 11 p.3

12 Table 1-3, 12 p.3

13 Prefixes Prefixes correspond to powers of 10 Each prefix has a specific abbreviation 13

14 Structure of Matter Matter is made up of molecules the smallest division that is identifiable as a (chemical) substance Molecules are made up of atoms correspond to elements (as in periodic table of elements) 14

15 More structure of matter Atoms are made up of nucleus, very dense, contains protons, positively charged, heavy neutrons, no charge, about same mass as protons protons and neutrons are made up of quarks nucleus is orbited by electrons, negatively charges, light Quarks and electrons are viewed as fundamental particle, no structure (or we have not discovered it yet keep looking) 15

16 Structure of Matter 16

17 Dimensional Analysis Technique to check the correctness of an equation, or correctness of a solution Dimensions (length, mass, time, combinations) can be treated as algebraic quantities add, subtract, multiply, divide Both sides of equation must have the same dimensions (cannot compare apples to oranges in an equation ) 17

18 Dimensional Analysis, cont. Cannot give numerical factors: this is its limitation Dimensions of some common quantities are listed in Table

19 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 19

20 Significant Figures A significant figure is one that is reliably known Accuracy number of significant figures When multiplying or dividing two or more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate 20

21 Operations with Significant Figures When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum If the last digit to be dropped is less than 5, drop the digit If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1 21

22 Conversions 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 See the table on the class web site for an extensive list of conversion factors Example: want to convert inches to cm 2.54 cm 15.0 in = 38.1cm 1in 22

23 Examples of various units measuring a quantity 23

24 Order of Magnitude Crude approximation Viewed as an estimate Order of magnitude is the power of 10 that applies 24

25 Table 1-1, 25 p3.

26 Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels 26

27 Types of Coordinate Systems Cartesian (also called rectangular) Plane polar 27

28 Cartesian coordinate system Also called rectangular coordinate system x- and y- axes Points are labeled (x,y) 28

29 Plane polar coordinate system Origin and reference line are noted Point is distance r from the origin in the direction of angle θ, counterclockwise from reference line Points are labeled (r,θ) 29

30 Trigonometry Review sin θ = cos θ = tan θ = opposite side hypotenuse adjacent side hypotenuse opposite side adjacent side 30

31 More Trigonometry Pythagorean Theorem r = x + y To find an angle, you need the inverse trig function for example, if sinθ=0.707, then θ 1 = sin = 45 Be sure your calculator is set appropriately for degrees or radians 31

32 Check Pythagorean Theorem: 5²=4²+3², or 25=16+9, Also 3=5 sinθ, or 4=5 cosθ Fig. P1-43, 32 p.21

33 Fig. 1-10, 33 p.17

34 Fig. P1-39, 34 p.21

35 Fig. 1-8, 35 p.15

36 Fig. P1-41, 36 p.21