Transcript uncertainty
Unit I - notes Significant Digits also called Significant Figures Significance is about precision of measurement. Non-zero #s are always significant. Zeros: initial – never; internal – always; final – sometimes – if zero is not there as a place holder then it is measured & significant. Measure to uncertainty – that is, the first digit you must estimate. Mini lab Ex. 1 – measure the width of a block of wood & give the answer in an appropriate # of sign. dig. ( in cm) Ex. 2 – measure the mass of a nickel. ( in g) Precision vs. Accuracy Mini lab Measure the width of the block of wood provided a) from the end of the ruler; b) from the beginning of the scale. Which measurement is more accurate? Which is more precise? Math & sign. Dig. When doing math & sign. dig weakest link. Least precise measure. Explain. Dimensional Analysis Algebra is doing the same things with letters you did with #s. Dimensional analysis is doing the same things with units (dimensions) you did with #s & letters. Dimensional analysis is analyzing dimensions (units) to determine what mathematical operation should be done with the #s. MKS/CGS 2 systems of measurement in physics MKS = meter kilogram second CGS = centimeter gram second Never hybridize the 2 – opportunity will be given from time to time for you to make that mistake so be on guard. You text does not deal w/ this issue but I will. MKS most frequently used CGS useful mainly for very small objects – ex. bugs or spiders. Metric Conversion km … m.dm.cm.mm…m…nm.Å square units – how many in2 in a ft2? cubic units Order of Magnitude - estimations Order of magnitude is the rounded power of 10 of a #expressed in scientific notation. Useful in making quick estimates. What is the order of mag. of each of the following: # of inches in foot? # of molecules in a mole? Mass of a proton? Mass of an e-? (in kg) Volume of a block of wood? CGS units of vol. Ways things can be related ? Direct = linear: annotated in science as y a x (a = proportional) Inverse: y a 1/x Quadratic: y a x2 Inverse square: y a 1/x2 In physics, @ our level @ least, we can write equations for linear or direct relationships only – therefore, we will endeavor to get equations in linear form. Handout problem & can lab which will follow will establish this point. When we write these equations we write them in terms variables given not x & y. See p. 19 + 16 fig. 1-16. The equations should be written L = .08 cm/gxm + 13.7 cm not y = .08 cm/g.x + 13.7 cm Functions What does it mean to say that a variable is a function of another variable? = physically dependent upon. Thus the terms independent variable (the x variable) & dependent variable (the y variable). In math, f(x) = x; b/c y is a function of x, that is, y is physically dependent upon x. y vs. x follows from this. This annotation seems to be a science thing not a math thing. Have you seen the annotation “y vs. x” before? Lab Report Format Purpose: Corresponds to ”Problem” in the scientific method. What are we attempting to determine in the investigation. Should address independent & dependent variables. Data table - discussed on the next slide. We will do most data tables on ExCel spreadsheets. Calculations - when we do labs we will attempt to get the computer to do most of the calculations. However, you will be required to show 1 calculation of each type in a lab report. Conclusion - interpretation of the data. Generally you will be given questions to answer as well. Data tables 1. 2. 3. 4. Stand alone – thus a title & that title should help make it stand alone. Should contain all data – known, measured, & calculated. Ex. 1. What data would be collected for determining the density of 10 ml (would it matter what volume we chose?) of HCl? Get with your study buddy & write a procedure. Talk it out. Data should be organized based on math principles not chronology. How would one organize the data for Ex. 1 above? Get with your study buddy & prepare a data table for these data. In the case of data to be graphed, data should be in x,y format as you have learned in math. What is the dep. variable in Table 1-4 p. 18? Problem 25 p. 19? I believe data tables for graphed data always ought to be vertically oriented! (& since I so believe that is the way we will do it – ziiinngggggg!) Should include units & the units should be in the headers not with the individual data. Rationale. Graphing See rules of graphing p.16 Add to those rules – draw plotted point within an open geometric figure. Use a different figure for each line if you are plotting more than one line on the same graph. Legend Interpretation of rule 4 - use as much of the page of graph paper as possible - more than half in each direction. Origin of all graphs is 0,0 but see jagged line fig. 1-15. Effectively some of the #s can be omitted along 1 or both axes. What are the increments along each axes on fig. 1-15? Notice that the #s .5 through 13 are omitted along the y axis. Graphs may be oriented portrait or landscape. Best fit/principle of uniformitarianism – rule # 8 graphing procedure p. 16. Slope has dimensions (or not) – see p. 19. slope = .08 cm/g not just .08 There is more to learn about slope – stay tuned! Post lab – C vs d In physics & (math as it turns out) slope is often a meaningful. From the lab we also learn a definition for p – what is it? Post lab - Can lab The point of this lab is using what we know about how various relationships graph to get data in a form we can write an equation, that is in linear form. From the original graph we could see we had an inverse relationship. Reason told us that we had a quadratic relationship b/c drain time was really a function of area (A=pr2). Putting these 2 together led us to graphing t vs 1/d2. This, in turn, gave us a linear relationship which allowed us to write an equation in the y = mx + b format. Physics What is your current view of what physics is? The study of matter & motion. Notice the 2 aspects matter & motion. What is matter? Anything that has mass. Therefore, physics is the study of objects & their motion (or perhaps lack of it). c v The Realm of Physics ? Relativistic Quantum Mechanics Relativistic Physics Quantum Mechanics Classical Physics 10-14 m 10-10 m Size Classical Physics Ordinary sized objects Ordinary speeds atoms --- celestial bodies Foundational to understanding modern physics. Modern Physics Quantum Mechanics extremely small objects ordinary speeds Relativistic Physics ordinary sized objects speeds approaching “c” Relativistic Quantum Mechanics extremely small objects speeds approaching “c” Topics studied in Physics Vectors Displacement Velocity Acceleration Force gravitational electrical nuclear Momentum Energy Electricity & magnetism Waves & optics Heat & behavior of gases