Unit I - notesUnit I - notes

Significant Digits also called Significant Digits also called Significant FiguresSignificant Figures

Significance is about precision of measurement.Significance is about precision of measurement. Non-zero #s are always significant.Non-zero #s are always significant. Zeros: initial – never; internal – always; Zeros: initial – never; internal – always;

final – sometimes – if zero is not there as a place final – sometimes – if zero is not there as a place holder then it is measured & significant.holder then it is measured & significant.

Measure to Measure to uncertaintyuncertainty – that is, the first digit you – that is, the first digit you must estimate.must estimate.

Mini labMini lab Ex. 1 – measure the width of a block of wood & give Ex. 1 – measure the width of a block of wood & give

the answer in an appropriate # of sign. dig. ( in cm)the answer in an appropriate # of sign. dig. ( in cm) Ex. 2 – measure the mass of a nickel. ( in g)Ex. 2 – measure the mass of a nickel. ( in g)

Precision vs. AccuracyPrecision vs. Accuracy

Mini labMini lab Measure the width of the block of Measure the width of the block of

wood provided a) from the end of the wood provided a) from the end of the ruler; b) from the beginning of the ruler; b) from the beginning of the scale. Which measurement is more scale. Which measurement is more accurate? Which is more precise?accurate? Which is more precise?

Math & sign. Dig.Math & sign. Dig.

When doing math & sign. dig - When doing math & sign. dig - weakest link. Least precise measure. weakest link. Least precise measure. Explain.Explain.

Dimensional AnalysisDimensional Analysis

Algebra is doing the same things Algebra is doing the same things with letters you did with #s.with letters you did with #s.

Dimensional analysis is doing the Dimensional analysis is doing the same things with units (dimensions) same things with units (dimensions) you did with #s & letters.you did with #s & letters.

Dimensional analysis is analyzing Dimensional analysis is analyzing dimensions (units) to determine what dimensions (units) to determine what mathematical operation should be mathematical operation should be done with the #s.done with the #s.

MKS/CGSMKS/CGS 2 systems of measurement in physics2 systems of measurement in physics MKS = meter kilogram secondMKS = meter kilogram second CGS = centimeter gram secondCGS = centimeter gram second Never hybridize the 2 – Never hybridize the 2 – opportunity will be given from opportunity will be given from

time to time for you to make that mistake so be on guard.time to time for you to make that mistake so be on guard.

You text does not deal w/ this issue but I You text does not deal w/ this issue but I will.will.

MKS most frequently usedMKS most frequently used CGS useful mainly for very small objects – CGS useful mainly for very small objects –

ex. bugs or spiders.ex. bugs or spiders.

Metric ConversionMetric Conversion

km … m.dm.cm.mm…km … m.dm.cm.mm……nm.Å…nm.Å square units – how many insquare units – how many in22 in a ft in a ft22?? cubic units cubic units

Order of magnitude is the rounded Order of magnitude is the rounded power of 10 of a #expressed in power of 10 of a #expressed in scientific notation.scientific notation.

Useful in making quick estimates.Useful in making quick estimates. What is the order of mag. of each of the following:What is the order of mag. of each of the following: # of inches in foot?# of inches in foot? # of molecules in a mole?# of molecules in a mole? Mass of a proton?Mass of a proton? Mass of an e-? (in kg)Mass of an e-? (in kg) Volume of a block of wood? CGS units of vol.Volume of a block of wood? CGS units of vol.

Order of Magnitude - estimationsOrder of Magnitude - estimations

Ways things can be relatedWays things can be related ?? Direct = linear: annotated in science as y Direct = linear: annotated in science as y x ( x ( = =

proportional)proportional) Inverse: y Inverse: y 1/x 1/x Quadratic: y Quadratic: y x x22

Inverse square: y Inverse square: y 1/x 1/x22

In physics, @ our level @ least, we can write equations for In physics, @ our level @ least, we can write equations for linear or direct relationships only – therefore, we will linear or direct relationships only – therefore, we will endeavor to get equations in linear form. Handout problem endeavor to get equations in linear form. Handout problem & can lab which will follow will establish this point.& can lab which will follow will establish this point.

When we write these equations we write them in terms When we write these equations we write them in terms variables given not x & y. See p. 19 + 16 fig. 1-16. The variables given not x & y. See p. 19 + 16 fig. 1-16. The equations should be written L = .08 cm/gxm + 13.7 cm notequations should be written L = .08 cm/gxm + 13.7 cm not

y = .08 cm/g.x + 13.7 cmy = .08 cm/g.x + 13.7 cm

FunctionsFunctions What does it mean to say that a variable is What does it mean to say that a variable is

a function of another variable?a function of another variable? = physically dependent upon. = physically dependent upon. Thus the terms independent variable (the Thus the terms independent variable (the

x variable) & dependent variable (the y x variable) & dependent variable (the y variable).variable).

In math, f(x) = x; b/c y is a function of x, In math, f(x) = x; b/c y is a function of x, that is, y is physically dependent upon x.that is, y is physically dependent upon x.

y vs. x follows from this. This annotation y vs. x follows from this. This annotation seems to be a science thing not a math seems to be a science thing not a math thing. Have you seen the annotation “y thing. Have you seen the annotation “y vs. x” before? vs. x” before?

Lab Report FormatLab Report Format Purpose: Corresponds to ”Problem” in the Purpose: Corresponds to ”Problem” in the

scientific method. What are we attempting to scientific method. What are we attempting to determine in the investigation. Should address determine in the investigation. Should address independent & dependent variables.independent & dependent variables.

Data table - discussed on the next slide. We will Data table - discussed on the next slide. We will do most data tables on ExCel spreadsheets.do most data tables on ExCel spreadsheets.

Calculations - when we do labs we will attempt to Calculations - when we do labs we will attempt to get the computer to do most of the calculations. get the computer to do most of the calculations. However, you will be required to show 1 However, you will be required to show 1 calculation of each type in a lab report.calculation of each type in a lab report.

Conclusion - interpretation of the data. Generally Conclusion - interpretation of the data. Generally you will be given questions to answer as well.you will be given questions to answer as well.

Data tablesData tables

1.1. Stand alone – thus a title & that title should help make it Stand alone – thus a title & that title should help make it stand alone.stand alone.

2. 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.

3.3. Data should be organized based on math principles not Data should be organized based on math principles not chronology. How would one organize the data for Ex. 1 chronology. How would one organize the data for Ex. 1 above? Get with your study buddy & prepare a data above? Get with your study buddy & prepare a data table for these data. In the case of data to be graphed, 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. 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 What is the dep. variable in Table 1-4 p. 18? Problem 25 p. 19? I believe data tables for graphed data always p. 19? I believe data tables for graphed data always ought to be vertically oriented! (& since I so believe that ought to be vertically oriented! (& since I so believe that is the way we will do it – ziiinngggggg!) is the way we will do it – ziiinngggggg!)

4.4. Should include units & the units should be in the headers Should include units & the units should be in the headers not with the individual data. Rationale.not with the individual data. Rationale.

GraphingGraphing See rules of graphing p.16See rules of graphing p.16 Add to those rules – draw plotted point within an open geometric figure. Use a 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 different figure for each line if you are plotting more than one line on the same graph.graph.

LegendLegend Interpretation of rule 4 - use as much of the page of graph paper as possible - Interpretation of rule 4 - use as much of the page of graph paper as possible -

more than half in each direction.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 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 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.on fig. 1-15? Notice that the #s .5 through 13 are omitted along the y axis.

Graphs may be oriented portrait or landscape.Graphs may be oriented portrait or landscape. Best fit/principle of uniformitarianism – rule # 8 graphing procedure p. 16.Best fit/principle of uniformitarianism – rule # 8 graphing procedure p. 16. Slope has dimensions (or not) – see p. 19.Slope has dimensions (or not) – see p. 19. slope = .08 cm/g not just .08 slope = .08 cm/g not just .08

There is more to learn about slope – stay tuned!There is more to learn about slope – stay tuned!

Post lab – C vs dPost lab – C vs d

In physics & (math as it turns out) In physics & (math as it turns out) slope is often a meaningful.slope is often a meaningful.

From the lab we also learn a From the lab we also learn a definition for definition for – what is it? – what is it?

Post lab - Can labPost lab - Can lab The point of this lab is using what we know The point of this lab is using what we know

about how various relationships graph to about how various relationships graph to get data in a form we can write an get data in a form we can write an equation, that is in linear form. From the equation, that is in linear form. From the original graph we could see we had an original graph we could see we had an inverse relationship. Reason told us that inverse relationship. Reason told us that we had a quadratic relationship b/c drain we had a quadratic relationship b/c drain time was really a function of area (A=time was really a function of area (A=rr22). ). Putting these 2 together led us to graphing Putting these 2 together led us to graphing t vs 1/dt vs 1/d22. This, in turn, gave us a linear . This, in turn, gave us a linear relationship which allowed us to write an relationship which allowed us to write an equation in the y = mx + b format.equation in the y = mx + b format.

PhysicsPhysics What is your current view of what What is your current view of what

physics is?physics is? The study of matter & motion.The study of matter & motion. Notice the 2 aspects matter & motion.Notice the 2 aspects matter & motion. What is matter?What is matter? Anything that has mass.Anything that has mass. Therefore, physics is the study of Therefore, physics is the study of

objects & their motion (or perhaps lack objects & their motion (or perhaps lack of it).of it).

The Realm of PhysicsThe Realm of Physics

?

Relativistic QuantumMechanics

Relativistic Physics

Quantum Mechanics Classical Physics

v

Size

c

10-14 m 10-10 m

Classical PhysicsClassical Physics

Ordinary sized objectsOrdinary sized objects Ordinary speedsOrdinary speeds

atoms ---atoms --- celestial bodies celestial bodies

Foundational to understanding Foundational to understanding modern physics.modern physics.

Modern PhysicsModern Physics Quantum MechanicsQuantum Mechanics

extremely small objectsextremely small objects

ordinary speedsordinary speeds

Relativistic PhysicsRelativistic Physics

ordinary sized objectsordinary sized objects

speeds approaching “c”speeds approaching “c”

Relativistic Quantum MechanicsRelativistic Quantum Mechanics

extremely small objectsextremely small objects

speeds approaching “c”speeds approaching “c”

Topics studied in PhysicsTopics studied in Physics

Vectors Vectors DisplacementDisplacement VelocityVelocity AccelerationAcceleration ForceForce gravitationalgravitational

electricalelectrical

nuclearnuclear

MomentumMomentum EnergyEnergy

Electricity & Electricity & magnetismmagnetism

Waves & opticsWaves & optics Heat & behavior of Heat & behavior of

gasesgases