IB+DP+Topic+1+Measurement+and+Uncertainties

1.1 Measurement in Physics //Essential idea:// Since 1948, the Systeme International d'Unites (SI) has been used as the preferred language of science and technology across the globe and reflects current best measurement practice.

Common terminology: Since the 18th century, scientists have sought to establish common systems of measurements to facilitate international collaboration across science disciplines and ensure replication and comparability of experimental findings. (1.6) Improvement in instrumentation: An improvement in apparatus and instrumentation, such as using the transition of cesium-133 atoms for atomic clocks, has led to more refined definitions of standard units. (1.8) Certainty: Although scientists are perceived as working towards finding “exact” answers, the unavoidable uncertainty in any measurement always exists. (3.6)
 * // Nature of science: //**

• Fundamental and derived SI units • Scientific notation and metric multipliers • Significant figures • Orders of magnitude • Estimation
 * // Understandings: //**

• Using SI units in the correct format for all required measurements, final answers to calculations and presentation of raw and processed data • Using scientific notation and metric multipliers • Quoting and comparing ratios, values and approximations to the nearest order of magnitude • Estimating quantities to an appropriate number of significant figures
 * // Applications and skills: //**

• Aim 2 and 3: this is an essential area of knowledge that allows scientists to collaborate across the globe • Aim 4 and 5: a common approach to expressing results of analysis, evaluation and synthesis of scientific information enables greater sharing and collaboration
 * // Aims: //**

• Metric (SI) multipliers can be found on page 5 of the physics data booklet
 * // Data booklet reference: //**

resource from [] [|SI Unit] from alevelnotes.com

Image from www.suggest-keywords.com
 * Prefix **

What are the symbols of the following prefixes: yotta, zetta, exa, peta, tera, pico, femto, atto, zepto, yocto? Y, Z, E, P, T, p, f, a, z, y
 * Question: **


 * [|Significant figures] ** from www.rpi.edu/dept/phys/Dept2/APPhys1

The significant figures of a number express a magnitude to a specified degree of accuracy.

1. Each of the digit of a number that is used to express it to the required degree of accuracy, starting from the first nonzero digit. 2. The first non zero digit is the first significant digit. After the first significant digit, everything is significant digit.

__//Q. Round this number to 3 s.f.//__ a. 0.003672195 First significant figure = first digit that is non zero: 3 >> 0.00307

b. 13523.57 First significant figure = first digit that is non zero: 1 >> 13900 Image from http://chemsite.lsrhs.net/measurement/sig_fig.html

Significant figures practice 20 questions [|Significant fiqures drill]
 * Rules for significant figures.pdf**

Orders of magnitude and estimates
The order of magnitude is the nearest power of ten. It gives the **estimation**, scale or the **relative size** of something such as distance, mass and time.
 * media type="youtube" key="8Are9dDbW24" width="560" height="315" || media type="youtube" key="bhofN1xX6u0" width="560" height="315" ||
 * [|Cosmic Eye] (Original HD Landscape Version 2018) [|Danail Obreschkow] published on 30 Apr 2018 || [|Powers of Ten - Ultimate Zoom] (micro-macro - Imax combined) published on 11 Feb 2011 ||

__//Class activity//__ State the ranges of magnitude of distances, masses and times that occur in the universe, from smallest to greatest. State ratios of quantities as differences of orders of magnitude. Estimate approximate values of everyday quantities to two significant figures and/or to the nearest order of magnitude.

3 things that you already knew, 2 things you discovered and 1 thing you would like to know further. media type="youtube" key="c9VYx_dJEDs" width="560" height="315" [|Size Comparison of the Universe] 2018 [|Times Infinity] Published on 9 Jan 2018 Distances: from 10 –15 m to 10 +25 m (sub-nuclear particles to extent of the visible universe). Masses: from 10 –30 kg to 10 +50 kg (electron to mass of the universe). Times: from 10 –23 s to 10 +18 s (passage of light across a nucleus to the age of the universe).
 * //3-2-1 activity//**
 * //After checking the ranges of magnitude of distances, masses and times, please watch the videoclip below and write;//**

SIZE OF THE UNIVERSE INFOGRAPHIC - from onlinescholing.net Scale of the Universe - link to awesome presentation about scale [|UNIVERSCALE] - link to cool website by Nikon   **//Homework: Do all odd number questions on page 3, 4, 6 and 7.//** **//Classwork: Complete the rest of even number questions in your notebook.//**

[|BIG NUMBERS AND STUFF PART 1] Richard Feynman talks about big numbers...  [|BIG NUMBERS AND STUFF PART 2] Feynman talks about black holes and quasars...  <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 13px; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 13px; text-align: left;">Lec 01: [|Units, Dimensions, and Scaling Arguments] | 8.01 Classical Mechanics (Walter Lewin)published on 9 Dec 2014 [|10 Embarrassing Architectural Failures] Published on 7 Sep 2013

1.2 Uncertainties and errors **//Essential idea://** Scientists aim towards designing experiments that can give a “true value” from their measurements, but due to the limited precision in measuring devices, they often quote their results with some form of uncertainty.

Uncertainties: “All scientific knowledge is uncertain… if you have made up your mind already, you might not solve it. When the scientist tells you he does not know the answer, he is an ignorant man. When he tells you he has a hunch about how it is going to work, he is uncertain about it. When he is pretty sure of how it is going to work, and he tells you, ‘This is the way it’s going to work, I’ll bet,’ he still is in some doubt. And it is of paramount importance, in order to make progress, that we recognize this ignorance and this doubt. Because we have the doubt, we then propose looking in new directions for new ideas.” (3.4) Feynman, Richard P. 1998. The Meaning of It All: Thoughts of a Citizen-Scientist. Reading, Massachusetts, USA. Perseus. P 13.
 * // Nature of science: //**

• Random and systematic errors • Absolute, fractional and percentage uncertainties • Error bars • Uncertainty of gradient and intercepts
 * // Understandings: //**

• Explaining how random and systematic errors can be identified and reduced • Collecting data that include absolute and/or fractional uncertainties and stating these as an uncertainty range (expressed as: best estimate ± uncertainty range) • Propagating uncertainties through calculations involving addition, subtraction, multiplication, division and raising to a power • Determining the uncertainty in gradients and intercepts
 * // Applications and skills: //**

• Aim 4: it is important that students see scientific errors and uncertainties not only as the range of possible answers but as an integral part of the scientific process • Aim 9: the process of using uncertainties in classical physics can be compared to the view of uncertainties in modern (and particularly quantum) physics
 * // Aims: //**


 * // Data booklet reference: //**

Question 1: “ What is the difference between a random and systematic error, and what is uncertainty? ” __** Error **__ is the __d ifference __ between the measured value and the ‘true value’ of the thing being measured.
 * __ Uncertainty __** is a quantification of the doubt about the measurement result.

Question 2: “ Why is it important to understand the level of uncertainty in scientific investigation and why is it important to verify this uncertainty? ”








 * Explain** how the effects of random errors may be reduced.
 * Calculate** quantities and results of calculations to the appropriate number of significant figures.
 * State** uncertainties as absolute, fractional and percentage uncertainties.

EXPERIMENT
 * 1 cm 3 of water has a mass of 1 gram.
 * Investigate how accurate two pieces of equipment are by measuring 20 cm 3 of water and see which instrument is most accurate.
 * The more accurately the volume is measured the closer to 20 grams the water wil become.
 * Measuring instrument || Mass of beaker || Mass of beaker and water || Calculated mass of water || How close the result was to 20g ||
 * Measuring cylindar ||  ||   ||   ||   ||
 * Burette ||  ||   ||   ||   ||
 * Beaker (small) ||  ||   ||   ||   ||
 * Beaker (large) ||  ||   ||   ||   ||

EXAMPLE 1: Equipment error in percentages: (Half of the smallest measurement/measured value) x 100 = % When using a ruler, the smallest measurement is 0.1 cm and the half of the smallest measurement is __ 0.05 __cm.



Image **UNCERTAINTIES Summary of Basic Rules** from

PRECISION (How close together a series of measurements are to each other) Precision is the degree to which several measurements provide answers very close to each other. It is an indicator of the scatter in the data.The lesser the scatter, higher the precision. ACCURACY (How close a measured value is to true value) Accuracy describes the nearness of a measurement to the standard or true value, i.e., a highly accurate measuring device will provide measurements very close to the standard, true or known values. Example: in target shooting a high score indicates the nearness to the bull's eye and is a measure of the shooter's accuracy.
 * Precision** //vs// **Accuracy from Indiana University**

The first diagram shows you a dart board in which a target shooter was precise but not accurate. The third in which the shooter was accurate but not precise. What would the target look like if you were a. accurate and precise or b. neither accurate nor precise? The pictures given below clearly describe Precision and Accuracy.
 * [|Image from]** www.cqeacademy.com

Your turn to define accuracy, precision and resolution:
 * <span style="font-family: verdana,helvetica,arial; font-size: 13.3333px;">**Accuracy:** The error between the real and measured value.
 * <span style="font-family: verdana,helvetica,arial; font-size: 13.3333px;">**Precision:** The random spread of measured values around the average measured values.
 * <span style="font-family: verdana,helvetica,arial; font-size: 13.3333px;">**Resolution:** The smallest to be distinguished magnitude from the measured value.



[|A Beginner's Guide to Uncertainty of Measurement] by Stephanie Bell [|Examples of uncertainty calculations] [|Uncertainties and Error Propagation] from rit,edu **PRACTICE QUESTIONS**

[|IB DP Physics Uncertainty worksheet] from [|HTP IB Physics]

1.3 Vectors and scalars Models: First mentioned explicitly in a scientific paper in 1846, scalars and vectors reflected the work of scientists and mathematicians across the globe for over 300 years on representing measurements in three-dimensional space. (1.10)
 * // Nature of science: //**

//** Understandings: **// • Vectors and scalar quantities • combination and resolution of vectors

• Solving vector problems graphically and algebraically Guidance • Resolution of vectors will be limited to two perpendicular directions • Problems will be limited to addition and subtraction of vectors and the multiplication and division of vectors by scalars
 * // Applications and skills: //**

• Aim 2 and 3: this is a fundamental aspect of scientific language that allows for spatial representation and manipulation of abstract concepts
 * // Aims: //**


 * // Data booklet reference: //**

**Examples of vectors and scalars**
velocity acceleration force momentum weight electric field strength magnetic field strength gravitational field strength angular velocity || distance speed mass time density electric potential difference electric charge gravitational potential temperature volume, density work, energy, power || [|Scalar and Vector Quantities] image from www.grc.nasa.gov
 * **Vectors** || **Scalars** ||
 * A quantity that has magnitude, unit and direction || A quantity with magnitude only and unit ||
 * displacement

[|Vectors worksheet from mathwarehouse]


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 * [|max/min gradients of a graph in Loggerpro] [|MadDogScience] Published on 14 Oct 2012 7min || [|B Physics Topic 1 Data Analysis #1(a) - (b)(i)] [|Daniel M] Published on 26 Aug 2015 10 min || [|IB Physics Topic 1 Data Analysis #1(b)(ii)]-end [|Daniel M] Published on 26 Aug 2015 || [|IB Physics Topic 1 Data Analysis #2] [|Daniel M] Published on 25 Aug 2015 ||


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 * [|IB Physics Topic 1 Data Analysis #3] [|Daniel M] Published on 26 Aug 2015 || [|IB Physics Topic 1 Data Analysis #4] [|Daniel M] Published on 26 Aug 2015 10 min || [|1-2 Data Analysis Slopes, Uncertainties, and Fits] [|IBMathandPhysics] Published on 23 May 2016 || [|1-2 Units and Uncertainty in Data Analysis] [|IBMathandPhysics] Published on 23 May 2016 ||