2: Measurements Lab
- Page ID
- 519407
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This experiment will introduce you to using a few laboratory tools and reporting data appropriately.
- 2.1: Required Supplies
- This page outlines the necessary supplies for the measurements experiment.
- 2.2: Background - Significant Figures in Measurements
- This page explains the distinction between counting discrete objects and measuring continuous quantities, focusing on precision. It states that counted numbers are exact, while measurements involve uncertainty, especially in the last digit. The concept of significant figures is introduced, with practical examples such as reading a graduated cylinder and using a balance and ruler to illustrate proper estimation techniques and the limitations of precision across different measuring devices.
- 2.3: Background - Counting Significant Figures and Using Scientific Notation
- This page explains significant figures in measurements, differentiating exact numbers (with infinite significant figures) from measured values (limited by estimation). It outlines rules for identifying significant zeros and emphasizes using scientific notation for clarity in representing measurements. Examples effectively illustrate proper formatting.
- 2.4: Background - Significant Figures in Calculations
- This page discusses the importance of significant figures in calculations to ensure measurement precision. It specifies rules for using significant figures in multiplication, division, addition, and subtraction, emphasizing that results should reflect the least number of significant figures or decimal places from the inputs. It also outlines the rounding guidelines based on the digits following the significant figures.
- 2.5: Background - Percent Error, Reporting Data, and Density
- This page covers percent error as a way to assess measurement accuracy using U.S. coins, detailing the calculation formula and the need for proper units. It also defines density as mass per unit volume, explains calculation methods, and describes techniques for measuring volume for various objects, including displacement and geometric formulas, with a focus on an experimental context involving coins.
- 2.6: Procedure
- This page provides a detailed guide for data collection tasks involving the measurement of coins and water density. Students are directed to measure the mass and diameter of a penny and nickel, calculate percent errors, measure the coins' height, and assume cylindrical volume calculations. Additionally, it includes instructions for assessing volume displacement with water and methods for measuring water's mass and density, accompanied by percent error calculations for density.
- 2.7: Data
- This page contains the data tables to be completed by students for the Measurements Lab.
- 2.8: Calculations
- This page contains a list of calculations needed to complete the data tables.
- 2.9: Lab Questions
- This page contains the questions students need to answer for the Measurements Lab.