From 8c209d1ae4959ffc6abf77a35f172da1c9c9fd2d Mon Sep 17 00:00:00 2001 From: KeshavAnandCode Date: Sat, 15 Nov 2025 23:55:07 -0600 Subject: [PATCH] Initial Push --- .gitignore | 35 ++++ AMSTUD Paper/main.pdf | Bin 0 -> 51709 bytes AMSTUD Paper/main.tex | 138 ++++++++++++++ AMSTUD Paper/references.bib | 151 +++++++++++++++ PhysicsGravitationLabReport/Sketch.pdf | Bin 0 -> 6984 bytes PhysicsGravitationLabReport/main.pdf | Bin 0 -> 135047 bytes PhysicsGravitationLabReport/main.tex | 228 +++++++++++++++++++++++ PhysicsInclinedPlaneLabReport/Sketch.pdf | Bin 0 -> 6984 bytes PhysicsInclinedPlaneLabReport/main.pdf | Bin 0 -> 124950 bytes PhysicsInclinedPlaneLabReport/main.tex | 190 +++++++++++++++++++ 10 files changed, 742 insertions(+) create mode 100644 .gitignore create mode 100644 AMSTUD Paper/main.pdf create mode 100644 AMSTUD Paper/main.tex create mode 100644 AMSTUD Paper/references.bib create mode 100644 PhysicsGravitationLabReport/Sketch.pdf create mode 100644 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+%Fancy-header package to modify header/page numbering (insert last name) +% +\usepackage{fancyhdr} +\pagestyle{fancy} +\lhead{} +\chead{} +\rhead{Anand \thepage} +\lfoot{} +\cfoot{} +\rfoot{} +\renewcommand{\headrulewidth}{0pt} +\renewcommand{\footrulewidth}{0pt} +%To make sure we actually have header 0.5in away from top edge +%12pt is one-sixth of an inch. Subtract this from 0.5in to get headsep value +\setlength\headsep{0.333in} + +\usepackage[style=mla]{biblatex} +\addbibresource{references.bib} % your .bib file name + + +\begin{document} +\begin{flushleft} + +%%%%First page name, class, etc +Keshav Anand\\ +Russell/Alexander\\ +American Studies\\ +31 October 2025\\ + + +%%%%Title +\begin{center} +A Synthesis of Research on the Efficacy of Narrative Assessment in Secondary Education +\end{center} + + +%%%%Changes paragraph indentation to 0.5in +\setlength{\parindent}{0.5in} +%%%%Begin body of paper here + + +%TODO: ADD MLA PAGES FOR ALL CITATIONS + +Assessment remains a critical component of education, serving as a means to evaluate student progress and mastery over a given subject. +Traditionally, quantitative assessments (e.g. multiple-choice tests, standardized exams) have been preferred for their objectivity and ease of grading \parencite{Lamiell2018}. +Even today, many standardized tests and important exams are primarily quantitative in nature, with American exams such as the SAT and ACT having recently undergone changes +to remove or optionalize essay components \parencite{McGrath2021_SATessay,Semos2024_ACTwriting}. While quantitative assessments have their merits, +their defined scope limits their ability to capture a student's critical thinking and creativity \parencite{KU200970}. +Conversely, narrative assessments (e.g. essays, projects, presentations) with subjective grading +\footnote{Structured written responses scored with a non-flexible rubric, such as numerical math problems or essay questions with rigid crieteria, are not considered narrative assessments in this context.} +allow students to express +understanding in a more holistic and authentic manner \parencite{KU200970}. Recent developments in educational trends due to the rise of Artificial Intelligence (AI) +following the COVID-19 pandemic have led many educators to reconsider their methods, accelerating changes in curriculum and assessment \parencite{Kamalov2023New}. +Hence, this paper synthesizes research on the efficacy of subjective narrative as +sessment in secondary education when compared +to traditional quantitative assessments.\\ + +A central advantage of narrative assessments is their ability to allow students to demonstrate higher-order thinking skills. +While quantitative assessments often reward students for accurate recall of facts, +narrative assessments provide a means to distinguish a satisfactory understanding from a nuanced comprehension. +This is particularly important to distinguish gifted students; while a standard 4-option multiple-choice question gives full credit for knowing the tested concept (and a 25\% change of guessing correctly), +both the student who barely understands a concept and the student who has mastered it receive the same score \parencite{Liu2023Multiple-choice}. +University professors second this notion, agreeing that multiple-choice questions (MCQs) are limited in their ability to assess higher-order cognition \parencite{Liu2023Multiple-choice}. +In the context of a secondary education setting, the impact of narrative assessments are particularly pronounced due to the focus on knowledge retention. +Failing to properly distinguish between levels of understanding can inadvertently incentivize surface-level memorization, +where students fail to recall basic information learned in a class after the subject is no longer tested \parencite{Kooloos2019The}. +In fact, \cite{Kooloos2019The} found that students lost about 33\% of gained knowledge when learning is geared towards short-term recall. +Known as the "forgetting curve," this rapid loss of information can only be mitigated by constant revisiting of material or understanding concepts at a deeper level \parencite{Kooloos2019The}. +Due to the open-ended nature of narrative assessments, students are encouraged to engage with material more deeply, +and when educators reward complex understanding, students are incentivized to internalize concepts rather than memorize facts \parencite{KU200970}. +Additionally, these benefits are compounded in secondary education as it promotes creativity, which is beneficial for growth and development at younger ages \parencite{Redó2021Dimensions}. +When considering that growth and development is the sole focus of secondary education itself, the creativity garnered by narrative assessments is an appealing option for educators.\\ + +Another vital component of narrative assessments is their ability to thoroughly evaluate student communication skills. +In an increasingly interconnected world, the ability to effectively communicate ideas is paramount, +with narrative assessments providing a platform for students to hone these skills \parencite{WILBY20191164}. +In fact, \cite{WILBY20191164} found that narrative assessments even have merits in STEM (Science, Technology, Engineering, and Mathematics) subjects, +where they researchers found that narrative assessments have use in the medical industry for summative decision making. +Due to the ubiquitous importance of writing and communication skills across disciplines, educators' primary rationale for using narrative assessments +lies in their ability to foster these skills \parencite{Wilby2019Discriminating}. +These motives are backed by scientific evidence beyond communication skills, as it has been repeatedly proven that the ability to communicate a certain concept +— especially when supported by metacognitive strategies such as planning, monitoring, and evaluation — +is correlated with mastery of that concept \parencite{Hamzah2022Systematic}. While narrative assessments promote such communication skills, +students who are not proficient writers may be disadvantages. \cite{Lo2021Assessing} found that assessing students through essays +requires an implied mastery of the English language, which may unfairly penalize non-native speakers. +This issue is particularly sensitive in secondary education, as the vast percentage of immigrants and non-native speakers +will have their course evaluation depend on their English proficiency. Hence, while narrative assessments promote communication skills, +educators must be wary of potential biases against non-native speakers.\\ + +While proponents of narrative assessments highlight their benefits, critics focus on the subjectivity of such assessments as a major flaw. +Unsurprisingly, bias and subjectivity is a primary complaint of students, where a majority often perceive essays and projects as unfairly graded \parencite{Bullock2019In}. +These complains are not without merit, as inconsistencies are bound in subjective evaluation due to educator bias and differences between sections and educators. +For example, the same history course can be taught by multiple teachers, where each teacher may have different expectations for essay responses. +In fact, \cite{LOPERAOQUENDO2024101992} found that inter-rater reliability (IRR) for essay grading was often low, +with even rubric-based grading systems failing to ensure consistency between graders. +This inconsistency can lead to student frustration and a perception of unfairness, which can negatively impact student motivation and engagement. +While many focus on the negative aspects of subjectivity, some researchers argue that subjectivity can be beneficial in certain contexts. +For example, positive expectation bias — where education hold higher expectations for certain students — can lead to improved performance +due to positive reinforcement of a student's potential and abilities \parencite{Boer2010Sustainability}. +Positive expectation bias is also useful in flattening performance outliers; +for example, a student having a bad day during an assessment date may be unfairly penalized in a quantitative assessment, +while positive expectation bias allows teachers to understand and compensate for performative outliers. +This not only benefits gifted students but also generally weaker students, and studies show +that teachers sometimes subconsciously use shifting standards to leniently grade struggling (yet hardworking) students \parencite{Gil-Hernández_2024}.\\ + + + +\newpage +\printbibliography[title={Works Cited}] + + +\end{flushleft} +\end{document} +\} \ No newline at end of file diff --git a/AMSTUD Paper/references.bib b/AMSTUD Paper/references.bib new file mode 100644 index 0000000..db8cc02 --- /dev/null +++ b/AMSTUD Paper/references.bib @@ -0,0 +1,151 @@ +@inbook{Lamiell2018, + title = {Some Historical Perspective on the Marginalization of Qualitative Methods Within Mainstream Scientific Psychology}, + ISBN = {9781351136426}, + url = {http://dx.doi.org/10.4324/9781351136426-2}, + DOI = {10.4324/9781351136426-2}, + booktitle = {Situating Qualitative Methods in Psychological Science}, + publisher = {Routledge}, + author = {Lamiell, James T.}, + year = {2018}, + month = jul, + pages = {11–26} +} + +@online{McGrath2021_SATessay, + author = {Steve McGrath}, + title = {College Board Updates on the SAT Essay and Subject Tests}, + year = {2021}, + url = {https://info.methodlearning.com/blog/college-board-updates-on-the-sat-essay-and-subject-tests}, + note = {Accessed: 2025-10-26}, + organization = {Method Learning Blog} +} + +@online{Semos2024_ACTwriting, + author = {Kristina Semos}, + title = {What’s Staying the Same on the New ACT? (Pt 2)}, + year = {2024}, + month = sep, + url = {https://www.ivyloungetestprep.com/blog/act-changes}, + note = {Accessed: 2025-10-26}, + organization = {IVY Lounge Test Prep} +} + +@article{KU200970, +title = {Assessing students’ critical thinking performance: Urging for measurements using multi-response format}, +journal = {Thinking Skills and Creativity}, +volume = {4}, +number = {1}, +pages = {70-76}, +year = {2009}, +issn = {1871-1871}, +doi = {https://doi.org/10.1016/j.tsc.2009.02.001}, +url = {https://www.sciencedirect.com/science/article/pii/S1871187109000054}, +author = {Kelly Y.L. Ku}, +keywords = {Critical thinking, Assessment, Response format, Higher education, Thinking skills}, +abstract = {The current paper discusses ambiguities in critical thinking assessment. The paper first reviews the components of critical thinking. It then discusses the features and issues of commonly used critical thinking tests and to what extend they are made compatible to the conceptualization of critical thinking. The paper argues that critical thinking tests utilizing a single multiple-choice response format measures only recognition or level of knowledge, and do not adequately capture the dispositional characteristics of test-takers. Multiple-choice response format does not reveal test-takers’ underlying reasoning for choosing a particular answer, nor does it reflect test-takers’ ability to think critically under unprompted situations. Whereas measurement that allows for responses in both multiple-choice and open-ended format makes it possible to assess individuals’ spontaneous application of thinking skills on top of their ability to recognize a correct response. Assessment consists of multi-response format should be pursued for effective evaluation of students’ critical thinking performance.} +} + +@article{Kamalov2023New,title={New Era of Artificial Intelligence in Education: Towards a Sustainable Multifaceted Revolution},author={Firuz Kamalov and David Santandreu Calonge and Ikhlaas Gurrib},journal={Sustainability},year={2023},doi={10.3390/su151612451}} + +@article{Liu2023Multiple-choice,title={Multiple-choice questions (MCQs) for higher-order cognition: Perspectives of university teachers},author={Qian Liu and Navé Wald and Chandima Daskon and T. Harland},journal={Innovations in Education and Teaching International},year={2023},volume={61},pages={802 - 814},doi={10.1080/14703297.2023.2222715}} + +@article{Kooloos2019The, +title={The Effect of Passive and Active Education Methods Applied in Repetition Activities on the Retention of Anatomical Knowledge}, +author={J. Kooloos and Esther M. Bergman and Marieke A G P Scheffers and A. Schepens‐Franke and M. Vorstenbosch}, +journal={Anatomical Sciences Education}, +year={2019}, +volume={13}, +pages={458 - 466}, +doi={10.1002/ase.1924} +} + +@article{WILBY20191164, +title = {Reliability of narrative assessment data on communication skills in a summative OSCE}, +journal = {Patient Education and Counseling}, +volume = {102}, +number = {6}, +pages = {1164-1169}, +year = {2019}, +issn = {0738-3991}, +doi = {https://doi.org/10.1016/j.pec.2019.01.018}, +url = {https://www.sciencedirect.com/science/article/pii/S0738399118307493}, +author = {Kyle John Wilby and Marjan J.B. Govaerts and Diana H.J.M. Dolmans and Zubin Austin and Cees {van der Vleuten}}, +keywords = {Assessment, Communication, Medical education, Pharmacy education}, +abstract = {Objective +To quantitatively estimate the reliability of narrative assessment data regarding student communication skills obtained from a summative OSCE and to compare reliability to that of communication scores obtained from direct observation. +Methods +Narrative comments and communication scores (scale 1–5) were obtained for 14 graduating pharmacy students across 6 summative OSCE stations with 2 assessors per station who directly observed student performance. Two assessors who had not observed the OSCE reviewed narratives and independently scored communication skills according to the same 5-point scale. Generalizability theory was used to estimate reliability. Correlation was used to evaluate the relationship between scores from each assessment method. +Results +A total of 168 narratives and communication scores were obtained. The G-coefficients were 0.571 for scores provided by assessors present during the OSCE and 0.612 for scores from assessors who provided scores based on narratives only. Correlation between the two sets of scores was 0.5. +Conclusion +Reliability of communication scores is not dependent on whether assessors directly observe student performance or assess written narratives, yet both conditions appear to measure communication skills somewhat differently. +Practice implications +Narratives may be useful for summative decision-making and help overcome the current limitations of using solely quantitative scores.} +} + +@article{Wilby2019Discriminating, +title={Discriminating Features of Narrative Evaluations of Communication Skills During an OSCE}, +author={K. Wilby and M. Govaerts and Z. Austin and D. Dolmans}, +journal={Teaching and Learning in Medicine}, +year={2019}, +volume={31}, +pages={298 - 306}, +doi={10.1080/10401334.2018.1529570} +} + +@article{Hamzah2022Systematic,title={Systematic Literature Review on the Elements of Metacognition-Based Higher Order Thinking Skills (HOTS) Teaching and Learning Modules},author={Hainora Hamzah and M. I. Hamzah and Hafizhah Zulkifli},journal={Sustainability},year={2022},doi={10.3390/su14020813}} + +@article{Lo2021Assessing, +title={Assessing content knowledge through L2: mediating role of language of testing on students’ performance}, +author={Y. Lo and D. Fung and Xuyan Qiu}, +journal={Journal of Multilingual and Multicultural Development}, +year={2021}, +volume={44}, +pages={1013 - 1028}, +doi={10.1080/01434632.2020.1854274} +} +@article{Redó2021Dimensions, +title={Dimensions of Creativity in Secondary School High-Ability Students}, +author={Núria Arís Redó and María Ángeles Millán Gutiérrez and José-Diego Vargas Cano}, +journal={European Journal of Investigation in Health, Psychology and Education}, +year={2021}, +volume={11}, +pages={953 - 961}, +doi={10.3390/ejihpe11030070} +} + +@article{Boer2010Sustainability,title={Sustainability of teacher expectation bias effects on long-term student performance.},author={H. Boer and R. Bosker and M. Werf},journal={Journal of Educational Psychology},year={2010},volume={102},pages={168-179},doi={10.1037/a0017289}} + +@article{Bullock2019In, +title={In Pursuit of Honors: A Multi-Institutional Study of Students' Perceptions of Clerkship Evaluation and Grading.}, +author={Justin L. Bullock and Cindy J. Lai and T. Lockspeiser and P. O’Sullivan and P. Aronowitz and Deborah Dellmore and C. Fung and Christopher Knight and K. Hauer}, +journal={Academic medicine : journal of the Association of American Medical Colleges}, +year={2019}, +doi={10.1097/acm.0000000000002905} +} + +@article{LOPERAOQUENDO2024101992, +title = {Rating writing: Comparison of holistic and analytic grading approaches in pre-service teachers}, +journal = {Learning and Instruction}, +volume = {94}, +pages = {101992}, +year = {2024}, +issn = {0959-4752}, +doi = {https://doi.org/10.1016/j.learninstruc.2024.101992}, +url = {https://www.sciencedirect.com/science/article/pii/S0959475224001191}, +author = {Carolina Lopera-Oquendo and Anastasiya A. Lipnevich and Ignacio Mañez}, +keywords = {Grades, Pre-service teachers, Holistic scoring, Analytic scoring, Rubrics}, +} + +@article {Gil-Hernández_2024, +author = {Carlos J. Gil-Hernández and Irene Pañeda-Fernández and Leire Salazar and Jonatan Castaño Muñoz }, +title = {Teacher Bias in Assessments by Student Ascribed Status: A Factorial Experiment on Discrimination in Education}, +journal = {Sociological Science}, +volume = {11}, +number = {27}, +issn = {2330-6696}, +url = {http://dx.doi.org/10.15195/v11.a27}, +doi = {10.15195/v11.a27}, +pages = {743--776}, +year = {2024}, +} \ No newline at end of file diff --git a/PhysicsGravitationLabReport/Sketch.pdf b/PhysicsGravitationLabReport/Sketch.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3fdd31bb80a4f1d3866b39e1c24cac2f8dcf1d10 GIT binary patch literal 6984 zcma)B2{@GB+olMk$*x4UvJ{zp#+s~IvxkHR6Jr}@#+HzfB_d16mI_hHzGO*}r7S5+ zks?dBh=hK~_r4?j`u}~`cYR!Doaa2}Irnqso%^|-`-mB;YaU0)pdn(ypGUjiLQoJm zgkcA@%f&g8uY5oRYR9B)qupS9G8E>tp01n^)a3Z)nfV-mq+FgxIz*9+Nh~%$L zx>Ix{;MbAPm5y)}z(u6G5@>caI(IrM9TE5gX6PK~gn>UY9iGkyu({JY9{npc=C9CO ziGeAAK*$7l5GoCpKEZ*AS0(wxyMZh0CLC?qekJ&+M@ 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+\usepackage{subcaption} % add in preamble + + +% ---------- Word-style margins ---------- +\setlength{\oddsidemargin}{0in} +\setlength{\evensidemargin}{0in} +\setlength{\textwidth}{6.5in} +\setlength{\topmargin}{-0.5in} +\setlength{\textheight}{9in} + +\setlength{\parindent}{0pt} + + +\titleformat{\section} % top-level section + {\Large\bfseries\scshape} % Large font, bold, small caps + {\thesection} % shows 1, 2, 3, ... + {1em} % spacing between number and title + {} + +\titleformat{\subsection} + {\large\bfseries\scshape} + {\thesubsection} + {1.5em} % slightly more spacing + {} + +\titleformat{\subsubsection} + {\normalsize\bfseries} + {\thesubsubsection} + {2em} % more spacing for deeper hierarchy + {} + +\begin{document} + + + +% ---------- SIMPLE HEADER ---------- +\pagenumbering{arabic} % start with Arabic page numbers +\setcounter{page}{1} + +% Header: title centered, partner left, date right +\begin{center} + \textbf{\large Experimentally Deriving Newton’s Universal Law of Gravitation by Measuring Mass, Distance, and G in a Simulation} +\end{center} + +\vspace{1em} + +\noindent +\textbf{Name:} Keshav Anand +\hfill +\textbf{Date:} 16 November 2025 +% ---------- MAIN DOCUMENT ---------- + +% Acknowledgment +\section*{Objectives} +Use the \href{http://phet.colorado.edu/sims/html/gravity-force-lab/latest/gravity-force-lab_en.html}{Gravitational force simulation} to determine the dependence of the gravitational force on the mass of the objects involved.\\ + +Use the same simulation to determine the dependence of the gravitational force on the distance between the two masses.\\ + +Determine the experimental value of the universal gravitational constant (G). (This is what relates the gravitational force to the masses and distance rather than being these proportional. G must be included in your final equation.)\\ + +Determine an Equation for the Universal Law of Gravitation based on your data, using only symbols. + +\section*{Introduction} + +\subsection*{Background} +The concept of gravitational force has been misunderstood for most of history, +commonly attributed to divine or supernatural causes until Sir Isaac Newton published his groundbreaking \textit{Principia}. +In the Principia, Newton asserted that every mass exerts an attractive force on every other mass, + a phenomenon described by Newton's Universal Law of Gravitation (NLUG). +This law states that the magnitude of the gravitational force between two masses is + + % Scalar (magnitude) form +\[ +F = G \frac{m_1 m_2}{r^2}, +\] + +where \(F\) is the gravitational force, \(m_1\) and \(m_2\) are the interacting masses, \(r\) is the distance between their centers. +\(G\) is the universal gravitational constant, a constant of proprtionality that has been calculated to be +\[ +G = 6.674 \times 10^{-11}\ \text{N}\,\text{m}^2\,\text{kg}^{-2}. +\] + +In the scientific community, NLUG is treated as an absolute truth, and many important discoveries and applications +rely on its accuracy. From engineering to astrophysics, NLUG has profound importance, and its validity +is vital to the functioning of scientific advancement. + +\subsection*{Purpose} + +This lab aims to use a computer simulation +to verify NLUG by deriving the relationship between gravitational force, masses of objects, and the distance +between them. First, a gravitation simulation will be used to derive the relationship between objects' +masses and the gravitational force. Then, the same process will be repeated with comparing gravitational +force to the distance between objects. Data collected from these two setups will be used to (hopefully) re-establish +the relationship of proportionality proposed by Newton, and the collected data will also solve for the +universal Gravitational constant, $G$. + + + + + + + +\section*{Materials} + +The following methods and apparatus were used to determine the coefficients of static and kinetic friction:\\ +\begin{itemize} + \item 119g Wooden block + \item Adjustable angle metal inclined plane with protractor +\end{itemize} + + +\section*{Procedure} +\begin{enumerate} + \item Set the plane angle to $0^\circ$ and place the block at the far end, roughly 10 cm from the edge. + \item Slowly raise the plane and stop when the block starts to slide down. + \item Record the angle value in a data table under \textbf{static friction}. + \item Repeat steps 1--3 five times, then take the average of the angles. This average angle will be used to calculate static friction. + \item Repeat step 1. + \item Slowly raise the plane while tapping the edge to overcome the static friction. Stop when the block starts to slide down the ramp without slowing down. + \item Record the angle value in a data table under \textbf{kinetic friction}. + \item Repeat steps 5--7 five times, then take the average of the angles for kinetic friction. +\end{enumerate} + +\section*{Experimental Setup} + +\begin{figure}[h!] % h! = “here” placement + \centering + \includegraphics[width=0.7\textwidth]{Sketch} % <-- your image file name + \caption{Experimental setup for measuring static and kinetic friction using an inclined plane.} + \label{fig:friction_setup} +\end{figure} + +\newpage + +\section*{Results} + +\begin{table}[h!] +\centering +\caption{Measured critical angles for static and kinetic friction.} +\label{tab:friction_angles} +\begin{tabularx}{0.8\textwidth}{@{}lcc@{}} +\toprule +\textbf{Trial} & \textbf{Static Friction Angle ($^\circ$)} & \textbf{Kinetic Friction Angle ($^\circ$)} \\ +\midrule +1 & 19.0 & 15.0 \\ +2 & 17.5 & 14.5 \\ +3 & 18.5 & 15.0 \\ +4 & 18.0 & 16.0 \\ +5 & 19.0 & 14.0 \\ +\midrule +\textbf{Average} & 18.4 & 14.9 \\ +\bottomrule +\end{tabularx} +\end{table} + + + +The coefficients of static and kinetic friction were calculated using the relationship: +\[ +\mu = \tan(\theta) +\] +where $\theta$ is the average critical angle measured for each case. + + +Average angle for static friction: +\[ +\theta_s = 18.4^\circ +\] + +Coefficient of static friction: +\[ +\mu_s = \tan(18.4^\circ) = 0.33 +\] + + +Average angle for kinetic friction: +\[ +\theta_k = 14.9^\circ +\] + +Coefficient of kinetic friction: +\[ +\mu_k = \tan(14.9^\circ) = 0.27 +\] +\\\\ +Note that the minute acceleration due to the tapping of the block is neglected, as it's acceleration is assumed to be negligible. Also neglected is the force of air resistance, as it is assumed to be very small compared to the other forces acting on the block. + +\section*{Error Analysis} + +The first major source of error lies in the method of raising the angle to the right amount. The acceleration of the raising of the block must be zero; otherwise, +the block may start to slide earlier than it should have. Hence, the raising of the block is assumed to be the major source of error in this experiment. +Alongside this, the human reaction time to accurately read the protractor within decent tolerance is also a source of error. +Since the coefficients of static and kinetic friction were calculated using $\tan{\theta}$ and involved precise decimal values, +inconsistency in the measured angles could result in either an overestimate or underestimate of the actual coefficients. + +\section*{Discussion} + +The physics concepts used in the lab are the coefficients of static and kinetic friction, which have major applications in the real world, specifically in materials science and engineering. +For example, understanding friction is crucial in designing systems like car wheels, where controlling the friction is vital to driving in different conditions (especially slippery roads). +Another such application of friction is in the design of screws, as the friction within threads is what allows them to hold materials together securely. Hence, a lower coefficient +of static friction would result in a looser screw, while a higher coefficient would result in a tighter screw, which can be crucial in construction, manufacturing, and architecture. +Understanding static and kinetic friction is not only important in product design but can be crucial to ensure safety in various applications, impacting everyday life. \\\\ +Another way that this lab can be carried out is by using a spring scale to directly meassure the force needed to start moving the block and keep it moving at a constant velocity. +This method would also accurate measure the coefficients of static and kinetic friction, although it may be prone to different sources of error. A second method this lab can be carried out +is by using a motion sensor to track the block's movement down the incline, and similar to the cart and ramp lab, the motion sensor can be used to derive the acceleration (by differentiating the velocity data). +From the acceleration, the net force acting on the block can be calculated using Newton's Second Law, which can be used to calculate the frictional coefficients. + +\section*{Conclusion} + + + +Through this lab, it was determined that the coefficient of static friction ($\mu_s$) of wood on metal is roughly \textbf{0.33}, and the coefficient of kinetic friction ($\mu_k$) is roughly \textbf{0.27}. +The coefficient of static friction can be compared to the established range $0.2-0.6$ for such surfaces. +The experimentally determined value falls within this range, indicating that the results are accurate and that the lab was completed successfully. +\end{document} diff --git a/PhysicsInclinedPlaneLabReport/Sketch.pdf 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+\usepackage[colorlinks=true, linkcolor=black, urlcolor=black, citecolor=black]{hyperref} + +\usepackage[T1]{fontenc} % ensures proper font encoding +\usepackage{textcomp} % provides \texteuro +\usepackage[font=small,labelfont=bf]{caption} +\usepackage{booktabs} % in your preamble +\renewcommand{\arraystretch}{1.2} % row height +\usepackage{subcaption} % add in preamble + + +% ---------- Word-style margins ---------- +\setlength{\oddsidemargin}{0in} +\setlength{\evensidemargin}{0in} +\setlength{\textwidth}{6.5in} +\setlength{\topmargin}{-0.5in} +\setlength{\textheight}{9in} + +\setlength{\parindent}{0pt} + + +\titleformat{\section} % top-level section + {\Large\bfseries\scshape} % Large font, bold, small caps + {\thesection} % shows 1, 2, 3, ... + {1em} % spacing between number and title + {} + +\titleformat{\subsection} + {\large\bfseries\scshape} + {\thesubsection} + {1.5em} % slightly more spacing + {} + +\titleformat{\subsubsection} + {\normalsize\bfseries} + {\thesubsubsection} + {2em} % more spacing for deeper hierarchy + {} + +\begin{document} + + + +% ---------- SIMPLE HEADER ---------- +\pagenumbering{arabic} % start with Arabic page numbers +\setcounter{page}{1} + +% Header: title centered, partner left, date right +\begin{center} + \textbf{\large Using an Inclined Plane to Determine Kinetic and Static Frictional Coefficient of a Wooden Block on a Metal Track} +\end{center} + +\vspace{1em} + +\noindent +\textbf{Lab Partners:} Jose P, Dheveshvar S., Amrutha V. +\hfill +\textbf{Date:} 29 October 2025 +% ---------- MAIN DOCUMENT ---------- + +% Acknowledgment +\section*{Objective} +This lab's objective is to determine the coefficient of static friction between an adjustable inclined plane and a block. + +\section*{Introduction} +Friction is a force that opposes the relative motion of two surfaces in contact. +The frictional force is directly proportional to the normal force between the surfaces and is characterized by the coefficient of friction, denoted by $\mu$.' +There are two main types of friction: static friction, which acts when the surfaces are at rest relative to each other, and kinetic friction, which acts when the surfaces are in motion relative to each other. +It is important to note that the static frictional force is equal to the remaining forces in the opposing direction until it reaches its maximum value, which is given by $F_{f_{s}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. +The kinetic frictional force is given by $F_{s_{k}} = \mu_k N$, where $\mu_k$ is the coefficient of kinetic friction. These coefficients can only be experimentally determined and are unique to the material +and composition of the two surfaces in contact. Hence, this experiment aims to use an inclined plane to deteerm the coefficients of static and kinetic friction between a wooden block and a metal track. + +\section*{Materials} + +The following methods and apparatus were used to determine the coefficients of static and kinetic friction:\\ +\begin{itemize} + \item 119g Wooden block + \item Adjustable angle metal inclined plane with protractor +\end{itemize} + + +\section*{Procedure} +\begin{enumerate} + \item Set the plane angle to $0^\circ$ and place the block at the far end, roughly 10 cm from the edge. + \item Slowly raise the plane and stop when the block starts to slide down. + \item Record the angle value in a data table under \textbf{static friction}. + \item Repeat steps 1--3 five times, then take the average of the angles. This average angle will be used to calculate static friction. + \item Repeat step 1. + \item Slowly raise the plane while tapping the edge to overcome the static friction. Stop when the block starts to slide down the ramp without slowing down. + \item Record the angle value in a data table under \textbf{kinetic friction}. + \item Repeat steps 5--7 five times, then take the average of the angles for kinetic friction. +\end{enumerate} + +\section*{Experimental Setup} + +\begin{figure}[h!] % h! = “here” placement + \centering + \includegraphics[width=0.7\textwidth]{Sketch} % <-- your image file name + \caption{Experimental setup for measuring static and kinetic friction using an inclined plane.} + \label{fig:friction_setup} +\end{figure} + +\newpage + +\section*{Results} + +\begin{table}[h!] +\centering +\caption{Measured critical angles for static and kinetic friction.} +\label{tab:friction_angles} +\begin{tabularx}{0.8\textwidth}{@{}lcc@{}} +\toprule +\textbf{Trial} & \textbf{Static Friction Angle ($^\circ$)} & \textbf{Kinetic Friction Angle ($^\circ$)} \\ +\midrule +1 & 19.0 & 15.0 \\ +2 & 17.5 & 14.5 \\ +3 & 18.5 & 15.0 \\ +4 & 18.0 & 16.0 \\ +5 & 19.0 & 14.0 \\ +\midrule +\textbf{Average} & 18.4 & 14.9 \\ +\bottomrule +\end{tabularx} +\end{table} + + + +The coefficients of static and kinetic friction were calculated using the relationship: +\[ +\mu = \tan(\theta) +\] +where $\theta$ is the average critical angle measured for each case. + + +Average angle for static friction: +\[ +\theta_s = 18.4^\circ +\] + +Coefficient of static friction: +\[ +\mu_s = \tan(18.4^\circ) = 0.33 +\] + + +Average angle for kinetic friction: +\[ +\theta_k = 14.9^\circ +\] + +Coefficient of kinetic friction: +\[ +\mu_k = \tan(14.9^\circ) = 0.27 +\] +\\\\ +Note that the minute acceleration due to the tapping of the block is neglected, as it's acceleration is assumed to be negligible. Also neglected is the force of air resistance, as it is assumed to be very small compared to the other forces acting on the block. + +\section*{Error Analysis} + +The first major source of error lies in the method of raising the angle to the right amount. The acceleration of the raising of the block must be zero; otherwise, +the block may start to slide earlier than it should have. Hence, the raising of the block is assumed to be the major source of error in this experiment. +Alongside this, the human reaction time to accurately read the protractor within decent tolerance is also a source of error. +Since the coefficients of static and kinetic friction were calculated using $\tan{\theta}$ and involved precise decimal values, +inconsistency in the measured angles could result in either an overestimate or underestimate of the actual coefficients. + +\section*{Discussion} + +The physics concepts used in the lab are the coefficients of static and kinetic friction, which have major applications in the real world, specifically in materials science and engineering. +For example, understanding friction is crucial in designing systems like car wheels, where controlling the friction is vital to driving in different conditions (especially slippery roads). +Another such application of friction is in the design of screws, as the friction within threads is what allows them to hold materials together securely. Hence, a lower coefficient +of static friction would result in a looser screw, while a higher coefficient would result in a tighter screw, which can be crucial in construction, manufacturing, and architecture. +Understanding static and kinetic friction is not only important in product design but can be crucial to ensure safety in various applications, impacting everyday life. \\\\ +Another way that this lab can be carried out is by using a spring scale to directly meassure the force needed to start moving the block and keep it moving at a constant velocity. +This method would also accurate measure the coefficients of static and kinetic friction, although it may be prone to different sources of error. A second method this lab can be carried out +is by using a motion sensor to track the block's movement down the incline, and similar to the cart and ramp lab, the motion sensor can be used to derive the acceleration (by differentiating the velocity data). +From the acceleration, the net force acting on the block can be calculated using Newton's Second Law, which can be used to calculate the frictional coefficients. + +\section*{Conclusion} + + + +Through this lab, it was determined that the coefficient of static friction ($\mu_s$) of wood on metal is roughly \textbf{0.33}, and the coefficient of kinetic friction ($\mu_k$) is roughly \textbf{0.27}. +The coefficient of static friction can be compared to the established range $0.2-0.6$ for such surfaces. +The experimentally determined value falls within this range, indicating that the results are accurate and that the lab was completed successfully. +\end{document}