From ef17e535b4835eaf2d395d375ac315f2a2497ce9 Mon Sep 17 00:00:00 2001 From: TiagoRG Date: Sat, 16 Dec 2023 21:49:45 +0000 Subject: [PATCH] [MCE] Pratical Signed-off-by: TiagoRG --- .gitmodules | 3 - .../mce/pratica-laboratorial/mce-tp1 | 1 - .../mce-tp1/MCE_23-24_RT1_G2.pdf | Bin 0 -> 543930 bytes .../MCE_Movimento de projéteis_2023-2024.pdf | Bin 0 -> 358042 bytes .../pratica-laboratorial/mce-tp1/src/Makefile | 13 ++ .../pratica-laboratorial/mce-tp1/src/TODO.md | 3 + .../mce-tp1/src/bibliography.bib | 0 .../mce-tp1/src/ch/analise-discussao.tex | 169 ++++++++++++++++++ .../mce-tp1/src/ch/anexos.tex | 21 +++ .../mce-tp1/src/ch/conclusao.tex | 15 ++ .../ch/detalhes-experimentais-relevantes.tex | 116 ++++++++++++ .../mce-tp1/src/ch/introducao.tex | 12 ++ .../mce-tp1/src/defs/acronyms.tex | 9 + .../mce-tp1/src/defs/definitions.tex | 9 + .../images/montagem-experimental-parte1.png | Bin 0 -> 61291 bytes .../images/montagem-experimental-parte2.png | Bin 0 -> 45952 bytes 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zAj47Ci&1C{9?ad}_0U)}5FQkPmHFsVCH0f6%zvFx!C9IApLhp5=SXzr`Q;Rh Xe4MT6Yzsb;<3{B;4!qs|r{n(xYzR9t literal 0 HcmV?d00001 diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/Makefile b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/Makefile new file mode 100644 index 0000000..bfb7ab5 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/Makefile @@ -0,0 +1,13 @@ +.PHONY: all compile clean + +all: compile clean + +compile: main.tex bibliography.bib + pdflatex main.tex + biber main + pdflatex main.tex + pdflatex main.tex + mv main.pdf ../report.pdf + +clean: + rm -f *.aux *.blg *.bbl *.toc *.log *.lof *.lot *.log.xml *.bcf *.out *.run.xml *.gz diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/TODO.md b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/TODO.md new file mode 100644 index 0000000..3170803 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/TODO.md @@ -0,0 +1,3 @@ +# TODO + +- Fix às imagens em ch:detalhes-experimentais-relevantes diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/bibliography.bib b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/bibliography.bib new file mode 100644 index 0000000..e69de29 diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/analise-discussao.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/analise-discussao.tex new file mode 100644 index 0000000..4c63f11 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/analise-discussao.tex @@ -0,0 +1,169 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Análise e Discussão} +\label{ch:analise-discussao} +{ +%%% +% Conteúdo da Análise e Discussão aqui + +\section{Parte A} +\label{sec:analise-discussao-parte1} + +\subsection{Análise} +\label{subsec:analise-discussao-parte1-analise} + +\subsubsection{Distância} +\label{subsec:analise-discussao-parte1-distancia} + +Esta distância é 10cm e será constante para todos os lançamentos sendo ela a distância entre os dois sensores de movimento. O erro associado a esta medição é de 1mm. + +\subsubsection{Tempo} +\label{subsec:analise-discussao-parte1-tempo} + +O tempo é medido pelo sistema de controlo dos sensores e é medido em segundo. O erro associado a esta medição é de 0.0001s. Este tempo é em média 0.04447s. A variação máxima do tempo é 0.0005s. + +\subsubsection{Velocidade} +\label{subsec:analise-discussao-parte1-velocidade} + +Para calcular a velocidade utilizamos a seguinte fórmula: + +\begin{equation} + v = \frac{d}{t} +\end{equation} + +O erro associado a esta medição é de 0.0001m/s. A velocidade média é 2.249m/s. A variação máxima da velocidade é 0.04778m/s. + +\subsection{Discussão} +\label{subsec:analise-discussao-parte1-discussao} + +Tendo em conta as medições anteriores da distância e do tempo, verifica-se que a distância foi constante e a variação do tempo bastante baixa (variação máxima de 0.0005s) o que implica uma exatidão alta nos valores da velocidade calculados (exatidão de 97.9\%).\bigskip + +Entre os possíveis motivos para a variação nos valores medidos de tempo podem se mencionar: +\begin{itemize} + \item A falta de consistência da força da mola; + \item A forma como a pessoa que dispara pode não o fazer exatamente da mesma forma em todos os disparos. +\end{itemize} + +\pagebreak + +\section{Parte B} +\label{sec:analise-discussao-parte2} + +\subsection{Análise} +\label{subsec:analise-discussao-parte2-analise} + +\subsubsection{Altura} +\label{subsec:analise-discussao-parte2-altura} + +O valor da altura será constante e será medido desde o nível do alvo até ao ponto de lançamento verticalmente. No caso desta experiência, a altura medida foi 26cm. + +\subsubsection{Ângulo} +\label{subsec:analise-discussao-parte2-angulo} + +Este ângulo varia de lançamento para lançamento, sendo medido utilizando as marcações do lançador. O erro associado a esta medição é de 0.5º. Os valores usados foram 30º, 34º, 38º, 40º e 43º. + +\subsubsection{Alcance} +\label{subsec:analise-discussao-parte2-alcance} + +A figura \ref{fig:parte2-chart} representa o alcance em função do ângulo. No eixo $x$ temos o ângulo de lançamento enquanto que no eixo $y$ temos o alcance médio de cada ângulo. + +\begin{figure}[ht] + \centering + \includegraphics[width=0.6\textwidth]{images/parte2chart.png} + \caption{Gráfico do alcance em função do ângulo} + \label{fig:parte2-chart} +\end{figure} + +\subsection{Discussão} +\label{subsec:analise-discussao-parte2-discussao} + +Tendo em conta os valores obtidos, verifica-se uma maior discrepância entre esses mesmos valores, especialmente para os três primeiros ângulos usados (30º, 34º e 38º) com variações de 0.051, 0.046 e 0.046, respetivamente.\bigskip + +Nesta experiência, estas variações podem se dever a diversos fatores, como por exemplo: +\begin{itemize} + \item A falta de consistência da força da mola; + \item A forma como a pessoa que dispara pode não o fazer exatamente da mesma forma em todos os disparos; + \item A resistência do ar; + \item As marcas existentes no alvo que podem causar confusão à pessoa que as vai verificar; + \item A pouca estabilidade do alvo; + \item Pequenas variações na forma de medição do alcance. +\end{itemize}\bigskip + +Para calcular o ângulo para o qual o alcance é máximo, é necessário calcular a derivada da função do alcance em função do ângulo e igualar a zero. A função do alcance em função do ângulo foi obtida utilizando o software Microsoft Excel que aproximou uma função polinomial de segundo grau aos pontos respetivos aos nossos valores. A equação obtida foi, tal como se pode ver no gráfico da figura \ref{fig:parte2-chart}: + +\begin{equation} + y = -0.0002x^2 + 0.0171x + 0.3381 +\end{equation} + +A derivada desta função em $x$ será: + +\begin{equation} + y' = -0.0004x + 0.0171 +\end{equation}\\ +Por sua vez, esta será igual a 0 quando $x = 42.75$º.\bigskip + +A altura de lançamento usada foi a mesma para todos os disparos de todos os ângulos o que implica que, baseado na experimentação, o ângulo para o qual se obtém maior alcance será $42.75$º. + +\pagebreak + +\section{Parte C} +\label{sec:analise-discussao-parte3} + +\subsection{Análise} +\label{subsec:analise-discussao-parte3-analise} + +\subsubsection{Comprimento do pêndulo} +\label{subsec:analise-discussao-parte3-comprimento} + +Distância entre o ponto de suspensão e extremidade do centro. Este valor é obtido por medição direta com o erro associado de 1mm. O valor obtido foi de 24.4cm. + +\subsubsection{Massas} +\label{subsec:analise-discussao-parte3-massas} + +As massas são obtidas por medição direta com o erro associado de 0.1g. Os valores obtidos foram 237.2g para o pêndulo e 66.5g para o projétil. + +\subsubsection{Ângulo} +\label{subsec:analise-discussao-parte3-angulo} + +Este é o ângulo máximo descrito pelo movimento do pêndulo. O erro associado a esta medição é de 0.1º. O valor médio foi 17º. + +\subsubsection{Altura} +\label{subsec:analise-discussao-parte3-altura} + +Este é o valor da altura máxima atingida pelo projétil, que é registada no ponto de maior ângulo. Pode ser calculada a partir da seguinte fórmula: + +\begin{equation} + h = L(1 - \cos(\theta)) +\end{equation} + +O valor médio obtido foi 10.66mm. + +\subsubsection{Velocidade} +\label{subsec:analise-discussao-parte3-velocidade} + +Este é o valor da velocidade inicial do projétil. Pode ser calculada a partir da seguinte fórmula: + +\begin{equation} + v = \left| \frac{m_{projetil}~+~m_{pendulo}}{m_{projetil}} * \sqrt{2*g*h} \right|~~~~~(SI) + \label{eq:parte3-velocidade-inicial} +\end{equation} + +Onde $g$ é a aceleração gravítica e $h$ é a altura máxima atingida pelo projétil (calculada anteriormente). + +\subsection{Discussão} +\label{subsec:analise-discussao-parte3-discussao} + +Tendo em conta os valores obtidos, verifica-se uma amplitude de 1º. Esta variação pode se dever a diversos fatores, como por exemplo: + +\begin{itemize} + \item A falta de consistência da força da mola; + \item A forma como a pessoa que dispara pode não o fazer exatamente da mesma forma em todos os disparos; + \item Incerteza associada ao instrumento de medição; + \item O atrito do pêndulo com o suporte. +\end{itemize} + +Usando a fórmula \ref{eq:parte3-velocidade-inicial} obtém-se para cada ângulo diferentes valores de velocidade inicial, sendo o valor da velocidade média 2.0879m/s. Este resultado deverá ser semelhante ao obtido da Parte A (secção \ref{subsec:analise-discussao-parte1-velocidade}), que ao comparar verifica-se uma diferença de 0.1611m/s. + +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/anexos.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/anexos.tex new file mode 100644 index 0000000..9e3c532 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/anexos.tex @@ -0,0 +1,21 @@ +\chapter*{Anexos} +\label{chap:anexos} +{ + \begin{figure}[H] + \centering + \includegraphics[width=1\textwidth]{images/tabela-parte1}\label{fig:tabela-parte1} + \caption{Tabela de resultados - Parte A} + \end{figure} + + \begin{figure} + \centering + \includegraphics[width=1\textwidth]{images/tabela-parte2}\label{fig:tabela-parte2} + \caption{Tabela de resultados - Parte B} + \end{figure} + + \begin{figure} + \centering + \includegraphics[width=1\textwidth]{images/tabela-parte3}\label{fig:tabela-parte3} + \caption{Tabela de resultados - Parte C} + \end{figure} +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/conclusao.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/conclusao.tex new file mode 100644 index 0000000..1a6e155 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/conclusao.tex @@ -0,0 +1,15 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Conclusões} +\label{ch:conclusoes} +{ +%%% +% Conteúdo da conclusão aqui + +Em todas as experiências, os objetivos essenciais foram cumpridos, contudo, verificámos alguns erros, como erros relacionados com medições que levaram a alguma disperidade entre valores calculados e valores teóricos. + +De forma a reduzir/minimizar a variação do fator humano no disparo (ex. O lançamento ser efetuado sempre pela mesma pessoa), nas medições de forma a aumentar a precisão. Podem ser efetuadas mais medições com instrumentos mais rigorosos. Um exemplo disto é o alvo utilizado para medir o alcance na Parte B. + +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/detalhes-experimentais-relevantes.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/detalhes-experimentais-relevantes.tex new file mode 100644 index 0000000..a9934b4 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/detalhes-experimentais-relevantes.tex @@ -0,0 +1,116 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Detalhes Experimentais Relevantes} +\label{ch:detalhes-experimentais-relevantes} +{ +%%% +% Conteúdo da introdução aqui + +\section{Parte A} +\label{sec:detalhes-experimentais-relevantes-parte1} + +\subsection{Material} +\label{subsec:detalhes-experimentais-relevantes-parte1-material} + +\begin{enumerate} + \item Lançador de projéteis + \item Suporte para o lançador de projéteis + \item Sensor de movimento + \item Sensor de movimento + \item Sistema de controlo dos sensores + \item Fita-métrica + \item Bola metálica +\end{enumerate} + +\begin{figure}[h] + \center + \includegraphics[width=0.8\textwidth]{images/montagem-experimental-parte1}\label{fig:montagem-experimental-parte1} +\end{figure} + +\subsection{Procedimento} +\label{subsec:detalhes-experimentais-relevantes-parte1-procedimento} + +Antes de iniciar qualquer procedimento experimental é necessário certificar que o lançador de projéteis está devidamente montado e que o sistema de controlo dos sensores está ligado e a funcionar corretamente. + +\begin{enumerate} + \item Preparar a montagem experimental como ilustrado na figura \ref{fig:montagem-experimental-parte1}; + \item Medir a distância entre os sensores de movimento; + \item Carregar o lançador de projéteis com a bola metálica na posição de tiro curto (SHORT RANGE); + \item Colocar o sistema de controlo dos sensores na posição de TWO GATES e carregar em START/STOP; + \item Disparar o projétil e registar o valor de tempo obtidos; + \item Efetuar 3 disparos e registar as respetivas medições. +\end{enumerate} + +\pagebreak + +\section{Parte B} +\label{sec:detalhes-experimentais-relevantes-parte2} + +\subsection{Material} +\label{subsec:detalhes-experimentais-relevantes-parte2-material} + +\begin{enumerate} + \item Lançador de projéteis + \item Suporte para o lançador de projéteis + \item Alvo + \item Fita-métrica + \item Bola metálica +\end{enumerate} + +\begin{figure}[h] + \center + \includegraphics[width=0.8\textwidth]{images/montagem-experimental-parte2}\label{fig:montagem-experimental-parte2} +\end{figure} + +\subsection{Procedimento} +\label{subsec:detalhes-experimentais-relevantes-parte2-procedimento} + +Antes de efetuar os lançamentos, é necessário verificar rigorosamente o ângulo de lançamento e fixar devidamente o alvo de modo a evitar imprecisões relacionadas com o mesmo. + +\begin{enumerate} + \item Preparar a montagem experimental como ilustrado na figura \ref{fig:montagem-experimental-parte2}; + \item Colocar o alvo a uma distância tal que a esfera caia sobre a sua superfície; + \item Carregar o lançador de projéteis com a bola na posição de tiro curto (SHORT RANGE); + \item Medir a altura de lançamento do projétil; + \item Disparar o projétil e registar o alcance obtido; + \item Efetuar 3 disparos e registar as respetivas medições para cada valor de ângulo (sendo esses ângulos: 34º, 38º, 40º e 43º). +\end{enumerate} + +\pagebreak + +\section{Parte C} +\label{sec:detalhes-experimentais-relevantes-parte3} + +\subsection{Material} +\label{subsec:detalhes-experimentais-relevantes-parte3-material} + +\begin{enumerate} + \item Suporte para o lançador de projéteis + \item Lançador de projéteis + \item Bola metálica + \item Pêndulo balístico + \item Balança + \item Fita-métrica +\end{enumerate} + +\begin{figure}[h] + \center + \includegraphics[width=0.8\textwidth]{images/montagem-experimental-parte3}\label{fig:montagem-experimental-parte3} +\end{figure} + +\subsection{Procedimento} +\label{subsec:detalhes-experimentais-relevantes-parte3-procedimento} + + +\begin{enumerate} + \item Preparar a montagem experimental como ilustrado na figura \ref{fig:montagem-experimental-parte3}; + \item Medir as massas do projétil e do pêndulo balístico; + \item Medir o comprimento do pêndulo; + \item Carregar o lançador de projéteis com a bola na posição de tiro curto (SHORT RANGE); + \item Disparar o projétil e registar o ângulo máximo descrito pelo pêndulo; + \item Efetuar 5 disparos e registar as respetivas medições. +\end{enumerate} + +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/introducao.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/introducao.tex new file mode 100644 index 0000000..5fd78a5 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/ch/introducao.tex @@ -0,0 +1,12 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Introdução} +\label{ch:introducao} +{ +%%% +% Conteúdo da introdução aqui + +Os conhecimentos necessários para as realizações da primeira e segunda parte do trabalho (lançamentos horizontal e com ângulo variável) foram obtidos na aula respetiva aos conteúdos do momento linear e lançamento oblíquo enquanto que para a terceira parte (lançamento contra um pêndulo balístico) foram obtidos na aula relativa às colisões. +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/defs/acronyms.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/defs/acronyms.tex new file mode 100644 index 0000000..8a47ffd --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/defs/acronyms.tex @@ -0,0 +1,9 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter*{Acrónimos} +\begin{acronym} + \acro{deti}[DETI]{Departamento de Eletrónica, Telecomunicações e Informática} + \acro{leci}[LECI]{Licenciatura em Engenharia de Computadores e Informática} + \acro{ua}[UA]{Universidade de Aveiro} +\end{acronym} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/defs/definitions.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/defs/definitions.tex new file mode 100644 index 0000000..fda4942 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/src/defs/definitions.tex @@ -0,0 +1,9 @@ +%! Author = TiagoRG +%! 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Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\documentclass{report} +\usepackage[T1]{fontenc} % Fontes T1 +\usepackage[utf8]{inputenc} % Input UTF8 +\usepackage[backend=biber, style=ieee]{biblatex} % para usar bibliografia +\usepackage{csquotes} +\usepackage[portuguese]{babel} %Usar língua portuguesa +\usepackage{blindtext} % Gerar texto automaticamente +\usepackage[printonlyused]{acronym} +\usepackage{hyperref} % para autoref +\usepackage{graphicx} +\usepackage{indentfirst} +\usepackage{float} +\usepackage{geometry} + +\geometry{ + paper=a4paper, + margin=45pt, + includefoot +} + +\bibliography{bibliography} + + +\begin{document} +%% +% Definições +\input{defs/definitions} +% +%%%%%% CAPA %%%%%% +% +\begin{titlepage} + +\begin{center} +% +\vspace*{50mm} +% +{\Huge \titulo}\\ +% +\vspace{10mm} +% +{\Large \empresa}\\ +% +\vspace{10mm} +% +{\LARGE \autores}\\ +% +\vspace{30mm} +% +\begin{figure}[h] +\center +\includegraphics{images/ua}\label{fig:ua-title-logo} +\end{figure} +\end{center} +\end{titlepage} + +%% Página de Título %% +\title{% +{\Huge\textbf{\titulo}}\\ +{\vspace{20mm}} +{\Large \departamento\\ \empresa} +} +% +\author{% + \autores \\ + \autorescontactos +} +% +\date{\today} +% +\maketitle + +%\pagenumbering{roman} + +%%%%%% RESUMO %%%%%% +\begin{abstract} + O principal objetivo deste trabalho é estudar o comportamento de uma esfera em diferentes tipos de movimentos. Para alcançar os objetivos pretendidos, foi necessário realizar 3 experiências, sendo estas o lançamento horizontal, lançamento com ângulo variável e por último lançamento contra um pêndulo balístico. As medições de comprimentos apresentam um erro de 1mm, medições de massas apresentam um erro de 0.1g e medições de ângulos apresentam um erro de 0.1º. A exatidão na primeira parte foi de 97.9\%. +\end{abstract} + + +\tableofcontents +%\listoftables % descomentar se necessário +%\listoffigures % descomentar se necessário + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\clearpage +\pagenumbering{arabic} + + +%%%%%% INTRODUÇÃO %%%%%% +\input{ch/introducao} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Capítulos +\input{ch/detalhes-experimentais-relevantes} +\input{ch/analise-discussao} + +%%%%%% CONCLUSÕES %%%%%% +\input{ch/conclusao} + + +%%%%%% ACRÓNIMOS %%%%%% +%\input{defs/acronyms} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\printbibliography + +\input{ch/anexos} + +\end{document} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/tp1-movimento-de-projeteis-g2.xlsx b/2ano/1semestre/mce/pratica-laboratorial/mce-tp1/tp1-movimento-de-projeteis-g2.xlsx new file mode 100644 index 0000000000000000000000000000000000000000..e4fbfe1d6da4c98550ba7a2c707d3a52cceb24fb GIT binary patch literal 28731 zcmeFY^OvmK(j{EBvCFn=mu=hTF59-NcGMFU} 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--git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/analise-discussao.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/analise-discussao.tex new file mode 100644 index 0000000..4b3a4a3 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/analise-discussao.tex @@ -0,0 +1,84 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Análise e Discussão} +\label{ch:analise-discussao} +{ +%%% +% Conteúdo da Análise e Discussão aqui + +\section{Parte A} +\label{sec:analise-discussao-parte1} + +\subsection{Resultados} \label{subsec:analise-discussao-parte1-resultados} + Para o cálculo da constante de calibração, foi utilizada a montagem referida no enunciado, e registados os valores de $I_s$ e $V_H$. + \par No gráfico abaixo é representada a reta de aproximação da função $V_h = f(I_s)$ , elaborada pelo software Excel com base nos dados obtidos experimentalmente. + +\begin{figure}[h] + \centering + \includegraphics[scale=0.6]{images/grafico1-parte-a.png} + \caption{Gráfico de representação linear de $I_s$ e $V_H$} + \label{fig:grafico1-parte-a} +\end{figure} + + Na seguinte tabela, estão denotados os valores experimentais utilizados na elaboração do gráfico apresentado acima, e o valor calculado para a constante de calibração, $C_c$. + +\begin{figure}[h] + \centering + \includegraphics[scale=0.6]{images/tabela1-parte-a.png} + \caption{Tabela de resultados (parte A)} + \label{fig:tabela1-parte-a} +\end{figure} + +\subsection{Análise} \label{subsec:analise-discussao-parte1-analise} + Quanto aos resultados obtidos, o valor obtido de $C_c$ foi calculado usando a equação (5), e este tem um erro associado que foi calculado utilizando a equação (2). \ O desvio associado foi de $\Delta C_c = 2.03 \times 10^{-2}$. + +\subsection{Discussão} + Após as medições e cálculos efetuados, foi obtido o gráfico \ref{fig:grafico1-parte-a} e a equação da reta de aproximação cujos valores divergem minimamente dos medidos. \ O declive desta equação foi utilizado para o cálculo de $C_c$. + \par Como $\frac{N}{l}$ e $\mu_0$ são valores constantes, a única variável no cálculo de $C_c$ é apenas o declive da reta da função $f(I_s)$, que está relacionado com os valores medidos, logo estes são a única influência no erro. + \par Estes erros podem ser, por exemplo, o erro associado aos instrumentos de medição, ou pequenas variações na calibração da sonda. + +\pagebreak + +\section{Parte B} +\label{sec:analise-discussao-parte2} + +\subsection{Resultados} +\label{subsec:analise-discussao-parte2-resultados} + Na parte B, foram efetuadas medições em 3 partes, repartidas em 3 tabelas e gráficos. \ Estas representam a variação dos campos magnéticos gerados pelas bobines, consoante a posição da sonda de Hall. + \par Na tabela 1, apenas a bobine imóvel tem corrente elétrica. \ Na tabela 2, apenas a bobine móvel tem corrente elétrica. \ Na tabela 3, as duas bobines estão ligadas em série, ambas com a mesma corrente elétrica. + \par Estas tabelas estão representadas na figura abaixo. + + \begin{figure}[H] + \centering + \includegraphics[scale=0.6]{images/tabelas1-3-parte-b.png} + \caption{Tabelas representativas dos campos magnéticos} + \end{figure} + + Em baixo está representado os gráficos das respetivas tabelas em função à posição da sonda de Hall. + + \begin{figure}[H] + \centering + \includegraphics[scale=0.6]{images/graficos1-3-parte-b.png} + \caption{Gráficos representativos das tabelas} + \end{figure} + +\subsection{Análise} +\label{subsec:analise-discussao-parte2-analise} + O Princípio da Sobreposição do campo magnético consiste em que, numa configuração de Helmholtz, a soma do valor dos campos individualmente gerados numa dada posição da sonda de Hall será igual ao valor medido com as duas bobines ativas. + + \par Ao observar os resultados obtidos, a propriedade fundamental do Princípio da Sobreposição verifica-se de forma aproximada, ou seja, embora a soma dos campos individualmente medidos não seja exatamente igual ao valor medido aquando da medição simultânea dos dois campos, os valores são próximos. + + \par Nos gráficos está apresentado de forma mais clara este princípio. \ Com isto, podemos afirmar que ocorre sobreposição dos campos magnéticos. + + \par Para estimar o nº de espiras, foi utilizada a equação (4) para calcular o campo magnético no eixo de um anel de corrente. \ Após obter o resultado do campo magnético, utiliza-se o $B_{max}$ obtido na tabela 3, usando a equação (6). + + +\subsection{Discussão} +\label{subsec:analise-discussao-parte2-discussao} + Dado por completo os cálculos necessários, e a análise dos resultados obtidos, e a discrepância entre os valores teóricos e práticos, para a verificação do Princípio da Sobreposição do campo magnético. \ Estes desvios são originados por margens de erro, nos valores que este está dependente, como a constante de calibração e as medições da diferença de potencial numa dada posição. + + \par No cálculo do nº de espiras, o erro associado à estimativa deve-se a diversos fatores, como os erros associados ao cálculo do valor máximo obtido no campo magnético, e o cálculo de $B(x)$. + +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/anexos.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/anexos.tex new file mode 100644 index 0000000..49d57da --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/anexos.tex @@ -0,0 +1,3 @@ +\chapter*{Anexos} +\label{chap:anexos} + diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/conclusao.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/conclusao.tex new file mode 100644 index 0000000..48776eb --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/conclusao.tex @@ -0,0 +1,15 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Conclusões} +\label{ch:conclusoes} +{ +%%% +% Conteúdo da conclusão aqui + +Na primeira parte do trabalho, foi possível obter a constante de calibração da sonda de efeito de Hall, que foi aproximadamente $0.0309$. Não existiram grandes problemas na realização desta parte, pelo que foi possível chegar ao valor da constante de calibração sem existir nenhum desvio significativo. + +Na segunda parte do trabalho, foi possível obter o campo magnético ao longo do eixo de duas bobines na configuração de Helmholtz, utilizando uma sonda de Hall. Também foi estimado o número de espiras das bobines, que foi aproximadamente $N = 80$ (cada bobine). Durante a experiência surgiram alguns problemas, nomeadamente erros na calibração da sonda, o que fez com que os valores obtidos não fossem imediatamente os esperados. + +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/detalhes-experimentais-relevantes.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/detalhes-experimentais-relevantes.tex new file mode 100644 index 0000000..2df8506 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/detalhes-experimentais-relevantes.tex @@ -0,0 +1,67 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Detalhes Experimentais Relevantes} +\label{ch:detalhes-experimentais-relevantes} +{ +%%% +% Conteúdo da introdução aqui +\section{Material} +\label{subsec:detalhes-experimentais-relevantes-material} + +\begin{enumerate} + \item Voltímetro + \item Amperímetro + \item Fonte de tensão de $15~V$ + \item Resistência de $10~\Omega$ + \item Reóstato de $330~\Omega$ + \item Sonda de efeito de Hall + \item Solenoide + \item Bobines de Helmholtz +\end{enumerate} + +\begin{figure}[H] + \centering + \includegraphics[width=1\linewidth]{images/esquema-montagem-experimental.png} + \caption{Montagem experimental} + \label{fig:detalhes-experimentais-relevantes-montagem-experimental} +\end{figure} + +\pagebreak + +\section{Parte A} +\label{sec:detalhes-experimentais-relevantes-parte1} + +Esta primeira parte do trabalho foi realizada com o objetivo de calibrar a sonda de efeito de Hall, obtendo assim a sua constante de calibração ($C_c$), a ser usada na segunda parte do trabalho. + +\subsection{Procedimento} +\label{subsec:detalhes-experimentais-relevantes-parte1-procedimento} + +\begin{enumerate} + \item Liga-se a sonda ao voltímetro e regula-se o potenciómetro da sonda para que o voltímetro indique $0~V$ quando não está sujeita a um campo magnético. + \item Monta-se agora o resto do circuito, como na figura \ref{fig:detalhes-experimentais-relevantes-montagem-experimental}. + \item Regista-se o valor $\frac{N}{l}$, que é o número de espiras por unidade de comprimento do solenoide. + \item Coloca-se a sonda no interior do solenoide, procurando o ponto onde a aproximação utilizada de solenoide infinito. + \item Ajusta-se o reóstato de modo a obter 10 valores de corrente $I_S$ diferentes, registando-se os diferentes valores da tensão $V_H$ para cada valor da corrente. +\end{enumerate} + +\section{Parte B} +\label{sec:detalhes-experimentais-relevantes-parte2} + +\subsection{Procedimento} +\label{subsec:detalhes-experimentais-relevantes-parte2-procedimento} + +\begin{enumerate} + \item Colocam-se as bobines na configuração de Helmholtz, com uma distância entre elas igual ao seu raio. + \item Registam-se os dados das bobines, nomeadamente o raio e posição de cada uma. + \item Monta-se agora o resto do circuito, como na figura \ref{fig:detalhes-experimentais-relevantes-montagem-experimental} apenas substituindo o solenoide por uma das bobines. + \item Ajusta-se o reóstato de modo a ter $I=0.50A$ que será constante durante toda a experiência. + \item Mede-se o campo magnético criado pela bobine ao longo do seu eixo, de centímetro a centímetro, registando cada par de valores: posição, tensão de Hall $(V_H)$. + \item Repetem-se os passos 3, 4 e 5, mas agora para a segunda bobine (usando as mesmas posições usadas anteriormente). + \item Ligam-se agora ambas as bobines, em série, e mais uma vez registam-se os valores da tensão de Hall para as mesmas posições utilizadas anteriormente. +\end{enumerate} + +\pagebreak + +%%% +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/introducao.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/introducao.tex new file mode 100644 index 0000000..f034e95 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/ch/introducao.tex @@ -0,0 +1,26 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter{Introdução} +\label{ch:introducao} +{ +%%% +% Conteúdo da introdução aqui +\section{Fórmulas} \label{sec:formulas} + Para a resolução deste trabalho, foram consideradas as seguintes fórmulas, após certas deduções: + \begin{itemize} + \item $B_{sol} = \mu_0 (\frac{N}{l}) I_s$ (1) + \item $\frac{\Delta C}{C} = \frac{\frac{\Delta N}{\Delta l}}{\frac{N}{l}} + \frac{\Delta m}{m}$ (2) + \item $B = C_c V_H$ (3) + \item $\vec{B}(x) = \frac{\mu_0 I R^2}{2(R^2 + (x - x_0)^2)^{3/2}}$ (4) + \item $C_c = \frac{\mu_0 \frac{N}{l}}{m}$ (5) + \item $\frac{N}{l} = \frac{B_{max}}{B_x}$ (6) + \end{itemize} + + Para algumas destas fórmulas foi usada a constante $\mu_0$ que representa a permeabilidade magnética do vácuo, e é equivalente a $4\pi \times 10^{-7}~~Tm/A$. +%%% +\section{Objetivos} \label{sec:objetivos} + O objetivo deste trabalho foi, na parte A, calibrar uma sonda de efeito de Hall, obtendo assim a sua constante de calibração ($C_c$), e calcular o seu respetivo erro. + + \par Na parte B, foi calculado o campo magnético ao longo do eixo de duas bobines na configuração de Helmholtz, utilizando uma sonda de Hall. \ Também foi estimado o número de espiras das bobines. +} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/defs/acronyms.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/defs/acronyms.tex new file mode 100644 index 0000000..8a47ffd --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/defs/acronyms.tex @@ -0,0 +1,9 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\chapter*{Acrónimos} +\begin{acronym} + \acro{deti}[DETI]{Departamento de Eletrónica, Telecomunicações e Informática} + \acro{leci}[LECI]{Licenciatura em Engenharia de Computadores e Informática} + \acro{ua}[UA]{Universidade de Aveiro} +\end{acronym} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/defs/definitions.tex b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/defs/definitions.tex new file mode 100644 index 0000000..fda4942 --- /dev/null +++ b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/defs/definitions.tex @@ -0,0 +1,9 @@ +%! Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\newcommand{\titulo}{Mecânica e Campo Eletromagnético - Trabalho Prático 1} +\newcommand\data{DATA} +\newcommand\autores{Tiago Garcia, Rúben Gomes, Bruno Santos} +\newcommand\autorescontactos{(114184) tiago.rgarcia@ua.pt, (113435) rlcg@ua.pt, (113446) brunommsantos@ua.pt} +\newcommand\departamento{Dept. de Eletrónica, Telecomunicações e Informática} +\newcommand\empresa{Universidade de Aveiro} diff --git a/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/images/esquema-montagem-experimental.png b/2ano/1semestre/mce/pratica-laboratorial/mce-tp2/src/images/esquema-montagem-experimental.png new file mode 100644 index 0000000000000000000000000000000000000000..00c877190d841bc6a5d93e13af532a8b408c33ec GIT binary patch literal 41927 zcmb@ubyQVt7d^TW1w}wIPuUB^B z8jcWz+Vk%ZTs$=@J_NmoB!mT&-O>)yUHLKl7yC1*m*8BN2-VgibFXuPpFMLC=!H^# zy=DuCT@^9nvEFKm3!+>88B6))sWz=1oMT``F`0M05{24tfBnd~R6}Gj9UPiGrq_5k 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Author = TiagoRG +%! GitHub = https://github.com/TiagoRG + +\documentclass{report} +\usepackage[T1]{fontenc} % Fontes T1 +\usepackage[utf8]{inputenc} % Input UTF8 +\usepackage[backend=biber, style=ieee]{biblatex} % para usar bibliografia +\usepackage{csquotes} +\usepackage[portuguese]{babel} %Usar língua portuguesa +\usepackage{blindtext} % Gerar texto automaticamente +\usepackage[printonlyused]{acronym} +\usepackage{hyperref} % para autoref +\usepackage{graphicx} +\usepackage{indentfirst} +\usepackage{float} +\usepackage{geometry} + +\geometry{ + paper=a4paper, + margin=45pt, + includefoot +} + +\bibliography{bibliography} + + +\begin{document} +%% +% Definições +\input{defs/definitions} +% +%%%%%% CAPA %%%%%% +% +\begin{titlepage} + +\begin{center} +% +\vspace*{50mm} +% +{\Huge \titulo}\\ +% +\vspace{10mm} +% +{\Large \empresa}\\ +% +\vspace{10mm} +% +{\LARGE \autores}\\ +% +\vspace{30mm} +% +\begin{figure}[h] +\center +\includegraphics{images/ua}\label{fig:ua-title-logo} +\end{figure} +\end{center} +\end{titlepage} + +%% Página de Título %% +\title{% +{\Huge\textbf{\titulo}}\\ +{\vspace{20mm}} +{\Large \departamento\\ \empresa} +} +% +\author{% + \autores \\ + \autorescontactos +} +% +\date{\today} +% +\maketitle + +%\pagenumbering{roman} + + + +\tableofcontents +%\listoftables % descomentar se necessário +%\listoffigures % descomentar se necessário + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\clearpage +\pagenumbering{arabic} + + +%%%%%% INTRODUÇÃO %%%%%% +\input{ch/introducao} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Capítulos +\input{ch/detalhes-experimentais-relevantes} +\input{ch/analise-discussao} + +%%%%%% CONCLUSÕES %%%%%% +\input{ch/conclusao} + +\pagebreak + +\section*{$B_{sol} = \mu_0 \frac{N}{l} I_S$} +\begin{itemize} + \item $B_{sol}$ - Campo magnético do solenóide (apenas paralelo ao eixo do solenóide) + \item $\mu_0$ - Permeabilidade magnética do vácuo (constante, $4\pi \times 10^{-7}~~Tm/A$) + \item $I_S$ - Corrente elétrica no solenóide +\end{itemize} + +\section*{$\frac{\Delta C}{C} = \frac{\frac{\Delta N}{\Delta l}}{\frac{N}{l}} + \frac{\Delta m}{m}$} +Equação usada para calcular o erro relativo da constante de calibração do sensor de Hall. + +\section*{$B = C_CV_V$} +Usada para calcular o campo magnético a partir da tensão de saída do sensor de Hall para as bobinas de Helmholtz. +\begin{itemize} + \item $B$ - Campo magnético + \item $C_C$ - Constante de calibração do sensor de Hall + \item $V_V$ - Tensão de saída do sensor de Hall +\end{itemize} + +\section*{$\vec{B}(x) = \frac{\mu_0 I R^2}{2(R^2 + (x - x_0)^2)^{3/2}}$} +As variáveis $x$ e $x_0$ anulam-se. +\begin{itemize} + \item $\vec{B}(x)$ - Campo magnético no ponto $x$ do eixo do solenóide + \item $\mu_0$ - Permeabilidade magnética do vácuo (constante, $4\pi \times 10^{-7}~~Tm/A$) + \item $I$ - Corrente elétrica no solenóide + \item $R$ - Raio do solenóide +\end{itemize} + +\section*{$C_C = \frac{\mu_0 \frac{N}{l}}{m}$} +Resolve parte 1 +\begin{itemize} + \item $C_C$ - Constante de calibração do sensor de Hall + \item $\mu_0$ - Permeabilidade magnética do vácuo (constante, $4\pi \times 10^{-7}~~Tm/A$) + \item $m$ - Declive do gráfico $V_V = f(I_S)$ +\end{itemize} + +\section*{$\frac{N}{l} = \frac{B_{max}}{B_x}$} +Usada para calcular o número de espiras (parte 2) + +%%%%%% ACRÓNIMOS %%%%%% +%\input{defs/acronyms} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\end{document}

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