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universal Gravitational constant, $G$. +\subsection*{Research Problem} +The research objective for this project is to verify the gravitational relationship between two objects and verify the +constant $G$. The primary problem of investigation is that theoretical mathematics often fails to adequately capture +a true relationship in the real world. Moreover, using physical objects and tools of measurements can result in +unwanted noisy data and is limited by the precision of measurement. Ergo, a simulation bridges this gap, +allowing for an accurate verification of NLUG. +\section*{Methodology} +\subsection*{Materials and Resources} -\section*{Materials} +As this lab was performed within a simulation, all physical materials are limited to a computer with at least 400 MB of memory to render the simulation. -The following methods and apparatus were used to determine the coefficients of static and kinetic friction:\\ +Within the simulation, the simulated materials include \begin{itemize} - \item 119g Wooden block - \item Adjustable angle metal inclined plane with protractor + \item Adjustable Mass, $m_1$ + \item Adjustable Mass, $m_2$ + \item 10 Meter Scale + \item Automatic Force Scale to Measure Gravitational Attraction + \item Two simulated people holding $m_1$ and $m_2$ from colliding into each other due to gravitation \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} +\subsection*{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.} + \includegraphics[width=0.7\textwidth]{ExperimentalSetup} % <-- your image file name + \caption{Experimental setup for the gravity simulation} \label{fig:friction_setup} \end{figure} -\newpage +Note that in Figure \ref{fig:friction_setup}, all inputs (independent variables) are denoted in blue, whereas outputs (dependent variables) are denoted in red + + +\subsection*{Procedure} +\begin{enumerate} + \item Set the location of mass 1 to exactly 2 meters on the scale, and set mass 2 to exactly 6 meters on the scale, with a distance between of 4 meters + \item Set the mass of objects 1 and 2 to exactly 100 kg + \item Set the force values to scientific notation, and uncheck the option for masses of constant size + \item Leaving the mass of $m_2$ constant, change the mass of $m_1$ to be the values listed below, and record both the force on $m_1$ by $m_2$ and the force on $m_2$ by $m_1$ + \subitem Mass values for $m_1$ (kg): 50, 100, 250, 500, 750, 1000 + \item Reset the simulation as detailed by steps 1-3 + \item Leaving the mass of $m_1$ constant, change the mass of $m_2$ to be the values listed below, and record both the force on $m_1$ by $m_2$ and the force on $m_2$ by $m_1$ + \subitem Mass values for $m_2$ (kg): 50, 100, 250, 500, 750, 1000 + \item Reset the simulation as detailed by steps 1-3 + \item Change the masses of both $m_1$ and $m_2$ to be the values listed below, and record both the force on $m_1$ by $m_2$ and the force on $m_2$ by $m_1$ + \subitem Mass values for $m_1$ and $m_2$ (kg): 50, 100, 250, 500, 750, 1000 + \item Reset the simulation as detailed by steps 1-3 + \item Leave $m_2$ at 10 meters on the scale (align the black dot for center of mass), and move $m_1$ based on its center to the below values on the scale, and record both the force on $m_1$ by $m_2$ and the force on $m_2$ by $m_1$ + \subitem Position values for $m_1$ (m): 0, 2, 4, 6, 8 + \item Reset the simulation as detailed by steps 1-3 + \item Leave $m_1$ at 0 meters on the scale (align the black dot for center of mass), and move $m_2$ based on its center to the below values on the scale, and record both the force on $m_1$ by $m_2$ and the force on $m_2$ by $m_1$ + \subitem Position values for $m_1$ (m): 10, 8, 6, 4, 2 + +\end{enumerate} + +Note that the above steps require the following raw data the be collected at each datapoint + +\begin{itemize} + \item Position of the center of mass of $m_1$, (m) + \item Position of the center of mass of $m_2$, (m) + \item Mass of $m_1$, (kg) + \item Mass of $m_2$, (kg) + \item Force on $m_1$ by $m_2$, (N) + \item Force on $m_2$ by $m_1$, (N) +\end{itemize} \section*{Results} +\subsection*{Raw Data} + \begin{table}[h!] \centering \caption{Measured critical angles for static and kinetic friction.}