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Fixed error analyusis

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KeshavAnandCode
2025-11-16 13:28:58 -06:00
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commit a8842609cb
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PhysicsGravitationLabReport/main.tex
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@@ -70,13 +70,13 @@
\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.
\begin {itemize}
\item 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.
\item Use the same simulation to determine the dependence of the gravitational force on the distance between the two masses.
\item 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.)
\item Determine an Equation for the Universal Law of Gravitation based on your data, using only symbols.
\end {itemize}
\section*{Introduction}
@@ -375,7 +375,7 @@ While all data was collected jointly, the five separate experimental setups can
\end{tabularx}
\end{table}
\subsection*{Analysis}
\subsection*{Discussion and Analysis}
The first major observation that can be made using the raw data is that for all data points (in all 5 tables),
\textbf{$F_{1\rightarrow2}$ (N)} = \textbf{$F_{2\rightarrow1}$ (N)}. This observation is \textbf{Newton's Third Law},
@@ -543,13 +543,20 @@ G = 6.67 \times 10^{-11}\,\text{N\,m}^2\text{/kg}^2
\label{eq:solvedNLUG}
\end{equation}
et force acting on the block can be calculated using Newton's Second Law, which can be used to calculate the frictional coefficients.
the force acting on the block can be calculated using Newton's Second Law, which can be used to calculate the frictional coefficients.
\section*{Conclusion}
\subsection*{Error Analysis}
One major source of error within this lab is the assumption that the simulation is entirely functional in simulating gravitational attraction.
In an real-world scenario, there are other external forces (friction, air resistance, electromagnetic forces) that can impact the gravitational attraction,
and if the simulation doesn't not properly isolate the gravitational force, the final relationship and the calculated gravitational constants can be off.
Additionally, the small nature of $G$ means that minor errors in any input variables or rounding errors have a profound impact on the
calculated force and gravitational constant. Moreover, the simulation only offers discrete input increments for distance and mass, whereas
the scale (particularly for distance) is free to move at any point in the screen. Hence, the distance intervals may be slightly inaccurate
as they depend on teh accurate placing of the two objects based on teh scale. Offering continuos distance inputs would offer a slight improvement.
Due to the relatively high number of trials conducted, these errors are relatively negligible in finding proportionalities; however, they can significantly impact the calculation of $G$.
Hence, $G$ was calculated using the default values for distance, ensuring that there would be no innacuracy of the data point.
\end{document}