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- \documentclass{article}
- \usepackage{graphicx}
- \begin{document}
- \begin{flushright}
- Alex Bliskovsky\\
- Jacobs 4\\
- \end{flushright}
- \section{Experimental Design}
- The purpose of this lab was calculate the weight of an object using two spring scales which support the object at two angles.
- \noindent
- We used the following equipment:
- \begin{enumerate}
- \item
- An Unknown Weight
- \item
- Two or Three Spring Scales
- \item
- String
- \item
- Meter Stick
- \end{enumerate}
- \begin{figure}[here]
- \includegraphics[scale=0.55]{Coke_Bottle_Weights}
- \caption{$\triangle ABC$ is formed with $\overline{AC}$ and $\overline{AB}$ as the strings with spring scales and $\overline{CB}$ as the ceiling.}
- \label{Setup}
- \end{figure}
- \section{Observations}
- \begin{tabular}{|l|l|}
- \hline
- \multicolumn{2}{|c|}{Measurements}\\
- \hline
- Component & Measurement\\
- \hline
- $h$ & 1.15 m \\
- $\overline{CB}$ & Unmeasured \\
- $\overline{CA}$ & 1.3 m \\
- $\overline{AB}$ & 1.86 m \\
- $T_1$ & 1.7 N\\
- $T_2$ & 1.1 N\\
- \hline
- \end{tabular}
- \section{Analysis}
- Because the object was at rest, we knew that the sum of the forces on the object was zero. This means that $T_1 + T_2 + mg = 0$, and by algebra $T_1 + T_2 = -mg$. If our measurements are accurate, $T_{1_{horizontal}} + T_{2_{horizontal}} = 0$, because the tensions are the only things acting on the object in the horizontal direction. Calculating the components of $T$ is simple trigonometry. To calculate the components, we need a few angles.
- \noindent
- First, let point $X$ be defined as the point where $\overline{CB}$ and $\overline{T_1+T_2}$ intersect.
- \[\angle CAX = \arccos{(\frac{h}{\overline{CA}})} = \theta_1\]
- \[\angle XAB = \arccos{(\frac{h}{\overline{AB}})} = \theta_2\]
- Next, we can calculate the vertical components of $T$:
- \[T_{1_v} = T_1 \cos{\theta_1}\]
- \[T_{2_v} = T_2 \cos{\theta_2}\]
- Because we know that $T_{1_h} + T_{2_h} = 0$, we don't need to calculate their components. As proven:
- \[T_{1_v} + T_{2_v} = T_1 + T_2 = -mg\]
- \section{Error Analysis}
- \subsection{Sources of Error}
- \subsection{Significant Digits}
- \section{Results}
- \end{document}
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