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\title{Lab 4: Newton's 2nd Law\\$\littleg$ by Atwood's Machine}
\author{Ben Wildeboer\\Calc-based Physics I\\Three Rivers CC}
\date{September 26, 2011}
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\section*{Description}
The purpose of this lab was to determine the value of $\littleg$ using Atwood's Machine and measuring the acceleration.

\section*{Data and Measurements}
See attached sheet.

\section*{Calculations}
\subsection*{Part I: Determining acceleration of the system}
$\Delta y = \displacement{0.650}$\\
$m_1 = \mass{.200}\\
m_2 = \mass{.210}\\
\text{average }t = \duration{2.402}\\ \\
y=y_0+\onehalf at^2\\
a=\dfrac{2(\Delta y)}{t^2}\\
a=\dfrac{(2(\displacement{0.650})}{(\duration{2.402})^2}=\acceleration{0.2253}$

\subsection*{Part II: Using acceleration of the system to find $\littleg$}
$F_1 + F_2 = F_{g_1} - F_{g_2}\\
m_2a+m_1a=m_1\littleg -m_2 \littleg \\
(m_2+m_1)a=(m_1-m_2)\littleg \\
\littleg = \quant{\dfrac{m_2+m_1}{m_2-m_1}}a \\
\littleg = \quant{\dfrac{\mass{0.210}+\mass{0.200}}{\mass{0.210}-\mass{0.200}}}\acceleration{0.2253}= \quant{\dfrac{\mass{0.410}}{\mass{0.010}}}\acceleration{0.2253}=\acceleration{9.2373}\\ \\
\textbf{\% error} = \dfrac{\littlegn - \acceleration{9.2373}}{\littlegn}=0.0574 \text{ or } 5.74\%$


\section*{Conclusions}
This lab demonstrated Newton's 2nd law by showing unbalanced forces result in an acceleration. Using that acceleration, we found we were able to fairly closely approximate the value for $\littleg$. Though our calculated magnitude for $\littleg$ showed an error of 5.73\%, this is a fairly close value considering possible errors such as human timing, friction from the pulley, and the use of a non-massless string.


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