Question

Evaluate the magnitude and direction of the resultant vector. \[ \begin{array}{l} |\vec{R}|= \\ \theta_{\mathrm{R}}= \end{array} \] ? The equilibrium vector has the same length as the vector \( \vec{R} \) but in the opposite direction. \[ \begin{array}{l} |\vec{E}|=|\vec{R}|=280 \mathrm{~kg} \quad 287^{\circ} \\ \theta_{\mathrm{E}}=\theta_{\mathrm{R}}+180^{\circ}= \end{array} \] ? Record \( \vec{F}_{1}, \vec{F}_{2}, \vec{R} \), and \( \vec{E} \) in the analytical result row of Table 1. \[ \begin{array}{l} F(x-200 \cos (60)=200 \cdot 0 \cdot 5-100 \\ F 1 y=200 \sin (60)=200 \frac{\sqrt{3}}{2}=100 \sqrt{3} \cdot 173.2 \end{array} \] \( 100-100 \sqrt{3} \) \[ \begin{array}{l} R_{x}=-73.2 \\ R_{y}=2732 \end{array} \] \begin{table} \captionsetup{labelformat=empty} \caption{Table 1:} \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline \backslashbox{Method}{results} & \( \vec{F}_{1} =m_{1} g \) & \( \boldsymbol{a} \equiv \theta_{1} \) & \( \left|\vec{F}_{2}\right| =m_{2} g \) & \( \beta \equiv \theta_{2} \) & \( |\vec{R}| \) & \( \theta_{\mathrm{R}} \) & \( |\vec{E}| \) & \( \gamma \equiv \theta_{\mathrm{E}} \) \\ \hline Experimental Measurement: & 0.2 & 60 & 0.2 & 150 & 0.4 & & & \\ \hline Graphical Results: & & & & & & & & \\ \hline Analytical Results & & & & & & & & \\ \hline \end{tabular} \end{table}

          Evaluate the magnitude and direction of the resultant vector.
\[
\begin{array}{l}
|\vec{R}|= \\
\theta_{\mathrm{R}}=
\end{array}
\]
? The equilibrium vector has the same length as the vector \( \vec{R} \) but in the opposite direction.
\[
\begin{array}{l}
|\vec{E}|=|\vec{R}|=280 \mathrm{~kg} \quad 287^{\circ} \\
\theta_{\mathrm{E}}=\theta_{\mathrm{R}}+180^{\circ}=
\end{array}
\]
? Record \( \vec{F}_{1}, \vec{F}_{2}, \vec{R} \), and \( \vec{E} \) in the analytical result row of Table 1.
\[
\begin{array}{l}
F(x-200 \cos (60)=200 \cdot 0 \cdot 5-100 \\
F 1 y=200 \sin (60)=200 \frac{\sqrt{3}}{2}=100 \sqrt{3} \cdot 173.2
\end{array}
\]
\( 100-100 \sqrt{3} \)
\[
\begin{array}{l}
R_{x}=-73.2 \\
R_{y}=2732
\end{array}
\]

\begin{table}
\captionsetup{labelformat=empty}
\caption{Table 1:}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline \backslashbox{Method}{results} & \( \vec{F}_{1} =m_{1} g \) & \( \boldsymbol{a} \equiv \theta_{1} \) & \( \left|\vec{F}_{2}\right| =m_{2} g \) & \( \beta \equiv \theta_{2} \) & \( |\vec{R}| \) & \( \theta_{\mathrm{R}} \) & \( |\vec{E}| \) & \( \gamma \equiv \theta_{\mathrm{E}} \) \\
\hline Experimental Measurement: & 0.2 & 60 & 0.2 & 150 & 0.4 & & & \\
\hline Graphical Results: & & & & & & & & \\
\hline Analytical Results & & & & & & & & \\
\hline
\end{tabular}
\end{table}

Evaluate the magnitude and direction of the resultant vector.

|R⃗|=
θR=

? The equilibrium vector has the same length as the vector R⃗ but in the opposite direction.

|E⃗|=|R⃗|=280 kg 287^∘
θE=θR+180^∘=

? Record F⃗1, F⃗2, R⃗, and E⃗ in the analytical result row of Table 1.

F(x-200 cos (60)=200 · 0 · 5-100

F 1 y=200 sin (60)=200 (√(3))/(2)=100 √(3)· 173.2

100-100 √(3)

Rx=-73.2

Ry=2732

labelformat=empty
Table 1:

Methodresults F⃗1 =m1 g a≡θ1 |F⃗2| =m2 g β≡θ2 |R⃗| θR |E⃗| γ≡θE

Experimental Measurement: 0.2 60 0.2 150 0.4

Graphical Results:

Analytical Results

Added by Aaron M.

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