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Revision as of 15:16, 23 March 2010 (edit) Ian (Talk | contribs) (New page: <math>\begin{align} & \mathbf{F}=F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j} \end{align}</math>) ← Previous diff		Revision as of 15:21, 23 March 2010 (edit) (undo) Ian (Talk | contribs) Next diff →
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	<math>\begin{align}		<math>\begin{align}
	& \mathbf{F}=F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j}		& \mathbf{F}=F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j}
		+	\end{align}</math>
		+
		+
		+	<math>F1=40\ \text{N}</math>
		+	and
		+	<math>\alpha 1=20{}^\circ
		+	</math>
		+	this gives
		+
		+
		+	<math>\begin{align}
		+	& \mathbf{F}1=40\cos 20{}^\circ
		+	\mathbf{i}+40\sin 20{}^\circ
		+	\mathbf{j}=40\times 0.94\mathbf{i}+40\times 0.342\mathbf{j} \\
		+	& =37.6\mathbf{i}+13.7\mathbf{j} \\
		+	\end{align}</math>
		+
		+
		+
		+	<math>F2=50\ \text{N}</math>
		+	and
		+	<math>\alpha 2=-30{}^\circ
		+	</math>
		+	this gives
		+
		+
		+	<math>\begin{align}
		+	& \mathbf{F}2=50\cos \left( -30
		+	\right) {}^\circ
		+	\mathbf{i}+50\sin \left( -30 \right) {}^\circ
		+	\mathbf{j}=50\times 0.866\mathbf{i}-50\times 0.50\mathbf{j} \\
		+	& =43.3\mathbf{i}+25\mathbf{j} \\
	\end{align}</math>		\end{align}</math>

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Revision as of 15:21, 23 March 2010

\displaystyle \begin{align} & \mathbf{F}=F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j} \end{align}

\displaystyle F1=40\ \text{N} and \displaystyle \alpha 1=20{}^\circ this gives

\displaystyle \begin{align} & \mathbf{F}1=40\cos 20{}^\circ \mathbf{i}+40\sin 20{}^\circ \mathbf{j}=40\times 0.94\mathbf{i}+40\times 0.342\mathbf{j} \\ & =37.6\mathbf{i}+13.7\mathbf{j} \\ \end{align}

\displaystyle F2=50\ \text{N} and \displaystyle \alpha 2=-30{}^\circ this gives

\displaystyle \begin{align} & \mathbf{F}2=50\cos \left( -30 \right) {}^\circ \mathbf{i}+50\sin \left( -30 \right) {}^\circ \mathbf{j}=50\times 0.866\mathbf{i}-50\times 0.50\mathbf{j} \\ & =43.3\mathbf{i}+25\mathbf{j} \\ \end{align}