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Solution 4.6a

From Mechanics

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(New page: <math>\begin{align} & \mathbf{F}=F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j} \end{align}</math>)
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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>
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and
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<math>\alpha 1=20{}^\circ
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</math>
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this gives
 +
 +
 +
<math>\begin{align}
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& \mathbf{F}1=40\cos 20{}^\circ
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\mathbf{i}+40\sin 20{}^\circ
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\mathbf{j}=40\times 0.94\mathbf{i}+40\times 0.342\mathbf{j} \\
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& =37.6\mathbf{i}+13.7\mathbf{j} \\
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\end{align}</math>
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 +
 +
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<math>F2=50\ \text{N}</math>
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and
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<math>\alpha 2=-30{}^\circ
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</math>
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this gives
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 +
 +
<math>\begin{align}
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& \mathbf{F}2=50\cos \left( -30
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\right) {}^\circ
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\mathbf{i}+50\sin \left( -30 \right) {}^\circ
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\mathbf{j}=50\times 0.866\mathbf{i}-50\times 0.50\mathbf{j} \\
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& =43.3\mathbf{i}+25\mathbf{j} \\
\end{align}</math>
\end{align}</math>

Revision as of 15:21, 23 March 2010

F=Fcosi+Fsinj


F1=40 N and 1=20 this gives


F1=40cos20i+40sin20j=40094i+400342j=376i+137j


F2=50 N and 2=30 this gives


F2=50cos30i+50sin30j=500866i50050j=433i+25j