Processing Math: Done
Solution 4.6a
From Mechanics
(Difference between revisions)
(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> | ||
+ | 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\textrm{.}94\mathbf{i}+40\times 0\textrm{.}342\mathbf{j} \\ | ||
+ | & =37\textrm{.}6\mathbf{i}+13\textrm{.}7\mathbf{j}\ \text{N}\\ | ||
+ | \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\textrm{.}866\mathbf{i}-50\times 0\textrm{.}50\mathbf{j} \\ | ||
+ | & =43\textrm{.}3\mathbf{i}-25\mathbf{j} \ \text{N}\\ | ||
\end{align}</math> | \end{align}</math> |
Current revision
i+Fsin
j
1=20
i+40sin20
j=40
0.94i+40
0.342j=37.6i+13.7j N
2=−30
−30
i+50sin
−30
j=50
0.866i−50
0.50j=43.3i−25j N