From Mechanics
(Difference between revisions)
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| | 4 (a) | | | 4 (a) |
- | | [[Image:test1ans2.gif]] | + | | <math>\begin{align} |
- | | (1 mark) | + | & Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\ |
| + | & Q=\frac{8\times 9.8\sin 40{}^\circ }{\cos 40{}^\circ }=65.8\text{ N} \\ |
| + | \end{align}</math> |
| + | |
| + | | (3 mark) |
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| | 4 (b) | | | 4 (b) |
- | | <math>\begin{align} | + | |<math>\begin{align} |
- | & R+T\sin 30{}^\circ =200\times 9 \textrm{.}8 \\ | + | & Q\cos 40{}^\circ +F=8\times 9.8\sin 40{}^\circ \\ |
- | & R+0 \textrm{.}5T=1960 \\ | + | & Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ =R \\ |
- | & R=1960-0 \textrm{.}5T \\ | + | & Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\ |
| + | & \text{ }-0.3(Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ ) \\ |
| + | & Q=\frac{8\times 9.8\sin 40{}^\circ -0.3\times 8\times 9.8\cos 40{}^\circ }{\cos 40{}^\circ +0.3\times \sin 40{}^\circ } \\ |
| + | & \text{ }=33.8\text{ N} \\ |
| \end{align}</math> | | \end{align}</math> |
- | | (3 marks) | + | |
| + | | (5 marks) |
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- | | 4 (c) | |
- | | <math></math> | |
- | <math>\begin{align} | |
- | & F=T\cos 30{}^\circ \\ | |
- | & T\cos 30{}^\circ =0\textrm{.}6(1960-0\textrm{.}5T) \\ | |
- | & T(\cos 30{}^\circ +0\textrm{.}3)=1176 \\ | |
- | & T=\frac{1176}{(\cos 30{}^\circ +0\textrm{.}3)}=1010\text{ N} \\ | |
- | \end{align}</math> | |
- | | (4 marks) | |
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| | 5 (a) | | | 5 (a) |
- | | <math>\begin{align} | + | | <math>\mathbf{v}=(\mathbf{i}+\mathbf{j})+(0.05\mathbf{i}-0.1\mathbf{j})t</math> |
- | & 5\mathbf{i}-2\mathbf{j}=4\mathbf{i}+3\mathbf{j}+10\mathbf{a} \\
| + | |
- | & \mathbf{a}=\frac{1}{10}(\mathbf{i}-5\mathbf{j})=\left( 0\textrm{.}1\mathbf{i}-0\textrm{.}5\mathbf{j} \right)\text{ m}{{\text{s}}^{\text{-2}}} \\
| + | |
- | \end{align}</math>
| + | |
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- | AG
| + | | (2 marks) |
- | | (3 marks) | + | |
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| | 5 (b) | | | 5 (b) |
- | | <math>\mathbf{r}=(4\mathbf{i}+3\mathbf{j})t+0\textrm{.}5(0\textrm{.}1\mathbf{i}-0\textrm{.}5\mathbf{j}){{t}^{2}}</math> | |
- | | (2 marks) | |
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- | | 5 (c) | |
| | <math>\begin{align} | | | <math>\begin{align} |
- | & \mathbf{r}=(4t+0\textrm{.}05{{t}^{2}})\mathbf{i}+(3t-0\textrm{.}25{{t}^{2}})\mathbf{j} \\ | + | & -(1+0.05t)=1-0.1t \\ |
- | & 3t-0\textrm{.}25{{t}^{2}}=0 \\
| + | & 0.05t=2 \\ |
- | & t(3-0\textrm{.}25t)=0 \\
| + | & t=40 \\ |
- | & t=0\text{ or }t=\frac{3}{0\textrm{.}25}=12\text{ s} \\ | + | |
- | & t=12\text{ s} \\ | + | |
| \end{align}</math> | | \end{align}</math> |
- | | (3 marks) | + | |
| + | | (4 marks) |
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- | | 5 (d) | |
- | | <math>\begin{align} | |
- | & \mathbf{v}=(4+0\textrm{.}1t)\mathbf{i}+(3-0\textrm{.}5t)\mathbf{j} \\ | |
- | & 3-0\textrm{.}5t=0 \\ | |
- | & t=6 \text{ s} \\ | |
- | \end{align}</math> | |
- | | (3 marks) | |
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- | | '''(11 marks)''' | + | | '''(6 marks)''' |
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Revision as of 09:19, 8 April 2012
Solutions
1 (a)
| \displaystyle \begin{align}
& 0=24.5-9.8t \\
& t=\frac{24.5}{9.8}=2.5\text{ seconds} \\
\end{align}
| (3 marks)
|
1 (b)
| \displaystyle \begin{align}
& {{0}^{2}}={{24.5}^{2}}+2\times (-9.8)\times s \\
& s=\frac{{{24.5}^{2}}}{2\times 9.8}=30.625\text{ m} \\
\end{align}
OR
\displaystyle s=\frac{1}{2}(24.5+0)\times 2.5=30.625\text{ m}
| (3 marks)
|
1 (c)
| 61.25 m
| (1 marks)
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| (7 marks)
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2 (a)
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| (1 marks)
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2 (b)
| T = 4900 N
| (1 marks)
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2 (c)
| \displaystyle \begin{align}
& T-4900=500\times 0.6 \\
& T=300+4900=5200\text{ N} \\
\end{align}
| (3 mark)
|
3 (d)
| \displaystyle \begin{align}
& 4800-4900=500a \\
& a=\frac{-100}{500}=-0.2\text{ m}{{\text{s}}^{\text{-2}}} \\
& 0.\text{2 m}{{\text{s}}^{-\text{2}}}\quad \text{downwards} \\
\end{align}
| (4 mark)
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| (9 marks)
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3 (a)
| \displaystyle R=5\times 9.8\cos 42{}^\circ =36.4\text{ N}
| (2 mark)
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3 (b)
| \displaystyle F=0.4R=14.6\text{ N}
| (2 marks)
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3 (c)
| \displaystyle \begin{align}
& 5\times 9.8\sin 42{}^\circ -14.6=5a \\
& a=\frac{18.22}{5}=3.64\text{ m}{{\text{s}}^{\text{-2}}} \\
\end{align}
| (3 marks)
|
3 (d)
| \displaystyle \begin{align}
& 2=\frac{1}{2}\times 3.64{{t}^{2}} \\
& t=\sqrt{\frac{4}{3.64}}=1.05\text{ seconds} \\
\end{align}
| (3 marks)
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| (10 marks)
|
4 (a)
| \displaystyle \begin{align}
& Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\
& Q=\frac{8\times 9.8\sin 40{}^\circ }{\cos 40{}^\circ }=65.8\text{ N} \\
\end{align}
| (3 mark)
|
4 (b)
| \displaystyle \begin{align}
& Q\cos 40{}^\circ +F=8\times 9.8\sin 40{}^\circ \\
& Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ =R \\
& Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\
& \text{ }-0.3(Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ ) \\
& Q=\frac{8\times 9.8\sin 40{}^\circ -0.3\times 8\times 9.8\cos 40{}^\circ }{\cos 40{}^\circ +0.3\times \sin 40{}^\circ } \\
& \text{ }=33.8\text{ N} \\
\end{align}
| (5 marks)
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| (8 marks)
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5 (a)
| \displaystyle \mathbf{v}=(\mathbf{i}+\mathbf{j})+(0.05\mathbf{i}-0.1\mathbf{j})t
| (2 marks)
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5 (b)
| \displaystyle \begin{align}
& -(1+0.05t)=1-0.1t \\
& 0.05t=2 \\
& t=40 \\
\end{align}
| (4 marks)
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| (6 marks)
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AG: Answer Given in Question – Working must justify answer.