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Solution to Test Paper 3

From Mechanics

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Line 123: Line 123:
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| 4 (a)
| 4 (a)
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| [[Image:test1ans2.gif]]
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| <math>\begin{align}
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| (1 mark)
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& Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\
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& Q=\frac{8\times 9.8\sin 40{}^\circ }{\cos 40{}^\circ }=65.8\text{ N} \\
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\end{align}</math>
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 +
| (3 mark)
|-
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| 4 (b)
| 4 (b)
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| <math>\begin{align}
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|<math>\begin{align}
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& R+T\sin 30{}^\circ =200\times 9 \textrm{.}8 \\
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& Q\cos 40{}^\circ +F=8\times 9.8\sin 40{}^\circ \\
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& R+0 \textrm{.}5T=1960 \\
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& Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ =R \\
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& R=1960-0 \textrm{.}5T \\
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& Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\
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& \text{ }-0.3(Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ ) \\
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& 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 } \\
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& \text{ }=33.8\text{ N} \\
\end{align}</math>
\end{align}</math>
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| (3 marks)
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| (5 marks)
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|-
 
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| 4 (c)
 
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| <math></math>
 
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<math>\begin{align}
 
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& F=T\cos 30{}^\circ \\
 
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& T\cos 30{}^\circ =0\textrm{.}6(1960-0\textrm{.}5T) \\
 
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& T(\cos 30{}^\circ +0\textrm{.}3)=1176 \\
 
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& T=\frac{1176}{(\cos 30{}^\circ +0\textrm{.}3)}=1010\text{ N} \\
 
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\end{align}</math>
 
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| (4 marks)
 
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|-
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| 5 (a)
| 5 (a)
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| <math>\begin{align}
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| <math>\mathbf{v}=(\mathbf{i}+\mathbf{j})+(0.05\mathbf{i}-0.1\mathbf{j})t</math>
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& 5\mathbf{i}-2\mathbf{j}=4\mathbf{i}+3\mathbf{j}+10\mathbf{a} \\
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& \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}}} \\
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\end{align}</math>
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AG
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| (2 marks)
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| (3 marks)
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|-
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| 5 (b)
| 5 (b)
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| <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>
 
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| (2 marks)
 
- 
- 
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|-
 
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| 5 (c)
 
| <math>\begin{align}
| <math>\begin{align}
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& \mathbf{r}=(4t+0\textrm{.}05{{t}^{2}})\mathbf{i}+(3t-0\textrm{.}25{{t}^{2}})\mathbf{j} \\
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& -(1+0.05t)=1-0.1t \\
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& 3t-0\textrm{.}25{{t}^{2}}=0 \\
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& 0.05t=2 \\
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& t(3-0\textrm{.}25t)=0 \\
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& t=40 \\
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& t=0\text{ or }t=\frac{3}{0\textrm{.}25}=12\text{ s} \\
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& t=12\text{ s} \\
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\end{align}</math>
\end{align}</math>
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| (3 marks)
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| (4 marks)
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|-
 
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| 5 (d)
 
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| <math>\begin{align}
 
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& \mathbf{v}=(4+0\textrm{.}1t)\mathbf{i}+(3-0\textrm{.}5t)\mathbf{j} \\
 
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& 3-0\textrm{.}5t=0 \\
 
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& t=6 \text{ s} \\
 
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\end{align}</math>
 
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| (3 marks)
 
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|
|
|
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| '''(11 marks)'''
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| '''(6 marks)'''

Revision as of 09:19, 8 April 2012

Solutions
1 (a) 0=245−98tt=98245=25 seconds (3 marks)


1 (b) 02=2452+2(−98)ss=2452298=30625 mORs=21(245+0)25=30625 m (3 marks)
1 (c) 61.25 m


(1 marks)
(7 marks)


2 (a) Image:test3ans1.gif (1 marks)


2 (b) T = 4900 N (1 marks)


2 (c) T−4900=50006T=300+4900=5200 N (3 mark)
3 (d) 4800−4900=500aa=500−100=−02 ms-202 ms−2downwards (4 mark)
(9 marks)


3 (a) R=598cos42=364 N (2 mark)


3 (b) F=04R=146 N (2 marks)


3 (c) 598sin42−146=5aa=51822=364 ms-2 (3 marks)


3 (d) 2=21364t2t=4364=105 seconds  (3 marks)


(10 marks)


4 (a) Qcos40=898sin40Q=cos40898sin40=658 N (3 mark)


4 (b) Qcos40+F=898sin40Qsin40+898cos40=RQcos40=898sin40 −03(Qsin40+898cos40)Q=cos40+03sin40898sin40−03898cos40 =338 N (5 marks)



(8 marks)


5 (a) v=(i+j)+(005i−01j)t


(2 marks)


5 (b) −(1+005t)=1−01t005t=2t=40 (4 marks)



(6 marks)


AG: Answer Given in Question – Working must justify answer.

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