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Solution to Test Paper 3

From Mechanics

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|-
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| 3 (a)
| 3 (a)
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|[[Image:test1ans1.gif]]
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|<math>R=5\times 9.8\cos 42{}^\circ =36.4\text{ N}</math>
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| (1 mark)
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| (2 mark)
|-
|-
| 3 (b)
| 3 (b)
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| <math>F=2\times 1\textrm{.}8=3\textrm{.}6\text{ N}</math>
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| <math>F=0.4R=14.6\text{ N}</math>
 +
 
| (2 marks)
| (2 marks)
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|-
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| 3 (c)
| 3 (c)
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| <math>R=2\times 9\textrm{.}8=19\textrm{.}6\text{ N}</math>
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| <math>\begin{align}
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| (2 marks)
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& 5\times 9.8\sin 42{}^\circ -14.6=5a \\
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& a=\frac{18.22}{5}=3.64\text{ m}{{\text{s}}^{\text{-2}}} \\
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\end{align}</math>
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| (3 marks)
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| 3 (d)
| 3 (d)
| <math>\begin{align}
| <math>\begin{align}
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& 4800-4900=500a \\
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& 2=\frac{1}{2}\times 3.64{{t}^{2}} \\
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& a=\frac{-100}{500}=-0.2\text{ m}{{\text{s}}^{\text{-2}}} \\
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& t=\sqrt{\frac{4}{3.64}}=1.05\text{ seconds} \\
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& 0.\text{2 m}{{\text{s}}^{-\text{2}}}\quad \text{downwards} \\
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\end{align}</math>
\end{align}</math>
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|
|
|
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| '''(8 marks)'''
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| '''(10 marks)'''

Revision as of 09:13, 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) Image:test1ans2.gif (1 mark)


4 (b) R+Tsin30=2009.8R+0.5T=1960R=1960−0.5T (3 marks)


4 (c)

F=Tcos30Tcos30=0.6(1960−0.5T)T(cos30+0.3)=1176T=1176(cos30+0.3)=1010 N

(4 marks)


(8 marks)


5 (a) 5i−2j=4i+3j+10aa=110(i−5j)=0.1i−0.5j ms-2AG  (3 marks)


5 (b) r=(4i+3j)t+0.5(0.1i−0.5j)t2 (2 marks)


5 (c) r=(4t+0.05t2)i+(3t−0.25t2)j3t−0.25t2=0t(3−0.25t)=0t=0 or t=30.25=12 st=12 s (3 marks)


5 (d) v=(4+0.1t)i+(3−0.5t)j3−0.5t=0t=6 s (3 marks)


(11 marks)


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

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