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Solution to Test Paper 3

From Mechanics

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Line 3: Line 3:
| 1 (a)
| 1 (a)
|<math>\begin{align}
|<math>\begin{align}
-
& 0=24.5-9.8t \\
+
& 0=24\textrm{.}5-9\textrm{.}8t \\
-
& t=\frac{24.5}{9.8}=2.5\text{ seconds} \\
+
& t=\frac{24\textrm{.}5}{9\textrm{.}8}=2\textrm{.}5\text{ seconds} \\
\end{align}</math>
\end{align}</math>
Line 13: Line 13:
| 1 (b)
| 1 (b)
| <math>\begin{align}
| <math>\begin{align}
-
& {{0}^{2}}={{24.5}^{2}}+2\times (-9.8)\times s \\
+
& {{0}^{2}}={{24\textrm{.}5}^{2}}+2\times (-9\textrm{.}8)\times s \\
-
& s=\frac{{{24.5}^{2}}}{2\times 9.8}=30.625\text{ m} \\
+
& s=\frac{{{24\textrm{.}5}^{2}}}{2\times 9\textrm{.}8}=30\textrm{.}625\text{ m} \\
\end{align}</math>
\end{align}</math>
Line 22: Line 22:
<p>
<p>
-
<math>s=\frac{1}{2}(24.5+0)\times 2.5=30.625\text{ m}</math>
+
<math>s=\frac{1}{2}(24\textrm{.}5+0)\times 2.5=30\textrm{.}625\text{ m}</math>
</p>
</p>
Line 57: Line 57:
| 2 (c)
| 2 (c)
| <math>\begin{align}
| <math>\begin{align}
-
& T-4900=500\times 0.6 \\
+
& T-4900=500\times 0\textrm{.}6 \\
& T=300+4900=5200\text{ N} \\
& T=300+4900=5200\text{ N} \\
\end{align}</math>
\end{align}</math>
Line 64: Line 64:
|-
|-
-
| 3 (d)
+
| 2 (d)
| <math>\begin{align}
| <math>\begin{align}
& 4800-4900=500a \\
& 4800-4900=500a \\
-
& a=\frac{-100}{500}=-0.2\text{ m}{{\text{s}}^{\text{-2}}} \\
+
& a=\frac{-100}{500}=-0\textrm{.}2\text{ m}{{\text{s}}^{\text{-2}}} \\
-
& 0.\text{2 m}{{\text{s}}^{-\text{2}}}\quad \text{downwards} \\
+
& 0\textrm{.}\text{2 m}{{\text{s}}^{-\text{2}}}\quad \text{downwards} \\
\end{align}</math>
\end{align}</math>
Line 81: Line 81:
|-
|-
| 3 (a)
| 3 (a)
-
|<math>R=5\times 9.8\cos 42{}^\circ =36.4\text{ N}</math>
+
|<math>R=5\times 9\textrm{.}8\cos 42{}^\circ =36\textrm{.}4\text{ N}</math>
| (2 mark)
| (2 mark)
Line 87: Line 87:
|-
|-
| 3 (b)
| 3 (b)
-
| <math>F=0.4R=14.6\text{ N}</math>
+
| <math>F=0\textrm{.}4R=14\textrm{.}6\text{ N}</math>
| (2 marks)
| (2 marks)
Line 95: Line 95:
| 3 (c)
| 3 (c)
| <math>\begin{align}
| <math>\begin{align}
-
& 5\times 9.8\sin 42{}^\circ -14.6=5a \\
+
& 5\times 9\textrm{.}8\sin 42{}^\circ -14\textrm{.}6=5a \\
-
& a=\frac{18.22}{5}=3.64\text{ m}{{\text{s}}^{\text{-2}}} \\
+
& a=\frac{18\textrm{.}22}{5}=3\textrm{.}64\text{ m}{{\text{s}}^{\text{-2}}} \\
\end{align}</math>
\end{align}</math>
Line 105: Line 105:
| 3 (d)
| 3 (d)
| <math>\begin{align}
| <math>\begin{align}
-
& 2=\frac{1}{2}\times 3.64{{t}^{2}} \\
+
& 2=\frac{1}{2}\times 3\textrm{.}64{{t}^{2}} \\
-
& t=\sqrt{\frac{4}{3.64}}=1.05\text{ seconds} \\
+
& t=\sqrt{\frac{4}{3\textrm{.}64}}=1\textrm{.}05\text{ seconds} \\
\end{align}</math>
\end{align}</math>
Line 124: Line 124:
| 4 (a)
| 4 (a)
| <math>\begin{align}
| <math>\begin{align}
-
& Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\
+
& Q\cos 40{}^\circ =8\times 9\textrm{.}8\sin 40{}^\circ \\
-
& Q=\frac{8\times 9.8\sin 40{}^\circ }{\cos 40{}^\circ }=65.8\text{ N} \\
+
& Q=\frac{8\times 9\textrm{.}8\sin 40{}^\circ }{\cos 40{}^\circ }=65\textrm{.}8\text{ N} \\
\end{align}</math>
\end{align}</math>
Line 134: Line 134:
| 4 (b)
| 4 (b)
|<math>\begin{align}
|<math>\begin{align}
-
& Q\cos 40{}^\circ +F=8\times 9.8\sin 40{}^\circ \\
+
& Q\cos 40{}^\circ +F=8\times 9\textrm{.}8\sin 40{}^\circ \\
-
& Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ =R \\
+
& Q\sin 40{}^\circ +8\times 9\textrm{.}8\cos 40{}^\circ =R \\
-
& Q\cos 40{}^\circ =8\times 9.8\sin 40{}^\circ \\
+
& Q\cos 40{}^\circ =8\times 9\textrm{.}8\sin 40{}^\circ \\
-
& \text{ }-0.3(Q\sin 40{}^\circ +8\times 9.8\cos 40{}^\circ ) \\
+
& \text{ }-0\textrm{.}3(Q\sin 40{}^\circ +8\times 9\textrm{.}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 } \\
+
& Q=\frac{8\times 9\textrm{.}8\sin 40{}^\circ -0.\textrm{.}\times 8\times 9\textrm{.}8\cos 40{}^\circ }{\cos 40{}^\circ +0.\times \sin 40{}^\circ } \\
-
& \text{ }=33.8\text{ N} \\
+
& \text{ }=33\textrm{.}8\text{ N} \\
\end{align}</math>
\end{align}</math>
Line 155: Line 155:
|-
|-
| 5 (a)
| 5 (a)
-
| <math>\mathbf{v}=(\mathbf{i}+\mathbf{j})+(0.05\mathbf{i}-0.1\mathbf{j})t</math>
+
| <math>\mathbf{v}=(\mathbf{i}+\mathbf{j})+(0\textrm{.}05\mathbf{i}-0\textrm{.}1\mathbf{j})t</math>
Line 164: Line 164:
| 5 (b)
| 5 (b)
| <math>\begin{align}
| <math>\begin{align}
-
& -(1+0.05t)=1-0.1t \\
+
& -(1+0\textrm{.}05t)=1-0\textrm{.}1t \\
-
& 0.05t=2 \\
+
& 0\textrm{.}05t=2 \\
& t=40 \\
& t=40 \\
\end{align}</math>
\end{align}</math>

Revision as of 09:30, 8 April 2012

Solutions
1 (a) 0=24.5−9.8tt=9.824.5=2.5 seconds (3 marks)


1 (b) 02=24.52+2(−9.8)ss=24.5229.8=30.625 mORs=21(24.5+0)25=30.625 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=5000.6T=300+4900=5200 N (3 mark)
2 (d) 4800−4900=500aa=500−100=−0.2 ms-20.2 ms−2downwards (4 mark)
(9 marks)


3 (a) R=59.8cos42=36.4 N (2 mark)


3 (b) F=0.4R=14.6 N (2 marks)


3 (c) 59.8sin42−14.6=5aa=518.22=3.64 ms-2 (3 marks)


3 (d) 2=213.64t2t=43.64=1.05 seconds  (3 marks)


(10 marks)


4 (a) Qcos40=89.8sin40Q=cos4089.8sin40=65.8 N (3 mark)


4 (b) Qcos40+F=89.8sin40Qsin40+89.8cos40=RQcos40=89.8sin40 −0.3(Qsin40+89.8cos40)Q=cos40+0sin4089.8sin40−0.89.8cos40 =33.8 N (5 marks)



(8 marks)


5 (a) v=(i+j)+(0.05i−0.1j)t


(2 marks)


5 (b) −(1+0.05t)=1−0.1t0.05t=2t=40 (4 marks)



(6 marks)


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