18 Block \(A\), of mass 0.2 kg , lies at rest on a rough plane. The plane is inclined at an angle \(\theta\) to the horizontal, such that \(\tan \theta = \frac { 7 } { 24 }\)
A light inextensible string is attached to \(A\) and runs parallel to the line of greatest slope until it passes over a smooth fixed pulley at the top of the slope. The other end of this string is attached to particle \(B\), of mass 2 kg , which is held at rest so that the string is taut, as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{27339c29-c4a1-480c-b882-930f8dacc7af-28_400_1022_731_511} 18

1. \(B\) is released from rest so that it begins to move vertically downwards with an acceleration of \(\frac { 543 } { 625 } \mathrm {~g} \mathrm {~m} \mathrm {~s} ^ { - 2 }\) Show that the coefficient of friction between \(A\) and the surface of the inclined plane is 0.17
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2. In this question use \(g = 9.81 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) When \(A\) reaches a speed of \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) the string breaks.
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3. 1. Find the distance travelled by \(A\) after the string breaks until first coming to rest.
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4. (ii) State an assumption that could affect the validity of your answer to part (b)(i).
   \includegraphics[max width=\textwidth, alt={}, center]{27339c29-c4a1-480c-b882-930f8dacc7af-31_2488_1716_219_153}