8 A crate, of mass 40 kg , is initially at rest on a rough slope inclined at \(30 ^ { \circ }\) to the horizontal, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-18_355_882_411_587} The coefficient of friction between the crate and the slope is \(\mu\).

1. Given that the crate is on the point of slipping down the slope, find \(\mu\).
2. A horizontal force of magnitude \(X\) newtons is now applied to the crate, as shown in the diagram.
   \includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-18_357_881_1208_575}
   1. Find the normal reaction on the crate in terms of \(X\).
   2. Given that the crate accelerates up the slope at \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find \(X\).
      [0pt] [5 marks]
      \includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-19_2484_1707_221_153}