A rough straight ramp is fixed to horizontal ground. The ramp is inclined at an angle $$\(\theta\)$$ to the horizontal, where $$\(\sin \theta=\frac{1}{7}\)$$. The points $$\(A\)$$ and $$\(B\)$$ are on a line of greatest slope of the ramp with $$\(A B=2.5 \mathrm{~m}\)$$ and $$\(B\)$$ above $$\(A\)$$, as shown in Figure 1. A package of mass $$\(2 \mathrm{~kg}\)$$ is projected up the ramp from $$\(A\)$$ with speed $$\(4 \mathrm{~ms}^{-1}\)$$ and first comes to instantaneous rest at $$\(B\)$$. The coefficient of friction between the package and the ramp is $$\(\mu\)$$. The package is modelled as a particle. Use the work-energy principle to find the value of $$\(\mu\)$$. (6)

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