A block of mass $2{\text{ }}kg$ is at rest on a horizontal floor. The coefficient of friction between the block and the floor is $\mu $. A force of magnitude $12{\text{ }}N$ acts on the block at an angle $\alpha $ to the horizontal, where $\tan \alpha = \frac{3}{4}$. When the applied force acts downwards as in Fig. 1 the block remains at rest.
a) Show that $\mu \geqslant \frac{6}{{17}}$.
When the applied force acts upwards as in Fig. 2 the block slides along the floor.
b) Find another inequality for $\mu $.

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