16 A block of mass \(m\) kg rests on rough horizontal ground. The coefficient of friction between the block and the ground is \(\mu\). A force of magnitude \(T \mathrm {~N}\) is applied at an angle \(\theta\) radians above the horizontal as shown in the diagram and the block slides without tilting or lifting.
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- Show that the acceleration of the block is given by \(\frac { T } { m } \cos \theta - \mu g + \frac { T } { m } \mu \sin \theta\).
For a fixed value of \(T\), the acceleration of the block depends on the value of \(\theta\). The acceleration has its greatest value when \(\theta = \alpha\).
- Find an expression for \(\alpha\) in terms of \(\mu\).