A uniform ladder of length 10.0m and mass 16.0kg is resting again… - Vidyadip

Question

A uniform ladder of length 10.0m and mass 16.0kg is resting against a vertical wall making an angle of 37° with it. The vertical wall is frictionless but the ground is rough. An electrician weighing 60.0kg climbs up the ladder. If he stays on the ladder at a point 8.00m from the lower end, what will be the normal force and the force of friction on the ladder by the ground? What should be the minimum coefficient of friction for the elctrician to work safely?

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Answer

$\text{R}_1=\mu\text{R}_2,\ \text{R}_2=16\text{g}+60\text{g}=745\text{N}$
$\text{R}_1\times10\cos37^\circ=16\text{g}\times5\sin37^\circ+60\text{g}\times8\times\sin37^\circ$
$\Rightarrow8\text{R}_1=\text{48g}+288\text{g}$
$\Rightarrow\text{R}_1=\frac{336\text{g}}{8}=412\text{N}=\text{f}$
Therefore $\mu=\frac{\text{R}_1}{\text{R}_2}=\frac{412}{745}=0.53$

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