4 A rigid thin uniform rod AB with length 2.4 m and weight 30 N is used in different situations.
- In the first situation, the rod rests on a small support 0.6 m from B and is held horizontally in equilibrium by a vertical string attached to A, as shown in Fig. 4.1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{42b6ee17-f0ae-4687-8392-281ba724a607-5_196_707_456_680}
\captionsetup{labelformat=empty}
\caption{Fig. 4.1}
\end{figure}
Calculate the tension in the string and the force of the support on the rod. - In the second situation, the rod rests in equilibrium on the point of slipping with end A on a horizontal floor and the rod resting at P on a fixed block of height 0.9 m , as shown in Fig. 4.2. The rod is perpendicular to the edge of the block on which it rests and is inclined at \(\theta\) to the horizontal.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{42b6ee17-f0ae-4687-8392-281ba724a607-5_208_746_1101_657}
\captionsetup{labelformat=empty}
\caption{Fig. 4.2}
\end{figure}
(A) Suppose that the contact between the block and the rod is rough with coefficient of friction 0.6 and contact between the end A and the floor is smooth.
Show that \(\tan \theta = 0.6\).
(B) Suppose instead that the contact between the block and the rod is smooth and the contact between the end A and the floor is rough. The rod is now in limiting equilibrium at a different angle \(\theta\) such that the distance AP is 1.5 m .
Calculate the normal reaction of the block on the rod.
Calculate the coefficient of friction between the rod and the floor.