3 A side view of a free-standing kitchen cupboard on a horizontal floor is shown in Fig. 3.1. The cupboard consists of: a base CE; vertical ends BC and DE; an overhanging horizontal top AD. The dimensions, in metres, of the cupboard are shown in the figure. The cupboard and contents have a weight of 340 N and centre of mass at G .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2aaae62-a5f3-47da-afa5-1dd4b37ea2d6-4_533_1356_477_392}
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\caption{Fig. 3.1}
\end{figure}
- Calculate the magnitude of the vertical force required at A for the cupboard to be on the point of tipping in the cases where the force acts
(A) downwards,
(B) upwards.
A force of magnitude \(Q \mathrm {~N}\) is now applied at A at an angle of \(\theta\) to AB , as shown in Fig. 3.2, where \(\cos \theta = \frac { 5 } { 13 } \left( \right.\) and \(\left. \sin \theta = \frac { 12 } { 13 } \right)\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2aaae62-a5f3-47da-afa5-1dd4b37ea2d6-4_303_1134_1619_504}
\captionsetup{labelformat=empty}
\caption{Fig. 3.2}
\end{figure} - By considering the vertical and horizontal components of the force at A , show that the clockwise moment of this force about E is \(\frac { 30 Q } { 13 } \mathrm { Nm }\).
With the force of magnitude \(Q \mathrm {~N}\) acting as shown in Fig. 3.2, the cupboard is in equilibrium and is on the point of tipping but not on the point of sliding.
- Show that \(Q = 221\) and that the coefficient of friction between the cupboard base and the floor must be greater than \(\frac { 5 } { 8 }\).