2 The rigid object shown in Fig. 2.1 is made of thin non-uniform rods. ABC is a straight line; \(\mathrm { BC } , \mathrm { BE }\) and ED form three sides of a rectangle. The centre of mass of the object is at G. The lengths are in centimetres. The weight of the object is 15 N .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ea3c0177-bf3b-4475-9ab1-ae628aeb0bf0-3_273_444_397_813}
\captionsetup{labelformat=empty}
\caption{Fig. 2.1}
\end{figure}
Initially, the object is suspended by light vertical strings attached to B and to C and hangs in equilibrium with AC horizontal.
- Calculate the tensions in each of the strings.
In a new situation the strings are removed. The object can rotate freely in a vertical plane about a fixed horizontal axis through A and perpendicular to ABCDE. The object is held in equilibrium with AC horizontal by a force of magnitude \(T \mathrm {~N}\) in the plane ABCDE acting at C at an angle of \(30 ^ { \circ }\) to CA . This situation is shown in Fig. 2.2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ea3c0177-bf3b-4475-9ab1-ae628aeb0bf0-3_356_451_1292_808}
\captionsetup{labelformat=empty}
\caption{Fig. 2.2}
\end{figure} - Calculate \(T\).
Calculate also the magnitude of the force exerted on the object by the axis at A .
The object is now placed on a rough horizontal table and is in equilibrium with ABCDE in a vertical plane and DE in contact with the table. The coefficient of friction between the edge DE and the table is 0.65 . A force of slowly increasing magnitude (starting at 0 N ) is applied at A in the direction AB . Assume that the object remains in a vertical plane.
- Determine whether the object slips before it tips.