5 In this question, all coordinates refer to the axes shown in Fig. 5.1.
Fig. 5.1 shows a system of four particles with masses \(4 m , 3 m , m\) and \(2 m\) at the points \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D . These points have coordinates \(( - 3,4 ) , ( 0,0 ) , ( 2,0 )\) and \(( 5,4 )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be1851d6-af11-40e1-8a36-5938ee7864d4-5_436_817_513_639}
\captionsetup{labelformat=empty}
\caption{Fig. 5.1}
\end{figure}
- Calculate the coordinates of the centre of mass of the system of particles.
A thin uniform rigid wire of mass \(12 m\) connects the points \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D with straight line sections, as shown in Fig. 5.2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be1851d6-af11-40e1-8a36-5938ee7864d4-5_460_903_1338_573}
\captionsetup{labelformat=empty}
\caption{Fig. 5.2}
\end{figure} - Calculate the coordinates of the centre of mass of the wire.
The particles at \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D are now fixed to the wire to form a rigid object, \(R\).
- Calculate the \(x\)-coordinate of the centre of mass of \(R\).