6 Fig. 6.1 shows a cross-section through a block of mass 5 kg which is on top of a trolley of mass 11 kg . The trolley is on top of a smooth horizontal surface. The coefficient of friction between the block and the trolley is 0.3 .
Throughout this question you may assume that there are no other resistances to motion on either the block or the trolley.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c1cfe41-d7a2-4f69-ae79-67d9f023c246-6_339_1317_552_294}
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\caption{Fig. 6.1}
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Initially, both the block and trolley are at rest. A constant force of magnitude 50 N is now applied horizontally to the trolley, as shown in Fig. 6.1.
- Show that in the subsequent motion the block will slide.
- Find the acceleration of
- the block,
- the trolley.
The same block and trolley are again at rest. An obstruction, in the form of a fixed horizontal pole, is placed in front of the block, the pole is 91 cm above the trolley and the width of the block is 56 cm as shown in Fig. 6.2, as well as the forward direction of motion.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c1cfe41-d7a2-4f69-ae79-67d9f023c246-6_426_1324_1793_269}
\captionsetup{labelformat=empty}
\caption{Fig. 6.2}
\end{figure}
It is given that the block is uniform and that the contact between the pole and the block is smooth.
A small horizontal force is now applied to the trolley in the forward direction of motion and gradually increased.
- Determine whether the block will topple or slide.