4
\includegraphics[max width=\textwidth, alt={}, center]{28562a1b-ec9a-40d2-bbb3-729770688971-2_449_1273_1829_438}
\(A , B\) and \(C\) are three points on a line of greatest slope of a smooth plane inclined at an angle of \(\theta ^ { \circ }\) to the horizontal. \(A\) is higher than \(B\) and \(B\) is higher than \(C\), and the distances \(A B\) and \(B C\) are 1.76 m and 2.16 m respectively. A particle slides down the plane with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The speed of the particle at \(A\) is \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see diagram). The particle takes 0.8 s to travel from \(A\) to \(B\) and takes 1.4 s to travel from \(A\) to \(C\). Find
- the values of \(u\) and \(a\),
- the value of \(\theta\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{28562a1b-ec9a-40d2-bbb3-729770688971-3_188_510_260_388}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{28562a1b-ec9a-40d2-bbb3-729770688971-3_196_570_255_1187}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A block of mass 2 kg is at rest on a horizontal floor. The coefficient of friction between the block and the floor is \(\mu\). A force of magnitude 12 N acts on the block at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). When the applied force acts downwards as in Fig. 1 the block remains at rest.