CAIE M1 2015 June — Question 4

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2015
SessionJune
TopicWork, energy and Power 1

4 A lorry of mass 12000 kg moves up a straight hill of length 500 m , starting at the bottom with a speed of \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and reaching the top with a speed of \(16 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The top of the hill is 25 m above the level of the bottom of the hill. The resistance to motion of the lorry is 7500 N . Find the driving force of the lorry. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{543cb1dd-40e8-4d66-8ca0-4f183f83f366-3_566_405_264_868} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} Four coplanar forces of magnitudes \(4 \mathrm {~N} , 8 \mathrm {~N} , 12 \mathrm {~N}\) and 16 N act at a point. The directions in which the forces act are shown in Fig. 1.
  1. Find the magnitude and direction of the resultant of the four forces. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{543cb1dd-40e8-4d66-8ca0-4f183f83f366-3_351_629_1260_758} \captionsetup{labelformat=empty} \caption{Fig. 2}
    \end{figure} The forces of magnitudes 4 N and 16 N exchange their directions and the forces of magnitudes 8 N and 12 N also exchange their directions (see Fig. 2).
  2. State the magnitude and direction of the resultant of the four forces in Fig. 2.