3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-06_323_1043_255_513}
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\caption{Figure 1}
\end{figure}
A rough ramp is fixed to horizontal ground.
The ramp is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 3 } { 7 }\)
The line \(A B\) is a line of greatest slope of the ramp, with \(B\) above \(A\) and \(A B = 6 \mathrm {~m}\), as shown in Figure 1.
A block \(P\) of mass 2 kg is pushed, with constant speed, in a straight line up the slope from \(A\) to \(B\). The force pushing \(P\) acts parallel to \(A B\).
The coefficient of friction between \(P\) and the ramp is \(\frac { 1 } { 3 }\)
The block is modelled as a particle and air resistance is negligible.
- Use the model to find the total work done in pushing the block from \(A\) to \(B\).
The block is now held at \(B\) and released from rest.
- Use the model and the work-energy principle to find the speed of the block at the instant it reaches \(A\).