6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1dea68fe-7916-41ed-894e-6b48f8d989bb-20_273_1058_246_443}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A rough straight ramp is fixed to horizontal ground. The ramp has length 15 m and is inclined at an angle \(\alpha\) to the ground, where \(\tan \alpha = \frac { 5 } { 12 }\). The line \(A B\) is a line of greatest slope of the ramp, where \(A\) is at the bottom of the ramp, and \(B\) is at the top of the ramp, as shown in Figure 3.
A particle \(P\) of mass 6 kg is projected up the ramp with speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from \(A\) in a straight line towards \(B\). The coefficient of friction between \(P\) and the ramp is 0.25
- Find the work done against friction as \(P\) moves from \(A\) to \(B\).
At the instant \(P\) reaches \(B\), the speed of \(P\) is \(v \mathrm {~ms} ^ { - 1 }\). After leaving the ramp at \(B\), the particle \(P\) moves freely under gravity until it hits the horizontal ground at the point \(C\). Immediately before hitting the ground at \(C\), the speed of \(P\) is \(w \mathrm {~ms} ^ { - 1 }\)
- Use the work-energy principle to find
- the value of \(v\),
- the value of \(w\).
\includegraphics[max width=\textwidth, alt={}, center]{1dea68fe-7916-41ed-894e-6b48f8d989bb-23_86_49_2617_1884}