5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ee5f81bc-1bdb-47a1-81e7-7e3cb8219e91-12_296_1125_246_470}
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\caption{Figure 2}
\end{figure}
A rough straight ramp is fixed to horizontal ground. The ramp is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 5 } { 12 }\)
The points \(A\) and \(B\) are on a line of greatest slope of the ramp, with \(A B = 2.5 \mathrm {~m}\) and \(B\) above \(A\), as shown in Figure 2.
A package of mass 1.5 kg is projected up the ramp from \(A\) with speed \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and first comes to instantaneous rest at \(B\).
The coefficient of friction between the package and the ramp is \(\frac { 2 } { 7 }\)
The package is modelled as a particle.
- Find the work done against friction as the package moves from \(A\) to \(B\).
- Use the work-energy principle to find the value of \(U\).
After coming to instantaneous rest at \(B\), the package slides back down the slope.
- Use the work-energy principle to find the speed of the package at the instant it returns to \(A\).