Edexcel M2 2023 January — Question 5

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2023
SessionJanuary
TopicWork, energy and Power 2

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ee5f81bc-1bdb-47a1-81e7-7e3cb8219e91-12_296_1125_246_470} \captionsetup{labelformat=empty} \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.
  1. Find the work done against friction as the package moves from \(A\) to \(B\).
  2. 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.
  3. Use the work-energy principle to find the speed of the package at the instant it returns to \(A\).