| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | November |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Limiting equilibrium both directions |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem on an inclined plane with friction. Part (a) requires resolving forces and finding limiting friction (routine but multi-step), part (b) applies the same method with friction reversed, and part (c) tests conceptual understanding. While it has 14 marks total and requires careful resolution of forces in two directions, it follows a completely standard template with no novel problem-solving required—slightly easier than the average A-level question due to its predictable structure. |
| Spec | 3.03e Resolve forces: two dimensions3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
\includegraphics{figure_4}
A heavy package is held in equilibrium on a slope by a rope. The package is attached to one end of the rope, the other end being held by a man standing at the top of the slope. The package is modelled as a particle of mass 20 kg. The slope is modelled as a rough plane inclined at $60°$ to the horizontal and the rope as a light inextensible string. The string is assumed to be parallel to a line of greatest slope of the plane, as shown in Figure 4. At the contact between the package and the slope, the coefficient of friction is 0.4.
\begin{enumerate}[label=(\alph*)]
\item Find the minimum tension in the rope for the package to stay in equilibrium on the slope. [8]
\end{enumerate}
The man now pulls the package up the slope. Given that the package moves at constant speed,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the tension in the rope. [4]
\item State how you have used, in your answer to part (b), the fact that the package moves
\begin{enumerate}[label=(\roman*)]
\item up the slope,
\item at constant speed.
\end{enumerate} [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q8 [14]}}