| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | String at angle to slope |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem on an inclined plane with a force at an angle. It requires resolving forces in two directions (parallel and perpendicular to the plane), applying F=μR for limiting friction, and solving simultaneous equations. While it involves multiple steps and careful angle work, it follows a well-practiced procedure with no novel insight required, making it slightly easier than the average A-level question. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(R = 45\cos 40° + 4g\cos 30°\) giving \(R \approx 68\) | M1 A2 (1, 0) DM1 A1 | (5) Accept 68.4 |
| (b) Use of \(F = \mu R\) with \(F + 4g\sin 30° = 45\cos 50°\) leading to \(\mu \approx 0.14\) | M1 M1 A2 (1, 0) DM1 A1 | (6) [11] Accept 0.136 |
**(a)** $R = 45\cos 40° + 4g\cos 30°$ giving $R \approx 68$ | M1 A2 (1, 0) DM1 A1 | (5) Accept 68.4
**(b)** Use of $F = \mu R$ with $F + 4g\sin 30° = 45\cos 50°$ leading to $\mu \approx 0.14$ | M1 M1 A2 (1, 0) DM1 A1 | (6) [11] Accept 0.136
---7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{9dbbbc01-fb66-460d-a42e-2c37ec8b451a-10_291_726_265_607}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
A package of mass 4 kg lies on a rough plane inclined at $30 ^ { \circ }$ to the horizontal. The package is held in equilibrium by a force of magnitude 45 N acting at an angle of $50 ^ { \circ }$ to the plane, as shown in Figure 3. The force is acting in a vertical plane through a line of greatest slope of the plane. The package is in equilibrium on the point of moving up the plane. The package is modelled as a particle. Find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the normal reaction of the plane on the package,
\item the coefficient of friction between the plane and the package.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2008 Q7 [11]}}