| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Horizontal force on slope |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two perpendicular directions (parallel and perpendicular to the plane) with a horizontal force component. While it requires careful handling of the geometry and the limiting friction condition, it follows a well-practiced method with no novel insight needed. Slightly easier than average due to being a routine two-part question with clear structure. |
| Spec | 3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03i Normal reaction force3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(\perp \text{ plane}: \quad R = 20\cos 60° + 5g\cos 30°\) | M1 A2(1,0) | M1 for resolving perpendicular to plane; A2 for correct equation |
| \(= 52.4\) (N) or 52 | A1 (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(F_r = \mu R\) | B1 | B1 for use of \(F=\mu R\) |
| \(\parallel \text{ plane}: \quad F + 20\cos 30° = 5g\cos 60°\) | M1 A2(1,0) | M1 for resolving parallel to plane |
| \(\mu = 0.137\) or 0.14 | A1 (5) |
## Question 3:
### Part (a):
| Working | Marks | Guidance |
|---------|-------|----------|
| $\perp \text{ plane}: \quad R = 20\cos 60° + 5g\cos 30°$ | M1 A2(1,0) | M1 for resolving perpendicular to plane; A2 for correct equation |
| $= 52.4$ (N) or 52 | A1 **(4)** | |
### Part (b):
| Working | Marks | Guidance |
|---------|-------|----------|
| $F_r = \mu R$ | B1 | B1 for use of $F=\mu R$ |
| $\parallel \text{ plane}: \quad F + 20\cos 30° = 5g\cos 60°$ | M1 A2(1,0) | M1 for resolving parallel to plane |
| $\mu = 0.137$ or 0.14 | A1 **(5)** | |
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{5c908e75-73df-46be-93bb-09dba2cb3b7e-04_432_780_210_584}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
A box of mass 5 kg lies on a rough plane inclined at $30 ^ { \circ }$ to the horizontal. The box is held in equilibrium by a horizontal force of magnitude 20 N , as shown in Figure 2. The force acts in a vertical plane containing a line of greatest slope of the inclined plane.\\
The box is in equilibrium and on the point of moving down the plane. The box is modelled as a particle.
Find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the normal reaction of the plane on the box,
\item the coefficient of friction between the box and the plane.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2012 Q3 [9]}}