| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion with applied force on slope |
| Difficulty | Standard +0.3 This is a standard M1 mechanics problem involving forces on a slope with friction. It requires resolving forces perpendicular and parallel to the plane, applying F=μR and Newton's second law. The 3-4-5 triangle simplifies calculations. While it has multiple steps, it follows a routine procedure with no novel insight required, making it slightly easier than average. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(R = 0.5g \cos \alpha = 0.4g\) | M1 A1 | |
| \(4 = F + 0.5g \sin \alpha\) | M1 A1 | |
| \(F = \mu R\) used | M1 | |
| \(4 = 0.4g\mu + 0.3g \Rightarrow \mu \approx 0.27(0)\) | M1 A1 | (7) |
| (b) \(0.5a = 0.3g - 0.27 \times 0.4g \Rightarrow a \approx (+) 3.76 \text{ m s}^{-2}\) (or 3.8) | M1 A2,1,0∇ | A1 (4) |
| (a) $R = 0.5g \cos \alpha = 0.4g$ | M1 A1 | |
| $4 = F + 0.5g \sin \alpha$ | M1 A1 | |
| $F = \mu R$ used | M1 | |
| $4 = 0.4g\mu + 0.3g \Rightarrow \mu \approx 0.27(0)$ | M1 A1 | (7) |
| (b) $0.5a = 0.3g - 0.27 \times 0.4g \Rightarrow a \approx (+) 3.76 \text{ m s}^{-2}$ (or 3.8) | M1 A2,1,0∇ | A1 (4) |
**Guidance:**
- (a) 1st two M1's require correct number of the correct terms, with valid attempt to resolve the correct relevant term (valid 'resolve' = x sin/cos).
- 4th M1 (dept) for forming equn in $\mu$ + numbers only.
- (b) In first equn, allow their $R$ or $F$ in the equation for full marks. A marks: f.t. on their $R$, $F$ etc. Deduct one A mark (up to 2) for each wrong term. (Note slight change from original scheme)
---4.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{3a8395fd-6e44-48a1-8c97-3365a284956a-05_273_611_319_676}
\end{center}
\end{figure}
A particle $P$ of mass 0.5 kg is on a rough plane inclined at an angle $\alpha$ to the horizontal, where tan $\alpha = \frac { 3 } { 4 }$. The particle is held at rest on the plane by the action of a force of magnitude 4 N acting up the plane in a direction parallel to a line of greatest slope of the plane, as shown in Figure 2. The particle is on the point of slipping up the plane.
\begin{enumerate}[label=(\alph*)]
\item Find the coefficient of friction between $P$ and the plane.
The force of magnitude 4 N is removed.
\item Find the acceleration of $P$ down the plane.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2006 Q4 [11]}}