| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2001 |
| Session | June |
| Marks | 11 |
| 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 on an inclined plane with a horizontal force. It requires resolving forces in two directions and applying friction at limiting equilibrium, but follows a routine procedure with no novel insight needed. Slightly easier than average due to the straightforward setup and clear numerical values. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram with 4 forces marked (allow \(F\) and \(R\) combined if clear) | B2 \(-1\) e.e. | (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = 3g\cos 30° + 30\sin 30°\) (3 terms) | M1 A2 \(-1\) e.e. | |
| \(= 40.46\ldots \approx 40.5 \text{ N}\) or \(40 \text{ N}\) | A1 | (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = 30\cos 30° - 3g\sin 30°\) (3 terms) | M1 A1 | |
| \(F = \mu R \Rightarrow \mu = \frac{F}{R} = \frac{11.28}{40.46}\) | M1 M1 | |
| \(\approx 0.28\) (or \(0.279\)) | A1 | (5 marks) Total: 11 |
## Question 4:
### Part (a):
Diagram with 4 forces marked (allow $F$ and $R$ combined if clear) | B2 $-1$ e.e. | (2 marks)
### Part (b) — Resolve perpendicular to plane $R(\uparrow)$:
$R = 3g\cos 30° + 30\sin 30°$ (3 terms) | M1 A2 $-1$ e.e. |
$= 40.46\ldots \approx 40.5 \text{ N}$ or $40 \text{ N}$ | A1 | (4 marks)
### Part (c) — Resolve parallel to plane $R(\leftarrow)$:
$F = 30\cos 30° - 3g\sin 30°$ (3 terms) | M1 A1 |
$F = \mu R \Rightarrow \mu = \frac{F}{R} = \frac{11.28}{40.46}$ | M1 M1 |
$\approx 0.28$ (or $0.279$) | A1 | (5 marks) **Total: 11**
---4.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-4_347_854_356_640}
\end{center}
\end{figure}
A small parcel of mass 3 kg is held in equilibrium on a rough plane by the action of a horizontal force of magnitude 30 N acting in a vertical plane through a line of greatest slope. The plane is inclined at an angle of $30 ^ { \circ }$ to the horizontal, as shown in Fig. 3. The parcel is modelled as a particle. The parcel is on the point of moving up the slope.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram showing all the forces acting on the parcel.
\item Find the normal reaction on the parcel.
\item Find the coefficient of friction between the parcel and the plane.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2001 Q4 [11]}}