| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2002 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion down rough slope |
| Difficulty | Standard +0.3 This is a standard M1 mechanics problem involving motion on a rough inclined plane. Part (a) uses basic kinematics (v² = u² + 2as), part (b) applies Newton's second law with friction to find μ, and part (c) requires finding when the suitcase comes to rest. All techniques are routine for M1 students with no novel problem-solving 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 |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(8^2 = 10^2 + 2a \times 5 \rightarrow a = -3.6 \text{ m s}^{-2}\) | M1 A1 | (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(R = 10g\cos 20°\) | B1 | |
| \(F = \mu R\) used | B1 | |
| \(10g\sin 20° - \mu \cdot 10g\cos 20° = 10(-3.6)\) | M1 A1 | |
| Solve: \(\mu = 0.75\) (or \(0.755\)) | M1 A1 | (6) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(AC\) maximum if speed at \(C = 0\) | ||
| \(\therefore 0^2 = 10^2 - 2 \times 3.6 \times s\) | M1 | |
| \(s \approx 13.9\) m (awrt) | A1 | (2) |
## Question 5:
### Part (a):
| Answer/Working | Marks | Notes |
|---|---|---|
| $8^2 = 10^2 + 2a \times 5 \rightarrow a = -3.6 \text{ m s}^{-2}$ | M1 A1 | **(2)** |
### Part (b):
| Answer/Working | Marks | Notes |
|---|---|---|
| $R = 10g\cos 20°$ | B1 | |
| $F = \mu R$ used | B1 | |
| $10g\sin 20° - \mu \cdot 10g\cos 20° = 10(-3.6)$ | M1 A1 | |
| Solve: $\mu = 0.75$ (or $0.755$) | M1 A1 | **(6)** |
### Part (c):
| Answer/Working | Marks | Notes |
|---|---|---|
| $AC$ maximum if speed at $C = 0$ | | |
| $\therefore 0^2 = 10^2 - 2 \times 3.6 \times s$ | M1 | |
| $s \approx 13.9$ m (awrt) | A1 | **(2)** |
---5.
\section*{Figure 3}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{14703bfa-abd8-4a8d-bc18-20d66eea409e-4_502_1154_339_552}
\end{center}
A suitcase of mass 10 kg slides down a ramp which is inclined at an angle of $20 ^ { \circ }$ to the horizontal. The suitcase is modelled as a particle and the ramp as a rough plane. The top of the plane is $A$. The bottom of the plane is $C$ and $A C$ is a line of greatest slope, as shown in Fig. 3. The point $B$ is on $A C$ with $A B = 5 \mathrm {~m}$. The suitcase leaves $A$ with a speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and passes $B$ with a speed of $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find
\begin{enumerate}[label=(\alph*)]
\item the decleration of the suitcase,
\item the coefficient of friction between the suitcase and the ramp.
The suitcase reaches the bottom of the ramp.
\item Find the greatest possible length of $A C$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2002 Q5 [10]}}