| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion down rough slope |
| Difficulty | Moderate -0.8 This is a straightforward mechanics problem requiring standard application of Newton's second law on an inclined plane with friction. Students resolve forces parallel to the slope (mg sin 25° - μR) and perpendicular (R = mg cos 25°), then use F=ma to find acceleration, followed by a basic kinematics calculation (s = ½at²). It's more routine than average A-level questions since it follows a well-practiced procedure with no conceptual surprises. |
| Spec | 3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(R = mg\cos 25\) | B1 | |
| \([F = 0.4mg\cos 25]\) | M1 | Using \(F = \mu R\) |
| \([mg\sin 25 - 0.4mg\cos 25 = ma]\) | M1 | Use of Newton's Second Law |
| \(a = 0.601\ \text{ms}^{-2}\) | A1 | |
| 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\left[s = \frac{1}{2} \times 0.601 \times 3^2\right]\) | M1 | Use of \(s = ut + \frac{1}{2}at^2\) |
| Distance \(= 2.70\) m | A1 FT | FT \(4.5 \times a\) from (i) |
| 2 |
# Question 3(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $R = mg\cos 25$ | **B1** | |
| $[F = 0.4mg\cos 25]$ | **M1** | Using $F = \mu R$ |
| $[mg\sin 25 - 0.4mg\cos 25 = ma]$ | **M1** | Use of Newton's Second Law |
| $a = 0.601\ \text{ms}^{-2}$ | **A1** | |
| | **4** | |
# Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\left[s = \frac{1}{2} \times 0.601 \times 3^2\right]$ | **M1** | Use of $s = ut + \frac{1}{2}at^2$ |
| Distance $= 2.70$ m | **A1 FT** | FT $4.5 \times a$ from **(i)** |
| | **2** | |
---3 A particle is released from rest and slides down a line of greatest slope of a rough plane which is inclined at $25 ^ { \circ }$ to the horizontal. The coefficient of friction between the particle and the plane is 0.4 .\\
(i) Find the acceleration of the particle.\\
(ii) Find the distance travelled by the particle in the first 3 s after it is released.\\
\hfill \mbox{\textit{CAIE M1 2017 Q3 [6]}}