| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with force at angle to slope |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem on a slope with a force at an angle. It requires resolving forces parallel and perpendicular to the slope and applying friction conditions, which are routine techniques for this topic. The question appears straightforward 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 |
|---|---|---|
| 4(a) | Correct force diagram with 3 extra forces shown | B1 |
| 4(b) | For resolving forces in the direction parallel to and/or perpendicular to the plane \(F + 25\cos 20° = 20 \times \sin 30°\) \(R + 25\cos 20° = 20 \times \cos 30°\) \(\mu = [7.5\text{...]\) \(\mu = 0.465\) | M1 A1 A1 M1 A1 |
**4(a)** | Correct force diagram with 3 extra forces shown | B1 |
**4(b)** | For resolving forces in the direction parallel to and/or perpendicular to the plane $F + 25\cos 20° = 20 \times \sin 30°$ $R + 25\cos 20° = 20 \times \cos 30°$ $\mu = [7.5\text{...]$ $\mu = 0.465$ | M1 A1 A1 M1 A1 | Use $F = \mu R$ to evaluate $\mu$
---4 A particle of mass 20 kg is on a rough plane inclined at an angle of $30 ^ { \circ }$ to the horizontal. A force of magnitude 25 N , acting at an angle of $20 ^ { \circ }$ above a line of greatest slope of the plane, is used to prevent the particle from sliding down the plane. The coefficient of friction between the particle and the plane is $\mu$.\\
(a) Complete the diagram below to show all the forces acting on the particle.\\
\includegraphics[max width=\textwidth, alt={}, center]{87b42689-791c-4f4e-a36e-bfae3191ca11-06_495_615_543_726}\\
(b) Find the least possible value of $\mu$.\\
\hfill \mbox{\textit{CAIE M1 2020 Q4 [6]}}