| Exam Board | SPS |
|---|---|
| Module | SPS SM Mechanics (SPS SM Mechanics) |
| Year | 2023 |
| Session | January |
| Marks | 7 |
| Topic | Motion on a slope |
| Type | Motion down rough slope |
| Difficulty | Moderate -0.3 This is a standard mechanics problem requiring a force diagram and resolution of forces on an inclined plane with friction. While it involves multiple steps (diagram, resolving parallel/perpendicular to plane, applying F=ma), these are routine textbook techniques with no novel insight required. The condition μ < tan θ is given, making part (iii) straightforward conceptual reasoning. Slightly easier than average due to its formulaic nature. |
| Spec | 3.03a Force: vector nature and diagrams3.03f Weight: W=mg3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
2.
A particle of mass $m$ is placed on a rough inclined plane.\\
The plane makes an angle $\theta$ with the horizontal.\\
The coefficient of friction between the particle and the plane is $\mu$ where $\mu < \tan \theta$. The particle is released from rest and accelerates down the plane.\\
(i) Draw a fully labelled diagram to show the forces acting on the particle.\\
(ii) Find an expression in terms of $g , \theta$ and $\mu$ for the acceleration of the particle.\\
(iii) Explain what would happen to the particle if $\mu > \tan \theta$.
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\hfill \mbox{\textit{SPS SPS SM Mechanics 2023 Q2 [7]}}