SPS SPS SM Mechanics 2023 January — Question 2 7 marks

Exam BoardSPS
ModuleSPS SM Mechanics (SPS SM Mechanics)
Year2023
SessionJanuary
Marks7
TopicMotion on a slope
TypeMotion down rough slope
DifficultyModerate -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.
Spec3.03a 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.
  1. Draw a fully labelled diagram to show the forces acting on the particle.
  2. Find an expression in terms of \(g , \theta\) and \(\mu\) for the acceleration of the particle.
  3. Explain what would happen to the particle if \(\mu > \tan \theta\). \section*{BLANK PAGE FOR WORKING}

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]}}