CAIE M2 2013 June — Question 4

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2013
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeLamina hinged at point with string support
DifficultyStandard +0.3 This is a standard M2 moments problem involving a lamina hinged at a point with string support. It requires taking moments about the hinge, resolving forces, and using the perpendicular distance formula. While it involves multiple steps, these are routine techniques for M2 students with no novel problem-solving required, making it slightly easier than average.
Spec6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks

4 \includegraphics[max width=\textwidth, alt={}, center]{10abedc3-c814-47c0-8ed4-849ef325feca-2_631_531_1117_806} A smooth hollow cylinder of internal radius 0.3 m is fixed with its axis vertical. One end of a light inextensible string of length 0.5 m is fixed to a point \(A\) on the axis. The other end of the string is attached to a particle \(P\) of mass 0.2 kg which moves in a horizontal circle on the surface of the cylinder (see diagram).
  1. Find the tension in the string.
  2. Find the least angular speed of \(P\) for which the motion is possible.
  3. Calculate the magnitude of the force exerted on \(P\) by the cylinder given that the speed of \(P\) is \(1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

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\includegraphics[max width=\textwidth, alt={}, center]{10abedc3-c814-47c0-8ed4-849ef325feca-2_631_531_1117_806}

A smooth hollow cylinder of internal radius 0.3 m is fixed with its axis vertical. One end of a light inextensible string of length 0.5 m is fixed to a point $A$ on the axis. The other end of the string is attached to a particle $P$ of mass 0.2 kg which moves in a horizontal circle on the surface of the cylinder (see diagram).\\
(i) Find the tension in the string.\\
(ii) Find the least angular speed of $P$ for which the motion is possible.\\
(iii) Calculate the magnitude of the force exerted on $P$ by the cylinder given that the speed of $P$ is $1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.

\hfill \mbox{\textit{CAIE M2 2013 Q4}}