CAIE M1 2011 November — Question 6 8 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2011
SessionNovember
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeRing on vertical rod equilibrium
DifficultyStandard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions and application of F=μR at limiting equilibrium. The two cases (friction up vs down) make it slightly above routine, but the setup is straightforward with clear geometry and standard techniques.
Spec3.03m Equilibrium: sum of resolved forces = 03.03u Static equilibrium: on rough surfaces
6 \includegraphics[max width=\textwidth, alt={}, center]{155bc571-80e4-4c93-859f-bb150a109211-3_465_410_1891_865} The diagram shows a ring of mass 2 kg threaded on a fixed rough vertical rod. A light string is attached to the ring and is pulled upwards at an angle of \(30 ^ { \circ }\) to the horizontal. The tension in the string is \(T \mathrm {~N}\). The coefficient of friction between the ring and the rod is 0.24 . Find the two values of \(T\) for which the ring is in limiting equilibrium.
AnswerMarks Guidance
M1For resolving forces horizontally
\(R = T\cos 30\)A1
M1For resolving forces vertically (either case)
\(F = T\sin 30 - 2g\)A1 (preventing upwards motion)
\(-F = T\sin 30 - 2g\)A1 (preventing downwards motion)
M1For using \(F = \mu R\) (either case) and attempting to solve for T
\(T = 2g/(\sin 30 \pm 0.24\cos 30)\) either caseA1
\(T = 28.3\) and \(T = 68.5\)A1 8 
| M1 | For resolving forces horizontally
$R = T\cos 30$ | A1 |
| M1 | For resolving forces vertically (either case)
$F = T\sin 30 - 2g$ | A1 | (preventing upwards motion)
$-F = T\sin 30 - 2g$ | A1 | (preventing downwards motion)
| M1 | For using $F = \mu R$ (either case) and attempting to solve for T
$T = 2g/(\sin 30 \pm 0.24\cos 30)$ either case | A1 |
$T = 28.3$ and $T = 68.5$ | A1 | 8
6\\
\includegraphics[max width=\textwidth, alt={}, center]{155bc571-80e4-4c93-859f-bb150a109211-3_465_410_1891_865}

The diagram shows a ring of mass 2 kg threaded on a fixed rough vertical rod. A light string is attached to the ring and is pulled upwards at an angle of $30 ^ { \circ }$ to the horizontal. The tension in the string is $T \mathrm {~N}$. The coefficient of friction between the ring and the rod is 0.24 . Find the two values of $T$ for which the ring is in limiting equilibrium.

\hfill \mbox{\textit{CAIE M1 2011 Q6 [8]}}
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