Year: 2013
Paper: 2
Question Number: 9
Course: LFM Pure and Mechanics
Section: Moments
No solution available for this problem.
All questions were attempted by a significant number of candidates, with questions 1 to 3 and 7 the most popular. The Pure questions were more popular than both the Mechanics and the Probability and Statistics questions, with only question 8 receiving a particularly low number of attempts within the Pure questions and only question 11 receiving a particularly high number of attempts.
Difficulty Rating: 1600.0
Difficulty Comparisons: 0
Banger Rating: 1485.6
Banger Comparisons: 1
The diagram shows three identical discs in equilibrium in
a vertical plane. Two discs rest, not in contact with each other,
on a horizontal surface
and the third disc rests on the other two. The angle at the upper
vertex of the triangle joining the centres of the discs is $2\theta$.
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\noindent
The weight of each disc is $W$.
The coefficient of friction between a disc and the horizontal surface
is $\mu$ and the coefficient of friction between the discs is also $\mu$.
\begin{questionparts}
\item Show that the normal reaction between the horizontal surface and
a disc in contact with the surface is $\frac32 W\,$.
\item Find the normal reaction between
two discs in contact and show that the magnitude of the frictional force between two discs in contact is
$\dfrac{W\sin\theta}{2(1+\cos\theta)}\,$.
\item Show that if
$\mu <2- \surd3\,$ there is no value of $\theta$ for which
equilibrium is possible.
\end{questionparts}
The average score on this question was below a quarter of the marks as a large number of attempts did not make progress beyond the first few steps of the solution, achieving just the marks for the resolution of forces required in the first part of the question. Many candidates forgot some of the forces involved and very few decided to take moments. Some of the more clever solutions took moments about one of the contact points, which removes the need for one of the steps resolving forces.