The diagram shows a ring of mass $$\(0.1 \mathrm{~kg}\)$$ threaded on a fixed horizontal rod. The rod is rough and the coefficient of friction between the ring and the rod is $$\(0.8\)$$. A force of magnitude $$\(T \mathrm{~N}\)$$ acts on the ring in a direction at $$\(30^{\circ}\)$$ to the rod, downwards in the vertical plane containing the rod. Initially the ring is at rest. Find the greatest value of $$\(T\)$$ for which the ring remains at rest. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_41 Year：2020 Question No：4(a)
Answer:
Resolving forces in either direction
$
R=T \sin 30+0.1 g, F=T \cos 30
$$
T \cos 30=0.8(T \sin 30+0.1 g)
$$
T=1.72(1.7166 \ldots)
$
$
R=T \sin 30+0.1 g, F=T \cos 30
$$
T \cos 30=0.8(T \sin 30+0.1 g)
$$
T=1.72(1.7166 \ldots)
$
Knowledge points:
4.1.1 identify the forces acting in a given situation； e.g. by drawing a force diagram.
4.1.3 use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero （Solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions.）
4.1.4 understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component
4.1.6 understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = nR or F G nR, as appropriate
Solution:
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