CAIE M1 2019 March — Question 1 4 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2019
SessionMarch
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeRing on vertical rod equilibrium
DifficultyModerate -0.3 This is a straightforward limiting equilibrium problem requiring resolution of forces in two perpendicular directions and application of F=μR. The setup is standard with clearly given values, requiring only routine application of mechanics principles with no conceptual challenges beyond basic A-level mechanics.
Spec3.03e Resolve forces: two dimensions3.03r Friction: concept and vector form3.03u Static equilibrium: on rough surfaces

\includegraphics{figure_1} A small ring \(P\) of mass \(0.03\) kg is threaded on a rough vertical rod. A light inextensible string is attached to the ring and is pulled upwards at an angle of \(15°\) to the horizontal. The tension in the string is \(2.5\) N (see diagram). The ring is in limiting equilibrium and on the point of sliding up the rod. Find the coefficient of friction between the ring and the rod. [4]

Question 1:
AnswerMarks Guidance
1R = 2.5 cos 15 B1
[F = µ × 2.5 cos 15]M1 Using F = µR
[2.5 sin 15 = 0.03g + F]M1 Resolve forces along the rod
µ = 0.144A1
4
AnswerMarks Guidance
QuestionAnswer Marks
Question 1:
1 | R = 2.5 cos 15 | B1
[F = µ × 2.5 cos 15] | M1 | Using F = µR
[2.5 sin 15 = 0.03g + F] | M1 | Resolve forces along the rod
µ = 0.144 | A1
4
Question | Answer | Marks | Guidance
\includegraphics{figure_1}

A small ring $P$ of mass $0.03$ kg is threaded on a rough vertical rod. A light inextensible string is attached to the ring and is pulled upwards at an angle of $15°$ to the horizontal. The tension in the string is $2.5$ N (see diagram). The ring is in limiting equilibrium and on the point of sliding up the rod. Find the coefficient of friction between the ring and the rod. [4]

\hfill \mbox{\textit{CAIE M1 2019 Q1 [4]}}