CAIE M1 2022 November — Question 3 6 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2022
SessionNovember
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeRing on wire with string
DifficultyStandard +0.3 This is a straightforward statics problem requiring resolution of forces in two directions and applying equilibrium conditions. The setup is standard (ring on wire with string), the angle is given, and students simply need to resolve the weight, tension, and normal reaction. It's slightly easier than average because it's a direct application of basic mechanics principles with no geometric complications or multi-step reasoning required.
Spec3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces

3 \includegraphics[max width=\textwidth, alt={}, center]{4a2bad7c-6720-414c-b336-060afb2255e9-05_610_591_257_778} A ring of mass 4 kg is threaded on a smooth circular rigid wire with centre \(C\). The wire is fixed in a vertical plane and the ring is kept at rest by a light string connected to \(A\), the highest point of the circle. The string makes an angle of \(25 ^ { \circ }\) to the vertical (see diagram). Find the tension in the string and the magnitude of the normal reaction of the wire on the ring.

Question 3:
AnswerMarks Guidance
AnswerMark Guidance
\(T\cos 25 = 40 + R\cos 50\)M1 Resolving in any direction e.g. horizontal, vertical, along radius or tangent
\(R\sin 50 = T\sin 25\)M1 Resolving in a second direction
Radially: \(T\cos 25 = R + 40\cos 50\); Tangentially: \(T\sin 25 = 40\sin 50\); Parallel to \(T\): \(T = R\cos 25 + 40\cos 25\); Perpendicular to \(T\): \(R\sin 25 = 40\sin 25\); Vertically: \(T\cos 25 = 40 + R\cos 50\); Horizontally: \(R\sin 50 = T\sin 25\)A1 Two correct equations
Solving equation(s) to find either \(T\) or \(R\)M1
\(T = 72.5\) NA1 From 72.504…
\(R = 40\) NA1
## Question 3:

| Answer | Mark | Guidance |
|--------|------|----------|
| $T\cos 25 = 40 + R\cos 50$ | M1 | Resolving in any direction e.g. horizontal, vertical, along radius or tangent |
| $R\sin 50 = T\sin 25$ | M1 | Resolving in a second direction |
| Radially: $T\cos 25 = R + 40\cos 50$; Tangentially: $T\sin 25 = 40\sin 50$; Parallel to $T$: $T = R\cos 25 + 40\cos 25$; Perpendicular to $T$: $R\sin 25 = 40\sin 25$; Vertically: $T\cos 25 = 40 + R\cos 50$; Horizontally: $R\sin 50 = T\sin 25$ | A1 | Two correct equations |
| Solving equation(s) to find either $T$ or $R$ | M1 | |
| $T = 72.5$ N | A1 | From 72.504… |
| $R = 40$ N | A1 | |

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\includegraphics[max width=\textwidth, alt={}, center]{4a2bad7c-6720-414c-b336-060afb2255e9-05_610_591_257_778}

A ring of mass 4 kg is threaded on a smooth circular rigid wire with centre $C$. The wire is fixed in a vertical plane and the ring is kept at rest by a light string connected to $A$, the highest point of the circle. The string makes an angle of $25 ^ { \circ }$ to the vertical (see diagram).

Find the tension in the string and the magnitude of the normal reaction of the wire on the ring.\\

\hfill \mbox{\textit{CAIE M1 2022 Q3 [6]}}