A-LevelMathematicsMechanics9709/42 · Oct/Nov 2023 · Q25 Marks

The diagram shows a smooth ring R, of mass mkg, threaded on a light inextensible string. A horizontal force of magnitude 2N acts on R. The ends of the string are attached to fixed points A and B on a vertical wall. The part AR of the string makes an angle of 30° with the vertical, the part BR makes an angle of 40° with the vertical and the string is taut. The ring is in equilibrium. [Figure 2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[M1] Attempt to resolve in at least one direction to form an equation. Correct number of terms; allow sign errors; allow sin/cos mix; allow with different T's.
[A1] Tsin 30+Tsin40-2=0 If different T's then allow M1A1A0 max.
[A1] Tcos 30-T cos 40-mg=0 Allow with their T.
[DM1] Attempt to solve for T or m From equation(s) with correct number of relevant terms.
[A1] Tension T = 1.75, m = 0.0175 T=1.7501... m=0.017497... awrt 1.75 for T www, and awrt 0.0175 for m www.

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