A-LevelMathematicsMechanics9709/42 · Oct/Nov 2018 · Q14 Marks
A smooth ring R of mass mkg is threaded on a light inextensible string ARB. The ends of the string are attached to fixed points A and B with A vertically above B. The string is taut and angle ARB = 90°. The angle between the part AR of the string and the vertical is 45°. The ring is held in equilibrium in this position by a force of magnitude 2.5 N, acting on the ring in the direction BR [Figure X.X]. Calculate the tension in the string and the mass of the ring.
- A smooth ring R of mass mkg is threaded on a light inextensible string ARB. The ends of the string are attached to fixed points A and B with A vertically above B. The string is taut and angle ARB = 90°. The angle between the part AR of the string and the vertical is 45°. The ring is held in equilibrium in this position by a force of magnitude 2.5 N, acting on the ring in the direction BR [Figure X.X]. Calculate the tension in the string and the mass of the ring.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] For resolving horizontally
- [A1] T = 1.25 N
- [M1] For resolving vertically
- [A1] Mass of ring = 0.177 kg
- [M1] Resolve forces along BR
- [M1] Resolve forces perpendicular to BR and eliminate T or m
- [A1] T = 1.25 N
- [A1] Allow m = √2/8
- [M1] Attempt to apply Lami's theorem,
- [M1] All three terms of Lami attempted
- [A1] T = 1.25 N
- [A1] Allow m = √2/8
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