A-LevelMathematicsMechanics9709/52 · Oct/Nov 2019 · Q510 Marks
A and B are two fixed points on a vertical axis with A above B. A particle P of mass 0.4 kg is attached to A by a light inextensible string of length 0.5 m. The particle P is attached to B by another light inextensible string. P moves with constant speed in a horizontal circle with centre O between A and B. Angle BAP = 30° and angle ABP = 70° [Figure X.X].
- (i)Given that the tensions in the two strings are equal, find the speed of P.[5]
- (ii)Given instead that the angular speed of P is 12 rad s¯¹, find the tensions in the strings.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] r = 0.5sin30 (= 0.25 m)
- [M1] Tcos30 - Tcos70 = 0.4g
- [A1] T = 7.6335..
- [M1] 7.6335sin30 + 7.6335sin70 = 0.4v² / 0.25
- [A1] v = 2.62 m s⁻¹
- [M1] Acos30 - Bcos70 = 0.4g and Asin30 + Bsin70 = 0.4 × 12² × 0.5sin30
- [A1] Both correct
- [M1] Attempt to solve for A or B
- [A1] A = 8.82 N
- [A1] B = 10.6 N
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