A-LevelMathematicsMechanics9709/51 · May/June 2017 · Q57 Marks
A uniform semicircular lamina of radius 0.7 m and weight 14 N has diameter AB. The lamina is in a vertical plane with A freely pivoted at a fixed point. The straight edge AB rests against a small smooth peg P above the level of A. The angle between AB and the horizontal is 30° and AP = 0.9 m (see diagram).
- (i)Show that the magnitude of the force exerted by the peg on the lamina is 7.12 N, correct to 3 significant figures.[4]
- (ii)Find the angle with the horizontal of the force exerted by the pivot on the lamina at A.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] OG = 2 × 0.7sin(π / 2) / (3π / 2) (= 0.297)
- [M1A1] 0.9R = 14(0.7cos30 – 0.297sin30)
- [A1] R = 7.12 N
- [M1] H = 7.12sin30 and V = 14 - Rcos30
- [M1] tanθ = (14 – 7.12cos30) / (7.12sin30)
- [A1] θ = 65.6
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