A-LevelMathematicsMechanics9709/52 · Feb/Mar 2019 · Q46 Marks
A particle P of mass 0.3 kg is attached to a fixed point A by a light elastic string of natural length 0.8 m and modulus of elasticity 16 N. The particle P moves in a horizontal circle which has centre O. It is given that AO is vertical and that angle OAP is 60° (see diagram).
- (a)Calculate the speed of P.[6]
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 (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] Resolve vertically
- Tcos60 = 0.3g
- [A1]
- T=6N
- [M1] Use T =λx/L
- T = 16e/0.8 (= 6 ) leads to e = 0.3
- [A1]
- r = (0.8 +0.3)sin60 ( = 1.1sin60)
- [M1] Use N2L horizontally
- Tsin60 = 0.3 v² /(1.1sin60)
- [A1]
- v = 4.06 m s-1
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