A-LevelMathematicsMechanics9709/52 · Feb/Mar 2018 · Q58 Marks
One end of a light inextensible string of length 0.4 m is attached to the lowest point of a hemisphere of radius 0.4 m fixed with its axis vertical. A particle P of mass 0.3 kg is attached to the other end of the string. The string is straight and makes an angle of 30° with the horizontal. P moves on the smooth inner surface of the hemisphere in a horizontal circle [Figure 5.1].
- (i)Calculate the smallest possible angular speed of P.[4]
- (ii)Given that the greatest possible tension in the string is 5 N, calculate the greatest possible speed of P.[4]
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 2018). The mark or mark type is shown in brackets.
- [M1] Rcos60 = 0.3g Resolve vertically
- [A1] R = 6 N
- [M1] 6cos30 = 0.3ω² × 0.4cos30 Use Newton's Second Law horizontally
- [A1] ω = 5√2 = 7.07 rad s⁻¹
- [M1] Rcos60 = 0.3g + 5sin30 Resolve vertically
- [A1] R = 11 N
- [M1] 11cos30 + 5cos30 = 0.3v² / (0.4cos30) Resolve horizontally
- [A1] v = 4 m s¯¹
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