A-LevelMathematicsMechanics9709/52 · Feb/Mar 2017 · Q57 Marks
Two particles P and Q have masses 0.4 kg and m kg respectively. P is attached to a fixed point A by a light inextensible string of length 0.5 m which is inclined at an angle of 60° to the vertical. P and Q are joined to each other by a light inextensible vertical string. Q is attached to a fixed point B, which is vertically below A, by a light inextensible string. The string BQ is taut and horizontal. The particles rotate in horizontal circles about an axis through A and B with constant angular speed ω rad s⁻¹ (see diagram). The tension in the string joining P and Q is 1.5 N. [Figure X.X]
- (i)Find the tension in the string AP and the value of ω.[4]
- (ii)Find m and the tension in the string BQ.[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 (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [M1] Resolve vertically for P (Tcos60 = 1.5 +0.4g)
- [A1] T=11 N
- [M1] Uses Newton's Second Law horizontally for P (Tsin60 = 0.4 ω² x0.5sin60)
- [A1] ω = √55 = 7.42
- [B1] Resolves vertically for Q (m = 0.15 (from mg = 1.5))
- [M1] Uses Newton's Second Law horizontally for Q (T* = 0.15 x 7.42² x 0.5sin60)
- [A1] T* = 3.57 N
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