A particle of mass 8kg is suspended in equilibrium by two light inextensible strings which make angles of 60° and 45° above the horizontal.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [B1] Correct 3 force diagram, including angles shown
2. [M1] Resolving forces horizontally.
3. [M1] Resolving forces vertically.
4. [A1] T₁ cos 60 = T₂ cos 45 and T₁ sin 60 + T₂ sin 45 = 8g
5. [M1] Attempting to solve for either T₁ or T₂
6. [A1] T₁ = 58.6 N
7. [A1] T₂ = 41.4 N
8. [M1] (Alternative) Applies Lami's Theorem – at least two terms correct.
9. [A1] (Alternative) T₁/sin135 = T₂/sin 150 = 80/sin 75
10. [M1] (Alternative) Solves for T₁.
11. [A1] (Alternative) T₁ = 58.6 N
12. [M1] (Alternative) Solves for T₂.
13. [A1] (Alternative) T₂ = 41.4 N