A particle of mass 2.4kg is held in equilibrium by two light inextensible strings, one of which is attached to point A and the other attached to point B. The strings make angles of 35° and 40° with the horizontal [Figure 2.1]. Find the tension in each of the two strings.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [*M1] Attempt to resolve horizontally or vertically to form an equation. Correct number of terms; allow sin/cos mix; allow sign errors – do not award this mark if using T for both (see SC later).
2. [A1] T₁ cos 35 = T₂ cos 40. Must be different Ts.
3. [A1] T₁ sin 35 + T₂ sin 40 = 2.4g. If same Ts, then SC B2 only for this equation.
4. [DM1] Attempt to solve for either tension. From equations with correct number of relevant terms. Must get a value for at least one tension. E.g. T₁ (cos 40 / cos 35) x sin 35 + sin 40 = 24
5. [A1] T₁ = 19.033621... T₂ = 20.353166... awrt 20.4 for T₁ www and 19(.0) for T₂.