A block of mass 5 kg is held in equilibrium near a vertical wall by two light strings and a horizontal force of magnitude X N, as shown in the diagram. The two strings are both inclined at 60° to the vertical. [Diagram]

Mark scheme

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

1. M1 Resolve horizontally or vertically or perpendicular to the upper string to reach an equation. Correct number of terms, Allow X for 100 in horizontal equation.
2. A1 Either horizontal and vertical equations correct or perpendicular correct. Must see X = 100 used for A1.
3. M1 Solve for either T_L or T_U using equation(s) with no missing term.
4. A1 Allow 7.73. T_L = 7.74 N
5. M1 Resolve either horizontally or vertically or perpendicular to the upper string. Must be using the tension T_low = 0. Equivalent to Lami as: 5g / sin 150 = X / sin 120 = T_up / sin 90
6. A1 Either horizontal and vertical equations correct or perpendicular correct.
7. M1 Eliminate T_up and/or solve for X
8. A1 Allow X = 50√3. Least value of X = 86.6