The diagram shows a block D of mass 100kg supported by two sloping struts AD and BD, each attached at an angle of 45° to fixed points A and B respectively on a horizontal floor. The block is also held in place by a vertical rope CD attached to a fixed point C on a horizontal ceiling. The tension in the rope CD is 500N and the block rests in equilibrium. [Figure X.X]

Mark scheme

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

1. [M1] Attempt to resolve vertically 4 terms; allow with TA and TB; allow sign errors; allow g missing.
2. [A1] Must have TA = TB = T. Allow if 500-2T cos 45-100g=0.
3. [A1] T=354N Allow 250√2, 500/√2. Allow if 500-2T cos 45-100g = 0 to obtain T=-354 and then state magnitude is 354. If TA and TB are different values then A0.
4. [M1] Attempt to resolve vertically and horizontally 3 terms vertically and 2 terms horizontally; allow sign errors; allow g missing. Must have TA = 0.
5. [A1] Allow -TB cos45+500–100g = 0 and F + TB sin 45 = 0 OR TB cos 45+500-100g = 0 and F + TB sin 45 = 0 OR -TB cos 45+500-100g = 0 and F-TB sin 45=0. For both equations correct.
6. [A1] F = 500 awrt 500 to 3sf.