A block of mass m kg is held in equilibrium below a horizontal ceiling by two strings, as shown in the diagram. One of the strings is inclined at 45° to the horizontal and the tension in this string is T N. The other string is inclined at 60° to the horizontal and the tension in this string is 20 N. Find T and m.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. [5] 20 cos 60 = T cos 45
2. [5] Resolve forces horizontally, 2 terms
3. [5] T = 10√2 or T = 14.1
4. [5] 20 sin 60 + T sin 45 = mg or W
5. [5] Resolve forces vertically, 3 terms
6. [5] 20 sin 60 + T sin 45 = mg
7. [5] m = 2.73 [= √3 + 1]
8. [5] Alternative method for question 3
9. [5] T/sin 150 = mg or W/sin 75 = 20/sin135
10. [5] Attempt at one pair of terms using Lami's Method
11. [5] T/sin 150 = mg/sin 75 = 20/sin 135
12. [5] All terms correct in Lami's Method
13. [5] Attempt to solve for either T or m or W
14. [5] T = 10√2 or T = 14.1
15. [5] m = 2.73 [= √3 + 1]
16. [5] Alternative method for question 3
17. [5] T/sin 30 = mg or W/sin 105 = 20/sin 45
18. [5] Attempt the triangle of forces method and state one equation which involves any two of the forces T, m and 20.
19. [5] T/sin 30 = mg/sin 105 = 20/sin 45
20. [5] All correct
21. [5] Attempt to solve for either T or m or W
22. [5] T = 10√2 or T = 14.1
23. [5] m = 2.73 [= √3 + 1]