Three coplanar forces of magnitudes 20N, 100N and F N act at a point. The directions of these forces are shown in the diagram. Given that the three forces are in equilibrium, find F and α. [Figure 4.1]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [M1] Attempt to resolve in any direction (For resolving. Allow sin/cos mix. Allow sign error. Correct number of terms.)
2. [A1] F cos α - 20 cos 40 - 100 sin 20 = 0 (Or [F cos α = 15.320...+ 34.202... = 49.5229...])
3. [A1] F sin α + 20 sin 40 – 100 cos 20 = 0 (Or [F sin α = 93.969... – 12.855... = 81.1135...])
4. [M1] F = √(49.5229...)² +(81.1135...)² (OE; Attempt to solve for F; one term missing in total)
5. [M1] α = tan⁻¹(81.1135... / 49.5229...) (OE; Attempt to solve for α; one term missing in total)
6. [A1] F = 95(.0), α = 58.6 (F = 95.0364... and α = 58.5943...)