Three coplanar forces of magnitudes 10N, 25 N and 20 N act at a point O in the directions shown in the diagram.

Mark scheme

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

1. [M1] 20 cos 30=25 cos 60+10cos α For resolving forces horizontally, all relevant terms included
2. [A1] [17.32=12.5+10cosα, → cosα = 0.4821] From α ≈ 61.18
3. [M1] Resultant = 20 sin 30+10sin 61.2-25 sin 60 For resolving forces vertically, all relevant terms included
4. [A1] Magnitude of resultant force = 2.89 N A0 for -2.89 N or for ±2.89 Ν. Allow 2.89 N downwards
5. [M1] X = 25 cos 60+10cos 45-20cos 30 For either horizontal or vertical component, correct number of relevant terms. Allow ±X and/or ±Y
6. [A1] Y = 20sin 30+10sin 45-25 sin 60 For both correct, allow unsimplified
7. [M1] R = √X²+Y² OE. Using a method to find the resultant force, using expressions for X and Y with at least 5 relevant terms.
8. [M1] α = tan⁻¹ Y/X OE. A method to find the direction, using expressions for X and Y with at least 5 relevant terms.
9. [A1] Resultant = 5.10 N, Direction = 63.8° below positive x-axis For both correct, angle clearly explained. May use a diagram with a correct arrow and arc for angle. Allow angle 296° (measured anticlockwise from +ve x-axis)