A-LevelMathematicsMechanics9709/42 · Feb/Mar 2022 · Q57 Marks

Four coplanar forces act at a point. The magnitudes of the forces are 10N, FN, GN and 2FN. The directions of the forces are as shown in the diagram.

(a)Given that the forces are in equilibrium, find the values of F and G.[5]
(b)Given instead that F = 3, find the value of G for which the resultant of the forces is perpendicular to the 10N force.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

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

[M1] Attempt to resolve vertically or horizontally (Correct number of terms.)
[A1] G sin 60° + 2F sin 40° - 10 = 0 (Correct resolution vertically.)
[A1] F + G cos 60° - 2F cos 40° = 0 (Correct resolution horizontally.)
[M1] Attempt to solve simultaneously for F or G (From equations with 3 relevant terms in each)
[A1] F = 4.53, G = 4.82 (For both correct.)
[M1] G sin 60° + 2 × 3 sin 40° - 10 = 0 (Resolve forces parallel to the 10 N force and equate this expression to zero, 3 terms.)
[A1] G = 7.09 to 3 sf

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