A-LevelMathematicsMechanics9709/42 · May/June 2021 · Q26 Marks

Coplanar forces of magnitudes 34 N, 30N and 26 N act at a point in the directions shown in the diagram.

Given that sin α = 8/13 and sin θ = 8/17, find the magnitude and direction of the resultant of the three forces.[6]

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 (May/June 2021). The mark or mark type is shown in brackets.

[M1] Resolve either horizontally or vertically with correct number of terms. Allow α and θ as in the question for this mark
[A1] [X=]30-34×8/17-26×5/13 [=4] Allow ±X as they may resolve forces left or right Allow [X=]30-34 sin 28-26 sin 23 angle 2s.f. or better
[A1] [Y=]34×15/17-26×12/13 [=6] Allow ±Y as they may resolve forces up or down Allow [Y=] 34cos 28-26 cos 23 angle 2s.f. or better
[M1] [R=]√X² + Y² Attempt to solve for the magnitude of the force
[M1] [β=] tan⁻¹(X/Y) or [β=]tan⁻¹(Y/X) Attempt to solve for the direction of the resultant force
[A1] R = √52 = 2√13 = 7.21 N and β = 56.3 above 30N force or anticlockwise from 30N force Must be a correct and clear explanation.

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