A-LevelMathematicsMechanics9709/41 · Oct/Nov 2017 · Q69 Marks

Coplanar forces, of magnitudes F N, 3F N, G N and 50 N, act at a point P, as shown in the diagram. [Figure 6.1]

(i)Given that F = 0, G = 75 and α = 60°, find the magnitude and direction of the resultant force.[4]
(ii)Given instead that G = 0 and the forces are in equilibrium, find the values of F and α.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[M1] X = 75 + 50 cos 60 (= 100) Y = 50 sin 60 (= 43.3) For resolving forces (either direction)
[A1] For both equations, unevaluated
[B1] Resultant = √(100² + 43.3²) = 109 N
[B1] Angle = arctan (43.3/100) = 23.4° Must state anticlockwise from the positive x-axis or show in a diagram
[B1] 50 cos α - F cos 50 = 0 Resolving forces horizontally
[B1] 50 sin α - 3F - F sin 50 = 0 Resolving forces vertically
[M1] tan α = (3F + F sin 50) / (F cos 50) For division to find α or for using Pythagoras to find F
[A1] α = 80.3
[A1] F = 13.1

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