A-LevelMathematicsMechanics9709/42 · Feb/Mar 2020 · Q58 Marks
Coplanar forces, of magnitudes FN, 3 N, 6 N and 4 N, act at a point P, as shown in the diagram. [Figure 5.1]
- (a)Given that α = 60, and that the resultant of the four forces is in the direction of the 3 N force, find F.[3]
- (b)Given instead that the four forces are in equilibrium, find the values of F and α.[5]
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 2020). The mark or mark type is shown in brackets.
- [M1] Resolve forces vertically and equate to zero
- [A1] Correct equation
- [A1] Allow F = 8/√3 or F = 8/3√3
- [M1] Resolve forces either vertically or horizontally
- [A1] Both equations correct [F sin α = 4] [F cos α = 0.464102...]
- [M1] Attempt to solve for F using Pythagoras or from a value found for α
- [M1] Attempt to solve for α using trigonometry or from a value found for F
- [A1] Both correct as shown [F = 4.0268..., α = 83.382...]
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