A-LevelMathematicsMechanics9709/41 · Oct/Nov 2021 · Q36 Marks
Coplanar forces of magnitudes 24 N, P N, 20 N and 36 N act at a point in the directions shown in the diagram. The system is in equilibrium. Given that sin α = 3/5, find the values of P and θ.
- mainGiven that sin α = 3/5, find the values of P and θ.[6]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] Attempt at resolving in any direction. Correct number of terms. No substitution for α required.
- [A1] Pcosθ=(36-24)cos36.9 or Pcosθ=(36-24)×0.8
- [A1] Psinθ+20=(24+36)sin36.9=14.4+21.6 or Psinθ+20=60×0.6=36
- [M1] Correct method for solving equations for P. OE. Pcosθ=9.6,Psinθ=16 P= √16² +9.6²
- [M1] Correct method for solving equations for θ. OE e.g. θ=tan⁻¹(5/3)
- [A1] P=18.7. Allow P=16√34/5. Allow P=18.6.
- [A1] θ=59[.0]
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