A-LevelMathematicsMechanics9709/43 · May/June 2018 · Q56 Marks
A particle of mass 3 kg is on a rough plane inclined at an angle of 20° to the horizontal. A force of magnitude P N acting parallel to a line of greatest slope of the plane is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is 0.35. Show that the least possible value of P is 0.394, correct to 3 significant figures, and find the greatest possible value of P.
- A particle of mass 3 kg is on a rough plane inclined at an angle of 20° to the horizontal. A force of magnitude P N acting parallel to a line of greatest slope of the plane is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is 0.35. Show that the least possible value of P is 0.394, correct to 3 significant figures, and find the greatest possible value of P.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] R = 3g cos 20° Correct normal reaction stated or used
- [M1] [F = 0.35×3gcos 20°] For use of F = µR
- [M1] [P + F = 3g sin 20° ] Attempted resolving equation for minimum case
- [A1] P = 0.394 (AG) Correct given answer from correct work
- [M1] [P₂ = F + 3g sin 20° ] Attempted resolving equation for maximum case
- [A1] P₂ = 20.1 (N)
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