A-LevelMathematicsMechanics9709/41 · May/June 2018 · Q36 Marks
A particle P of mass 8 kg is on a smooth plane inclined at an angle of 30° to the horizontal. A force of magnitude 100 N, making an angle of θ° with a line of greatest slope and lying in the vertical plane containing the line of greatest slope, acts on P [Figure X.X].
- (i)Given that P is in equilibrium, show that θ = 66.4, correct to 1 decimal place, and find the normal reaction between the plane and P.[4]
- (ii)Given instead that θ = 30, find the acceleration of P.[2]
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 2018). The mark or mark type is shown in brackets.
- [M1] Attempt to resolve forces along the plane (2 terms)
- [A1] 100 cos θ = 8 g sin 30 → θ = 66.4
- [M1] Resolve forces perpendicular to the plane (3 terms)
- [A1] R = 161
- [M1] Apply Newton's 2nd law parallel to the plane (3 terms)
- [A1] a = 5.83
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →