A particle of mass 1.3 kg rests on a rough plane inclined at an angle θ to the horizontal, where tan θ = 12/5. The coefficient of friction between the particle and the plane is μ.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [B1] Resolve forces perpendicular to plane. Allow 67.4 used
2. [B1] Resolve forces parallel to plane. Allow 67.4 used
3. [M1] Use F = μR
4. [A1] AG Must be from exact working here
5. [M1] For applying Newton's second law along the plane and also using F = μR (3 terms)
6. [A1] a = 3.08 ms⁻²
7. [M1] Use s = ut + ½at² with u = 0 and their a ≠ g to find the distance moved in the first 2 seconds
8. [M1] WD = F × d
9. [A1] WD = 49.2 J
10. Alternative method for question 4(iii)
11. [M1] Finding v after 2 seconds and using WD = PE loss – KE gain
12. [M1] (Implicitly covers s = ut + ½at² and WD=Fd as intermediate steps in PE/KE calculations)
13. [A1] WD = 49.2 J