Three points A, B and C lie on a line of greatest slope of a plane inclined at an angle of 30° to the horizontal, with AB = 1 m and BC = 1m, as shown in the diagram. A particle of mass 0.2kg is released from rest at A and slides down the plane. The part of the plane from A to B is smooth. The part of the plane from B to C is rough, with coefficient of friction μ between the plane and the particle. [Figure 7.1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. [M1] Attempt PE or KE for motion from A to B
2. [M1] Attempt PE loss = KE gain from A to B
3. [A1] vB² = 10
4. [B1] R = 0.2 × 10 × cos 30 = √3
5. [M1] For using F = µR where R must be a component of 0.2g
6. [M1] Attempt to find either PE loss or WD against F from B to C
7. [M1] Apply work-energy equation for motion from B to C as KE at B + PE at B = WD against F + KE at C with VB ≠ 0
8. [A1] vc = √5 = 2.24 ms⁻¹
9. (M1) Attempt to find acceleration a for motion from A to B
10. (M1) Use v² = u² + 2as in attempt to find speed at B
11. (A1)
12. [M1] Attempt PE loss for motion from A to C
13. [M1] Attempt KE gain for motion from A to C
14. [A1] Both PE loss and KE gain correct
15. [B1] R = 0.2 × 10 × cos 30 = √3
16. [M1] For using F = µR where R must be a component of 0.2g
17. [M1] Attempt WD against F
18. [M1] Attempt work-energy equation for motion from A to C
19. [A1] vc = √5 = 2.24 ms⁻¹
20. [M1] Attempt to find a for motion from B to C, using vB² = 10, vC = 0
21. [M1] Attempt Newton's 2nd law for motion from B to C
22. [M1] Use F = µR where R is a component of 0.2g but R = 0.2g is M0
23. [A1] Any correct exact form such as 2/√3
24. [M1] Attempt PE loss for motion from B to C
25. [M1] Work-Energy equation for motion from B to C in the form PE at B + KE at B = WD against F using vB² = 10, vc = 0
26. [M1] Use F = µR leading to an equation in μ where R is a component of 0.2g
27. [A1] Any correct exact form such as 2/√3
28. [M1] Attempt PE loss for motion from A to C
29. [M1] Work-Energy equation for motion from B to C
30. [M1] Use F = µR leading to an equation in u where R is a component of 0.2g
31. [A1] Any correct exact form such as 2/√3