Two particles, A and B, of masses 0.2kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a small fixed smooth pulley which is attached to the bottom of a rough plane inclined at an angle θ to the horizontal where sinθ = 0.6. Particle A lies on the plane, and particle B hangs vertically below the pulley, 0.25 m above horizontal ground. The string between A and the pulley is parallel to a line of greatest slope of the plane (see diagram). The coefficient of friction between A and the plane is 1.125. Particle A is released from rest. [Figure 7]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. [B1] Allow cos37 or better for 0.8.
2. [*M1] Where R is a component of weight. Must have 1.125×0.2g×0.8 or 1.125×0.2g×0.6 or with using cos37 or sin 37 or better for 0.8 and 0.6 respectively. These 2 marks may be embedded in the N2L equation(s).
3. [*M1] Correct number of terms; allow sign errors; allow sin/cos mix. Dimensionally correct.
4. [A1] For any 2 correct equations. Allow sin37 or better for 0.6. Allow their possibly incorrect F.
5. [A1] Must be positive.
6. [DM1] From equations with the correct number of relevant terms. If a found first then substituting into an equation with the correct number of relevant terms and solving. If resolved equations incorrect and no working seen, then this mark is implied by the correct T value for their equations. Dependent on previous 2 M marks
7. [A1]
8. [*M1] Use of v²=u² +2as with u=0 and using s=0.25, |their 4.8|, a≠±g. Must be a complete method to get an expression for v or v².
9. [*M1] 3 terms; allow sign errors; allow sin/cos mix; allow their non-zero F from part (a); Dimensionally correct; must be using 0.2 for the mass. Allow θ=37 or better. For reference a=−3 (or –2.99 if using θ=36.9).
10. [DM1] Using constant acceleration formula(e) using a negative acceleration to get an expression in s only. Dependent on previous 2 M marks.
11. [A1] AWRT 0.650. Allow 0.651 from use of θ=36.9 .