A block A of mass 2kg and a particle B of mass 0.5kg are connected by a light inextensible string inclined at 15° to the horizontal. They are pulled across a horizontal surface with acceleration 1.2 ms⁻² by a force of magnitude 6N, applied to A, acting at 20° above the horizontal as shown in the diagram. [Figure 8.1] The string and the force applied to A are in the same vertical plane. The contact between B and the surface is smooth and the contact between A and the surface is rough.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [M1] Tcos15=0.5×1.2 N2L for B – correct number of terms, allow sin/cos mix ONLY.
2. [A1] T = 0.621 N Allow (3√6-3√2)/5.
3. [*M1] Attempt to resolve vertically for A to form an equation Correct number of terms, allow sign errors and sin/cos mix, allow their (possibly incorrect) T from 8(a).
4. [A1] 6 sin 20+ R_A = 2g + T sin15 R_A=18.10864...
5. [*M1] Attempt at N2L for A Correct number of terms, allow sign errors and sin/cos mix, allow their (possibly incorrect) T from 8(a).
6. [A1] 6 cos 20-T cos15-F=2×1.2 F=2.63815...
7. [DM1] Use of F = µR to get an equation in μ only Dependent on both previous M1 marks.
8. [A1] μ = 0.146 μ = 0.1456848...