A block B, of mass 2kg, lies on a rough inclined plane sloping at 30° to the horizontal. A light rope, inclined at an angle of 20° above a line of greatest slope, is attached to B. The tension in the rope is T N. There is a friction force of F N acting on B (see diagram). The coefficient of friction between B and the plane is μ. [Figure X.X]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

1. [M1] Attempt to resolve parallel to the plane 4 terms; allow sin/cos mix; allow sign errors; allow g missing.
2. [A1] Correct equation.
3. [A1] T=18.5 awrt 18.5 .
4. [M1] Attempt resolve perpendicular to the plane 3 terms; allow sin/cos mix: allow sign errors; allow with T or their T; allow g missing.
5. [M1] Use of F = μR to get an equation in μ only Where R is a two term expression with a component of 2g and a component of their T; allow g missing.
6. [A1] μ = 0.455 awrt 0.455; allow 0.46 or 0.45; do not allow 5/11
7. [*B1] Max F = 0.8×(2g cos30-15sin20) [=0.8×12.1902......=9.7521......]
8. [*B1] 15cos20-2gsin30[=4.0953......]
9. [DB1] [State 4.0953......<9.7521......,] hence the block does not move [up the plane] Must have correct values (to at least 1 sf) to compare for this mark. No incorrect statement seen.