Two particles P and Q of masses 2.5kg and 0.5kg respectively are connected by a light inextensible string that passes over a small smooth pulley fixed at the top of a plane inclined at an angle of 30° to the horizontal. Particle P is on the plane and Q hangs below the pulley such that the level of Q is 2m below the level of P (see diagram). Particle P is released from rest with the string taut and slides down the plane. The plane is rough with coefficient of friction 0.2 between the plane and P.

Mark scheme

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

1. [B1] Note: F = 0.5g cos 30 = 5√3/2 = 4.330127019.
2. [M1] Correct number of dimensionally correct/relevant terms; allow sign errors; allow sin/cos mix. Using this twice to get equations for P and Q; allow different T's (equations with 0.5 and 2.5). Using once to get a system equation (equation with 0.5+2.5).
3. [A1] EITHER: Both correct; allow their F; must be the same T. OR: correct system equation; allow their F.
4. [DM1] Where R is a component of weight of P only; from equation(s) with the correct number of dimensionally correct/relevant terms.
5. [A1] Allow 15-5√3 / 6. 1.05662433. AWRT 1.06 from correct work.
6. [B1] Where x is the distance P moves down the plane or Q moves vertically upwards, or where y is the vertical distance of Q below P's starting point. Allow x = 1.3 or better; allow y = 0.67 or better.
7. [B1] Using their x(≠ 2or 1 or 0), 0 < x < 2; or their y(≠2or 1 or 0), 0< y < 2.
8. [B1] Using their x(≠ 2or 1 or 0), 0 < x < 2; or their y(≠2or 1 or 0), 0< y < 2.
9. [DM1] Attempt at work energy equation; dimensionally correct; 5 relevant terms; allow sign errors; allow sin/cos mix. Must be using correct values of x or y.
10. [A1] 1.67859014 AWRT 1.68 from correct work.