A block of mass 5 kg is being pulled straight down a line of greatest slope of a rough plane by a force of magnitude 20 N. The plane is inclined at an angle of 10° to the horizontal and the 20 N force acts at an angle of 35° above the line of greatest slope of the plane (see diagram). The coefficient of friction between the block and the plane is 0.4. The speed of the block when it passes a point O is 2 m s⁻¹. [Figure 5] Find the speed of the block when it has moved 3 m down the plane from O.

Mark scheme

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

1. [*M1] For resolving in any direction to form an equation; Correct number of relevant dimensionally correct terms; allow sin/cos mix; allow sign errors.
2. [A1] R=5gcos10-20sin35 [=37.76885892]; OE. For reference F=15.10754357
3. [A1] 20cos 35+5g sin10-F = 5a [25.06544977 – F = 5a]; OE, allow with their possibly incorrect F . Allow F-20cos35-5g sin10=5a .
4. [DM1] For use of F=0.4R to get an equation in a only; From both dimensionally correct equations with the correct number of relevant terms. For reference a=1.99 [1.99158124...].
5. [DM1] v² = 2²+2×(their1.99)×3; Dependent on both previous M marks. M0 if their calculated a is negative from using N2L down the plane. M0 if their calculated a is positive from using N2L up the plane. Their calculated 1.99 and 3 must be same sign. For use of v² =u² +2as or any complete method to get an equation in v or v², where v² > 0.
6. [A1] Speed = 3.99ms⁻¹; 3.993680939...