A block A of mass 80kg is connected by a light, inextensible rope to a block B of mass 40kg. The rope joining the two blocks is taut and is parallel to a line of greatest slope of a plane which is inclined at an angle of 20° to the horizontal. A force of magnitude 500N inclined at an angle of 15° above the same line of greatest slope acts on A [Figure X.X]. The blocks move up the plane and there is a resistance force of 50N on B, but no resistance force on A.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] Attempt to apply Newton's second law to either block A or block B, resolving parallel to the plane. Must include at least three terms relevant to the block (e.g., tension, weight component, applied force component, resistance, mass × acceleration). Allow sign errors, sin/cos mix, g missing.
2. [A1] Correctly formulate two independent equations (one for block A and one for block B) involving tension T and acceleration a. E.g., for B: T - 40g sin 20° - 50 = 40a; for A: 500 cos 15° - 80g sin 20° - T = 80a (using g=10: T - 400 sin 20° - 50 = 40a and 500 cos 15° - 800 sin 20° - T = 80a).
3. [M1] Attempt to solve the two simultaneous equations for acceleration (a) or tension (T). This involves correctly combining the equations to eliminate one variable.
4. [A1] Acceleration = 0.188 ms⁻² (Allow AWRT 0.19).
5. [A1] Tension = 194 N.
6. [M1] For use of a constant acceleration formula (suvat) and solving for time t with their positive acceleration (a), leading to a positive value of t. e.g., v = u + at. 1.2 = 0 + (their 0.188)t. Ensure a≠±10, a≠±g. Allow if acceleration from part (a) was negative and its absolute value is used here.
7. [A1] Time = 6.39 s (Allow 6.38 or 6.32 from a=0.19).