Two particles of masses 1.2 kg and 0.8 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest with both particles 0.64 m above the floor (see diagram). In the subsequent motion the 0.8 kg particle does not reach the pulley. [Figure 6]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

1. [M1] Apply Newton's law to either of the particles
2. [A1] Both equations correct: 12 - T = 1.2a and T - 8 = 0.8a
3. [M1] Solve for a and T
4. [A1] a = 2 ms⁻² and T = 9.6N
5. [M1] Attempt to find time t₁ taken for 1.2kg particle to reach ground and/or its speed v at the ground
6. [A1] t₁ = 0.8
7. [A1] v = 2 × 0.8 = 1.6
8. [M1] For attempting to find the time t₂ and/or distance travelled s₂ as 0.8kg particle comes to rest
9. [A1] t₂ = 0.16
10. [A1] s₂ = 0.128
11. [B1] Finding the distance s₃ travelled downwards in t₃ seconds t₃ = 1 - 0.8 - 0.16 = 0.04, s₃ = 1/2 × 10 × 0.04²
12. [B1] Total distance travelled = 0.64 + 0.128 + 0.008 = 0.776m