A 2.0 kg trolley moving east at 3.0 m/s runs into a stationary 4.0 kg trolley and the two move off joined together on a smooth track. What is their common speed straight after the collision?

1. The track is smooth and no outside push acts along it, so the two trolleys form an isolated system. 2. Take east as the positive direction. 3. Before the collision the moving trolley has momentum 2.0 kilograms multiplied by 3.0 metres per second, which is 6.0 kilogram metres per second east. 4. The second trolley is at rest, so it contributes nothing, and the total momentum before is 6.0 kilogram metres per second east. 5. After the collision the trolleys move as one body of mass 2.0 plus 4.0, which is 6.0 kilograms. 6. Total momentum after must also be 6.0 kilogram metres per second, so the common speed is 6.0 divided by 6.0, which is 1.0 metres per second east. 7. The 1.5 metres per second answer traps anyone who averages the two speeds instead of conserving momentum. 8. The 3.0 metres per second answer keeps the original speed and forgets the added mass, and the 0.5 metres per second answer divides by 12 kilograms by adding the masses twice. _Source: Siyavula Physical Sciences Grade 12 (Everything Science, CC BY 4.0), Chapter 2: Momentum and impulse_