After an empty freight train car of mass 10,000 kg at 2.00 m/s collides with a loaded car at rest, what is the speed of the coupled cars after the collision?

To find the speed of the coupled cars after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision must equal the total momentum after the collision, assuming no external forces act on the system.

First, we calculate the initial momentum of the system. The empty freight train car has a mass of 10,000 kg and is moving at 2.00 m/s. The loaded car is at rest, which means its velocity is 0 m/s. The initial momentum of the moving car is:

[ \text{Momentum}_{\text{initial}} = \text{mass} \times \text{velocity} = (10,000 , \text{kg}) \times (2.00 , \text{m/s}) = 20,000 , \text{kg m/s}. ]

The momentum of the loaded car is zero since it is at rest. Thus, the total initial momentum of the system is 20,000 kg m/s.

After the collision, the two cars couple together and will move as a single entity. The total mass of the coupled cars is:

[ \text{Total mass} = 10,000 \