Two carts with mass of 4 kg and 3 kg move toward each other on a frictionless track with velocity 5 m/s. They collide and stick together; the speed of the final structure has to be determined.
The two carts form a closed structure and there is no friction. This allows the use of the law of conservation of momentum according to which the total momentum of the system does not change. Let the speed of the final structure be v.
The sum of the initial momentum of the carts before collision is 4*5 - 3*5 = 5 kg*m/s. The final mass of the two carts is 4 + 3 = 7 kg. As the final momentum is equal to the initial momentum (4+3)*v = 5
=> v = 5/7
The final speed of the structure created by the two carts is equal to 5/7 m/s