Final answer:
The total mass of the carts is the independent variable, and the final velocity of the carts after the collision is the dependent variable. Experiments on a frictionless track should demonstrate conservation of momentum, with total momentum and, for elastic collisions, kinetic energy staying constant regardless of the initial mass and velocity settings.
Step-by-step explanation:
The total mass of the carts is the independent variable in your experiment because you are intentionally changing it to observe its effect on momentum. The final velocity of the carts after the collision is known as the dependent variable because it changes in response to the variations in the total mass of the carts involved in the collision.
Considering conservation of momentum, when you run your experiment on a frictionless track, the total momentum of the system will be conserved during the collision. This means that the total momentum before the collision will be equal to the total momentum after the collision, regardless of whether the collision is elastic or perfectly inelastic. If you experiment with changing the elasticity of the collision, you will notice that in perfectly elastic collisions, total kinetic energy is also conserved, whereas it is not in perfectly inelastic collisions.
In summary, when calculating the final velocities or center-of-mass momentum, you should apply the principles of conservation of momentum, which state that the momentum of a closed system remains constant if external forces do not act upon it. For elastic collisions, kinetic energy will also be conserved.