Final answer:
The collision is inelastic since the carts stick together and kinetic energy is not conserved. Friction, if present, would affect the center-of-mass velocity after the collision by changing the total mechanical energy. For the two carts moving at different speeds and sticking together, the final velocity is calculated by conservation of momentum.
Step-by-step explanation:
When Cart A with velocity +10 m/s and Cart B with velocity -v on a frictionless surface have an inelastic collision and stick together, the collision is best classified as inelastic because the carts do not bounce off each other and kinetic energy is not conserved. The concept of elasticity of a collision refers to whether kinetic energy is conserved during the collision, and inelastic collisions are characterized by the loss of kinetic energy. If there were friction present, it would act as an external force and could potentially change the center-of-mass velocity both before and after the collision by adding non-conservative forces into the system, which could do work and change the total mechanical energy.
Regarding the calculation of the velocity of the center of mass, it is calculated by taking the total momentum of the system and dividing it by the total mass. Since momentum is always conserved, friction doesn't affect the total momentum before the collision; thus, the center-of-mass velocity before the collision remains the same. After the collision, if friction acts, it could slow down the joined carts, thus changing the center-of-mass velocity.
In the case of the problem involving two carts (675 grams and 500 grams) moving in the same direction at different speeds, after their inelastic collision, the velocity of the two joined carts can be found using the conservation of momentum equation: m1v1 + m2v2 = (m1 + m2)vfinal.