Final answer:
Momentum is conserved in a collision as long as no external forces act on the system, irrespective of the number of objects. The total momentum before and after the collision must remain constant. The conservation of kinetic energy depends on the nature of the collision (elastic or inelastic).
Step-by-step explanation:
The question of whether momentum is conserved in a collision involving any number of objects on the presence of external forces. Momentum is a conserved quantity in a closed system where no external forces are acting. In your scenarios, when there are no external forces acting on the system of masses, the law of conservation of momentum applies regardless of the number of objects involved.
In your example with Mass A and Mass B, since external forces are not considered, we can analyze the momentum before and after the collision. The conservation of momentum states that the total momentum of a system remains constant if no external forces are involved. In the case of Mass A and B, where A is moving with a velocity of 12 m/s and B is initially at rest, after the collision they move together with a velocity of 4 m/s. To determine if momentum is conserved, we would calculate the total momentum before and compare it with after the collision. If the momentum is the same, it is conserved.
For collisions, such as the one between two equal mass objects coming to rest or one being at rest while another moves with an unknown velocity, we deduce that momentum is conserved based on the principle of conservation of momentum if no external forces act on them. The conservation of kinetic energy, however, depends on whether the collision is elastic or inelastic. An example answer for the given scenarios would be:
- Mass A and B collision: Momentum is conserved, and kinetic energy is not conserved.
- Equal masses coming to rest: Momentum is conserved, and kinetic energy is not conserved.
- One object at rest and the other moving with unknown velocity post-collision: Momentum is conserved, and whether kinetic energy is conserved depends on additional information regarding the velocities after the collision