Final answer:
To determine the velocity v of two masses m1 and m2 on a frictionless surface, additional details such as initial velocities or forces are required. In collision problems like Mass A and Mass B, the conservation of momentum can be used to determine final velocities after the collision.
Step-by-step explanation:
The question about two masses m1 and m2 moving on a frictionless surface cannot be answered without additional information about their initial velocities or the specifics of their interaction. To find velocity v, we need either the initial velocity of each mass or details about the forces acting on them.
In collision problems, the conservation of momentum is often used to determine the final velocities of interacting bodies. For instance, when two objects collide, the total momentum before the collision equals the total momentum after the collision. This principle can be applied to find missing velocities in such problems.
In the example of the collision between Mass A (1.0 kg) and Mass B (3.0 kg), we find the center-of-mass velocity by using the conservation of momentum:
Initial momentum = (1.0 kg)(8 m/s) = 8 kg·m/s
After collision, the masses stick together: total mass = 1.0 kg + 3.0 kg = 4.0 kg
Using conservation of momentum, we can find the final velocity after the collision:
8 kg·m/s = (4.0 kg)(v_final)
v_final = 8 kg·m/s / 4.0 kg
v_final = 2 m/s
Therefore, the change in the center-of-mass velocity of the system is 2 m/s. No change in center-of-mass velocity would be observed in perfectly elastic collisions between two masses where there is no loss of kinetic energy.