Final answer:
During a perfectly inelastic collision, kinetic energy decreases although momentum is conserved. Calculations comparing initial and final kinetic energies after collision, where objects stick together and move as one, reveal this loss of kinetic energy.
Step-by-step explanation:
When two spheres or objects collide and stick together, such a collision is known as a perfectly inelastic collision. In such collisions, momentum is conserved, but kinetic energy is not; it is, in fact, reduced. Given the two examples involving Sphere 1 of mass m and Sphere 2 of mass 2m, the kinetic energy Ki will decrease during the collision because the objects stick together and move as one. By using the conservation of momentum and given velocities, one can find the final velocity of the combined mass. Then, the initial kinetic energy can be compared to the final kinetic energy to determine the change in kinetic energy.
To compute the kinetic energy change using a specific example, we consider Mass A (2.0 kg) at 15 m/s colliding with Mass B (4.0 kg) at 7.0 m/s. After the collision, they stick together and move as a single object. Calculations would show that the resulting kinetic energy of the two objects together is less than the sum of their kinetic energies before the collision, due to energy lost to sound, heat, and other forms of non-mechanical energy.