Final answer:
A collision in which neither object breaks and maintains both momentum and kinetic energy is termed an elastic collision, while a perfectly inelastic collision results in objects sticking together with possible deformation.
Step-by-step explanation:
A phrase to describe a collision in which neither object breaks would be an elastic collision. In an elastic collision, such as the one illustrated in Figure 8.6, both momentum and internal kinetic energy are conserved. This means that after the collision, the total momentum and the total kinetic energy remain the same as they were before the collision, without any permanent deformation or breakage of the objects involved.
In contrast, a perfectly inelastic collision is a situation where two objects collide and stick together. Although the total momentum is still conserved according to the principles of conservation of momentum, the kinetic energy is not. This type of collision could result in objects getting deformed or generating heat instead of remaining intact. For scenarios that specifically involve no breakage and possible rebound, the term 'elastic collision' fits well.