Final answer:
When two objects have the same momentum, the one with the smaller mass will have larger kinetic energy, because it must have a higher velocity. Conversely, if they have the same kinetic energy, the object with larger mass will have a higher momentum due to its larger mass.
Step-by-step explanation:
Understanding Momentum and Kinetic Energy.When considering two objects, one with a small mass and another with a large mass, that both have the same momentum, it's important to understand the relationship between momentum (p), mass (m), and velocity (v). Momentum is calculated as the product of mass and velocity (p = mv). To have the same momentum, a small mass must move with a larger velocity compared to a large mass.
When comparing kinetic energy (K), which is given by the formula K = (1/2)mv², the object with the smaller mass but higher velocity will have a larger kinetic energy. This is because kinetic energy is proportional to the square of velocity, and since the smaller mass has a higher velocity to maintain the same momentum, its kinetic energy will be greater. If the scenario is reversed and two objects have the same kinetic energy, then the large mass object must have a larger momentum. Since kinetic energy is the same, the larger mass object compensates for its lower velocity with its greater mass, leading to a greater momentum (p = mv).