Final answer:
Objects fall at the same rate in a vacuum due to gravity's constant acceleration, but air resistance can vary their fall time in air. The gravitational potential energy of an object depends on its mass and height, while inertia correlates with mass alone.
Step-by-step explanation:
The physics of how objects fall is an interesting study of gravity and air resistance. When objects are released, they fall due to gravity's constant acceleration toward Earth. However, the presence or absence of air can significantly affect their fall. In a vacuum, where air resistance is negligible, all objects would fall at the same rate, regardless of their mass. This was famously demonstrated by astronaut David R. Scott on the Moon in 1971.
In air, the situation is different. Air resistance affects objects based on their shape, surface area, and velocity. For example, a hammer, a marble, and a paper ball dropped from the same height will not hit the ground at the same time because air resistance is more significant for objects with a larger surface area in comparison to their mass, such as the paper ball. Meanwhile, a marble experiences less air resistance than a paper ball due to its smaller surface area and greater density.
If we consider energy concepts, the hammer, being more massive, will have the greatest gravitational potential energy when at a certain height above the ground, since potential energy depends on both mass and height. On the contrary, the paper ball will have the least inertia because inertia is a measure of an object's resistance to changes in its state of motion and depends on mass.