Final answer:
In the absence of air resistance, mass does not affect the rate at which objects fall; all objects accelerate toward Earth at the same rate. Air resistance, however, can affect the fall rate and depends on an object's surface area and shape. This demonstrates the equivalence principle, where gravity's effect does not depend on mass.
Step-by-step explanation:
The question "Does mass affect the rate at which an object falls?" refers to a core principle in physics. In the absence of air resistance, objects fall toward the Earth's surface with the same constant acceleration regardless of their mass. This was demonstrated by Galileo's experiments, which showed that if two objects are dropped from the same height and there is no air resistance, they will hit the ground at the same time. This means that the acceleration due to gravity is the same for all objects, irrespective of their mass.
However, in real-world conditions, air resistance can affect the rate at which an object falls. This resistance depends on the object's surface area and shape, not its mass. Therefore, if two objects have different shapes or sizes, the one with the larger surface area will encounter more air resistance and may fall more slowly, not because of its mass but because of its interaction with the air.
Returning to the initial example, if the room in Figure 24.4 were falling at the rate of gravity and the man were twice as massive as the woman, they would still fall at the same rate if we ignore air resistance, thus adhering to the equivalence principle. The equivalence principle states that the effects of gravity are locally indistinguishable from the effects of acceleration, and it would be violated if mass did indeed affect the rate of falling when air resistance is negligible.