Yes, the mass of an object does affect its speed while falling under the influence of gravity. In the absence of air resistance, all objects, regardless of their mass, will fall at the same rate in a vacuum. This concept is known as the "equivalence principle" and was famously demonstrated by Galileo Galilei.
According to this principle, in the absence of air resistance, all objects experience the same acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s^2) near the surface of the Earth. This means that all objects will increase their speed by 9.8 m/s for each second they fall.
However, when air resistance is present, the situation becomes more complex. Air resistance is a force that opposes the motion of objects through the air and depends on various factors, including the object's mass, shape, and surface area. For objects with different masses but similar shapes and surface areas, air resistance affects them differently.
In the presence of air resistance, heavier objects will experience a greater gravitational force due to their larger mass. This increased gravitational force will cause them to accelerate more initially. However, as they fall faster, the air resistance acting on them increases. Eventually, a balance is reached between the gravitational force pulling the object downward and the air resistance pushing against it. At this point, the object reaches its terminal velocity, which is the maximum speed it can achieve while falling.
In summary, in a vacuum or under conditions of negligible air resistance, the mass of an object does not affect its speed while falling. However, when air resistance is present, heavier objects will initially accelerate faster due to their greater gravitational force but will ultimately reach the same terminal velocity as lighter objects.