The misconception that heavy objects fall faster than light ones is a common one, but it is not accurate. In reality, in the absence of air resistance, all objects, regardless of their mass, fall at the same rate in a vacuum near the Earth's surface. This principle was famously demonstrated by Galileo Galilei and is known as the "equivalence principle" or "universal acceleration due to gravity."
The reason heavy and light objects fall at the same rate can be understood by considering Newton's law of universal gravitation and Newton's second law of motion. According to Newton's law of universal gravitation, the force of gravity between two objects is given by:
F = (G * m₁ * m₂) / r²
In this equation, G represents the gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between their centers of mass. The force of gravity depends on the masses of the objects involved.
However, when we consider Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a), we can see that the acceleration due to gravity is independent of the mass of the object. So, even though the force of gravity acting on a heavier object is greater, the heavier object also has more mass, resulting in the same acceleration as a lighter object.
As a result, when you drop two objects of different masses from the same height in a vacuum, they will both fall to the ground at the same rate. This principle was famously tested by Galileo, who dropped objects of different masses from the Leaning Tower of Pisa to demonstrate this concept.
It's worth noting that in real-world situations where air resistance is present, objects of different shapes and masses may fall at slightly different rates due to variations in air resistance. However, in the absence of air resistance, all objects experience the same acceleration due to gravity and fall at the same rate.