Mass does not affect the acceleration due to gravity. All objects, regardless of their mass, accelerate at the same rate due to gravity (approximately 9.8 m/s² near the Earth's surface), neglecting air resistance.
Explanation
While a more massive object experiences a greater gravitational force, it also has greater inertia (resistance to acceleration). These two effects cancel each other out, resulting in the same acceleration for all objects. Let's break this down:
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Newton's Law of Universal Gravitation: The force of gravity (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers:
F = G (m1 m2) / r²
Where G is the gravitational constant. In the context of an object falling to Earth, m1 is the mass of the Earth, m2 is the mass of the object, and r is the distance from the center of the Earth to the object.
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Newton's Second Law of Motion: Force (F) equals mass (m) times acceleration (a):
F = m * a
Why Acceleration is Constant
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Force of Gravity Increases with Mass: A more massive object experiences a larger gravitational force (F is proportional to m2 in the equation above).
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Inertia Increases with Mass: The object's resistance to changes in motion (inertia) is also directly proportional to its mass (m).
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Acceleration Remains Constant: When we combine these two laws, we can derive the acceleration due to gravity:
F = m * a (Newton's Second Law)
G (m1 m2) / r² = m2 * a (Substituting the force of gravity)
a = (G * m1) / r² (Dividing both sides by m2 - the mass of the object)
Notice that the object's mass (m2) cancels out! The acceleration (a) depends only on the gravitational constant (G), the mass of the Earth (m1), and the distance from the center of the Earth (r).
Example
Imagine dropping a feather and a bowling ball simultaneously. Ideally, in a vacuum (no air resistance), they would fall at the same rate and hit the ground at the same time. The bowling ball experiences a much greater gravitational force, but because it is much more massive, it also requires more force to accelerate. The feather experiences a much smaller gravitational force, but it requires far less force to accelerate because its mass is tiny. The ratio of force to mass is the same for both.
Air Resistance
In the real world, air resistance significantly affects lighter objects with a large surface area, such as feathers. Air resistance acts as an opposing force, slowing the feather down much more than the bowling ball. This is why the bowling ball appears to fall faster.
