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Difficulty: MediumGravity and Free Fall

A construction crew uses a pile driver machine that drops a solid steel hammer freely onto a concrete pillar. The operator replaces the original 500-kg500\text{-kg} hammer with a 1,000-kg1,000\text{-kg} hammer and drops it from the exact same height.

Ignoring air resistance and guide rail friction, which of the following statements correctly describes how the final free-fall speed of the heavier hammer compares to the original lighter hammer?

  1. The speeds will be exactly the same, because gravitational acceleration is independent of an object's mass.Answer
  2. B
    The heavier hammer will fall faster, because a larger mass results in a greater gravitational acceleration.
  3. C
    The heavier hammer will fall slower, because its increased mass creates more inertia to resist the downward pull.
  4. D
    The heavier hammer will fall faster, because mass and weight are identical properties that directly dictate an object's falling speed.

Answer

The final speeds will be exactly the same because the acceleration due to gravity is independent of the falling object's mass.
In the absence of air resistance and friction, all objects in free fall experience the exact same uniform acceleration due to gravity, regardless of their mass. Because both hammers are dropped from the same height and accelerate at the same rate, they will achieve the exact same speed just before impact.

Step-by-Step Solution

1
Identify the forces acting on both hammers during their descent.
Since air resistance and friction are ignored, the only force acting on the hammers is the downward pull of gravity.
Establishing that the objects are in a state of free fall is required to determine their rate of acceleration.
2
Relate gravitational force to acceleration using Newton's laws.
The downward force is weight (F=mgF = mg), and Newton's second law is F=maF = ma. Equating them gives mg=mamg = ma, which simplifies to a=ga = g.
This mathematical relationship proves that the mass (mm) cancels out, meaning acceleration depends only on gravity (gg).
3
Compare the final velocities of the two hammers.
Both hammers drop from the exact same height with the same constant acceleration. Therefore, their final speeds just before impact must be equal.
According to kinematic equations, identical initial conditions (starting from rest) and identical acceleration over the same distance result in the exact same final velocity.

Key Concept

Independence of Mass in Free Fall
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Topics

Gravity and Free Fall

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