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Difficulty: MediumGravity and Free Fall

A 50-kg50\text{-kg} solid iron block and a 10-kg10\text{-kg} solid iron block are dropped simultaneously from a height of 100 m100\text{ m} inside a large vacuum chamber. Which of the following statements correctly describes the acceleration of the two blocks as they fall?

  1. Both blocks will experience an identical downward acceleration of approximately 9.8 m/s29.8 \text{ m/s}^2.Answer
  2. B
    The 50-kg50\text{-kg} block will accelerate five times faster than the 10-kg10\text{-kg} block due to its greater mass.
  3. C
    Both blocks will experience an identical downward acceleration of approximately 9.8 km/h29.8 \text{ km/h}^2.
  4. D
    The 50-kg50\text{-kg} block will accelerate at 490 m/s2490 \text{ m/s}^2 and the 10-kg10\text{-kg} block at 98 m/s298 \text{ m/s}^2.

Answer

Both blocks will experience an identical downward acceleration of approximately 9.8 m/s29.8 \text{ m/s}^2.
In the absence of air resistance, all objects near Earth's surface fall with the same constant acceleration due to gravity, which is roughly 9.8 m/s29.8 \text{ m/s}^2. Although the 50-kg50\text{-kg} block experiences a stronger gravitational force (weight), it also has proportionally more inertia resisting motion. These two factors perfectly balance each other out, resulting in an identical rate of acceleration for both blocks.

Step-by-Step Solution

1
Identify the forces acting on the objects during their fall in the vacuum chamber.
The only force acting on both blocks is the gravitational pull of the Earth (their weight).
Because the chamber is a vacuum, air resistance is completely eliminated.
2
Apply Newton's Second Law of Motion (F=maF = ma) to determine the rate of acceleration.
Acceleration (aa) is equal to the force of gravity divided by the mass of the object (a=Fma = \frac{F}{m}).
This formula shows the relationship between the downward force, the object's inertia, and its resulting acceleration.
3
Calculate the theoretical acceleration for both masses.
Since the force of gravity (FF) is equal to mass times gravitational acceleration (F=m×gF = m \times g), the formula simplifies to a=m×gma = \frac{m \times g}{m}, which means a=ga = g.
The mass variable cancels itself out mathematically, proving that acceleration due to gravity is independent of an object's mass.

Key Concept

In a vacuum, all objects experience free fall at the exact same rate of gravitational acceleration, roughly 9.8 m/s29.8 \text{ m/s}^2, because their proportionally greater weight is perfectly offset by their proportionally greater inertia.
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Topics

Gravity and Free Fall

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