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Difficulty: EasyMechanics and Motion

A science teacher simultaneously drops a steel hammer and a bird feather from the same height inside a sealed vacuum chamber that contains no air. Which of the following best predicts the motion of the two objects?

  1. A
    The hammer will hit the bottom first because an object with greater mass experiences a larger downward acceleration.
  2. Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.Answer
  3. C
    The feather will hit the bottom first because an object with less mass attains downward velocity more quickly in a vacuum.
  4. D
    The hammer will hit the bottom first because its weight measured in metric units causes it to reach terminal velocity sooner.

Answer

Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.
In the absence of air resistance, the only force acting on falling objects is gravity. Although a heavier object experiences a greater gravitational pull (weight), it also has proportionally greater inertia (resistance to acceleration). As a result of a=Fm=ga = \frac{F}{m} = g, all objects accelerate downward at the constant rate of approximately 9.8 m/s29.8\text{ m/s}^2 on Earth, reaching the surface at the exact same time when released together from the same height.

Step-by-Step Solution

1
Identify the external forces acting on the objects inside the chamber.
Only the downward force of gravity acts on the objects, as air resistance is zero in a vacuum.
Recognizing the environmental conditions determines whether drag forces affect the fall.
2
Apply Newton's second law of motion (F=maF = ma) to determine acceleration due to gravity.
The acceleration is calculated as a=Fgm=mgm=ga = \frac{F_g}{m} = \frac{mg}{m} = g.
Demonstrates that the mass mm cancels out, proving acceleration is independent of mass.
3
Compare the arrival times of both falling objects released from the same height.
Since both start from rest with identical acceleration gg, both take time t=2hgt = \sqrt{\frac{2h}{g}} to reach the bottom.
Confirms that both items strike the floor simultaneously.

Key Concept

Acceleration due to gravity in free fall without air resistance
Estimated Time:45s
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Topics

Mechanics and Motion

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