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Difficulty: MediumMechanics and Motion

An equipment container weighs 120 N120\text{ N} on Earth, where the acceleration due to gravity is approximately 10 m/s210\text{ m/s}^2. The container is transported to an orbital space station where it is in a weightless environment. If an astronaut applies a constant net horizontal force of 36 N36\text{ N} to the container, what is its resulting acceleration?

  1. A
    0.3 m/s20.3\text{ m/s}^2
  2. B
    30 m/s230\text{ m/s}^2
  3. 3 m/s23\text{ m/s}^2Answer
  4. D
    3 m/s3\text{ m/s}

Answer

3 m/s23\text{ m/s}^2
Mass measures an object's inertia and does not change when moving between Earth and orbit. Using the Earth weight W=120 NW = 120\text{ N} and gravity g=10 m/s2g = 10\text{ m/s}^2, the container's mass is m=12 kgm = 12\text{ kg}. In orbit, applying a net force of 36 N36\text{ N} yields an acceleration of a=F/m=36 N/12 kg=3 m/s2a = F/m = 36\text{ N} / 12\text{ kg} = 3\text{ m/s}^2.

Step-by-Step Solution

1
Determine the mass of the container from its Earth weight
Mass m=Wg=120 N10 m/s2=12 kg\text{Mass } m = \frac{W}{g} = \frac{120\text{ N}}{10\text{ m/s}^2} = 12\text{ kg}
Weight is the force of gravity acting on mass (W=mgW = mg). Mass is an intrinsic property of the object and remains unchanged regardless of location.
2
Apply Newton's Second Law of Motion (F=maF = ma) in the orbital environment
a=Fnetm=36 N12 kg=3 m/s2a = \frac{F_{\text{net}}}{m} = \frac{36\text{ N}}{12\text{ kg}} = 3\text{ m/s}^2
Although the container is weightless in orbit, its inertia (mass) remains 12 kg12\text{ kg}. A net force produces an acceleration inversely proportional to that mass.

Key Concept

Newton's Second Law (F=maF = ma) and the distinction between mass (inertia) and weight (gravitational force).
Estimated Time:1m 0s
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Topics

Mechanics and Motion

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