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Difficulty: MediumMass versus Weight

At an Earth-based testing facility (where g=10 m/s2g = 10 \text{ m/s}^2), a suspended spring scale reads 750 N750 \text{ N} when a communications satellite module is attached to it. The module is later transported to a planetary outpost where the local gravitational acceleration is 4 m/s24 \text{ m/s}^2. Which of the following correctly identifies the module's mass and its new weight at the outpost?

  1. Mass = 75 kg75 \text{ kg}, Weight = 300 N300 \text{ N}Answer
  2. B
    Mass = 75 kg75 \text{ kg}, Weight = 750 N750 \text{ N}
  3. C
    Mass = 750 kg750 \text{ kg}, Weight = 3000 N3000 \text{ N}
  4. D
    Mass = 300 N300 \text{ N}, Weight = 75 kg75 \text{ kg}

Answer

Mass = 75 kg75 \text{ kg}, Weight = 300 N300 \text{ N}
The correct answer accurately separates the concepts of mass and weight. First, the mass is found by dividing the Earth weight by Earth's gravity (750 N/10 m/s2=75 kg750 \text{ N} / 10 \text{ m/s}^2 = 75 \text{ kg}). Because mass never changes regardless of location, it stays 75 kg75 \text{ kg}. The new weight is then found by multiplying this constant mass by the outpost's gravity (75 kg×4 m/s2=300 N75 \text{ kg} \times 4 \text{ m/s}^2 = 300 \text{ N}).

Step-by-Step Solution

1
Calculate the module's mass using its weight on Earth.
m=Wg=750 N10 m/s2=75 kgm = \frac{W}{g} = \frac{750 \text{ N}}{10 \text{ m/s}^2} = 75 \text{ kg}.
Weight is the product of mass and gravitational acceleration (W=mgW = mg). Rearranging this formula allows us to find the intrinsic mass.
2
Determine the module's mass at the planetary outpost.
The mass remains 75 kg75 \text{ kg}.
Mass is a measure of the amount of matter in an object. It is an invariant property that does not change when moved to a different gravitational field.
3
Calculate the module's new weight at the planetary outpost.
Wnew=m×goutpost=75 kg×4 m/s2=300 NW_{new} = m \times g_{outpost} = 75 \text{ kg} \times 4 \text{ m/s}^2 = 300 \text{ N}.
Weight is a force that depends on the local gravitational pull. The new weight must be calculated using the outpost's specific gravitational acceleration.

Key Concept

Mass is an invariant property representing the amount of matter (measured in kilograms), whereas weight is the gravitational force acting on that mass (measured in Newtons) and varies depending on the local gravitational field.
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Topics

Mass versus Weight

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