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Difficulty: MediumMass versus Weight

An automated logistics drone is transporting a sealed supply crate. On Earth, where the gravitational acceleration is considered to be 10 m/s210 \text{ m/s}^2, the crate has a measured weight of 1400 N1400 \text{ N}. The crate is then delivered to a controlled low-gravity research habitat where the local gravitational acceleration is maintained at 3.5 m/s23.5 \text{ m/s}^2.

What is the weight of the crate inside the low-gravity habitat in Newtons?

Answer: 490 N

Answer

490
To find the new weight, first determine the crate's mass, which does not change. Dividing the Earth weight (1400 N1400 \text{ N}) by Earth's gravity (10 m/s210 \text{ m/s}^2) gives a mass of 140 kg140 \text{ kg}. Then, multiply this invariant mass by the habitat's gravity (3.5 m/s23.5 \text{ m/s}^2) to find the new weight: 140 kg×3.5 m/s2=490 N140 \text{ kg} \times 3.5 \text{ m/s}^2 = 490 \text{ N}.

Step-by-Step Solution

1
Calculate the mass of the crate on Earth.
m=1400 N10 m/s2=140 kgm = \frac{1400 \text{ N}}{10 \text{ m/s}^2} = 140 \text{ kg}
Mass is an intrinsic property of the object that remains constant regardless of location.
2
Calculate the weight of the crate in the low-gravity habitat.
W=140 kg×3.5 m/s2=490 NW = 140 \text{ kg} \times 3.5 \text{ m/s}^2 = 490 \text{ N}
Weight is the force exerted by gravity on a mass, which changes depending on the local gravitational acceleration.

Key Concept

Mass is invariant, while weight depends on the local gravitational field.
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Topics

Mass versus Weight

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