A standard shipping crate is measured on Earth (where the acceleration due to gravity is ) using a mechanical balance scale. The balance scale determines that the crate has a mass of . The crate is then transported to a planetary outpost where the local gravitational acceleration is . At the outpost, the crate is hoisted using a heavy-duty spring scale. This spring scale was manufactured and calibrated on Earth to display mass in kilograms based on Earth's gravity. What numerical value will this spring scale display when weighing the crate at the outpost?
Answer: 160 kg
Answer
160
The true mass of the crate is 400 kg, which does not change based on location. On the outpost, the crate's weight (force) is 400 kg × 4 m/s² = 1600 N. The spring scale stretches based entirely on this 1600 N force. Because it was calibrated on Earth (where the acceleration due to gravity is 10 m/s²), its internal mechanism is designed to display '1 kg' for every 10 N of force it supports. Therefore, an applied force of 1600 N causes the scale to point to 1600 / 10 = 160.
Step-by-Step Solution
Key Concept
Mass is an invariant property of matter, while weight is the localized gravitational force acting on that mass. A spring scale measures force (weight) rather than mass, meaning a spring scale calibrated in kilograms on Earth will display incorrect mass readings in different gravitational fields.