A mining crew extracts a dense mineral boulder. In their vessel's main processing bay, whe… — Armed Services Vocational Aptitude Battery (ASVAB)

A mining crew extracts a dense mineral boulder. In their vessel's main processing bay, where artificial gravity is maintained at $10 \text{ m/s}^2$ , a spring scale indicates the boulder has a weight of $1500 \text{ N}$ . The boulder is then transported to a storage facility on a small moon where the local gravitational acceleration is $2 \text{ m/s}^2$ . What are the mass and weight of the boulder at the lunar storage facility?

A
Mass: $30 \text{ kg}$ , Weight: $300 \text{ N}$
B
Mass: $150 \text{ kg}$ , Weight: $1500 \text{ N}$
Mass: $150 \text{ kg}$ , Weight: $300 \text{ N}$ Answer
D
Mass: $1500 \text{ kg}$ , Weight: $300 \text{ N}$

Answer

The mass is

150 \text{ kg}

and the weight is

300 \text{ N}

The correct answer accurately calculates the initial mass as

150 \text{ kg}

using the weight on the vessel (

1500 \text{ N} / 10 \text{ m/s}^2

). Because mass is an invariant property, it remains

150 \text{ kg}

on the moon. The new weight is then found by multiplying this mass by the moon's local gravity (

150 \text{ kg} \times 2 \text{ m/s}^2 = 300 \text{ N}

Step-by-Step Solution

Calculate the mass of the boulder using its initial weight and the artificial gravity in the processing bay.

m = \frac{W_1}{g_1} = \frac{1500 \text{ N}}{10 \text{ m/s}^2} = 150 \text{ kg}

Mass is an intrinsic property that must be determined first to calculate weight in other environments.

Determine the mass of the boulder at the lunar storage facility.

The mass remains

150 \text{ kg}

Mass is an invariant measure of the amount of matter and does not change with location or local gravity.

Calculate the new weight of the boulder using the local gravitational acceleration on the small moon.

W_2 = m \times g_2 = 150 \text{ kg} \times 2 \text{ m/s}^2 = 300 \text{ N}

Weight is the gravitational force acting on an object, which depends on the local acceleration due to gravity.

Key Concept

Mass is an intrinsic, invariant property representing the amount of matter, whereas weight is the location-dependent gravitational force acting upon that mass.

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