A specialized rover is designed to operate on both Earth (where gravitational acceleration… — Armed Services Vocational Aptitude Battery (ASVAB)

A specialized rover is designed to operate on both Earth (where gravitational acceleration is $10\text{ m/s}^2$ ) and an exoplanet (where gravitational acceleration is $15\text{ m/s}^2$ ). The rover carries a scientific payload that is measured to have a weight of $600\text{ N}$ on Earth. When the rover arrives on the exoplanet, it suspends the payload from a spring scale to verify its properties, and later pushes the payload horizontally across a frictionless ice field to accelerate it at $4\text{ m/s}^2$ . What will the spring scale read, and what horizontal force must the rover apply?

Spring scale: $900\text{ N}$ ; Horizontal force: $240\text{ N}$ Answer
B
Spring scale: $900\text{ N}$ ; Horizontal force: $3600\text{ N}$
C
Spring scale: $9000\text{ N}$ ; Horizontal force: $2400\text{ N}$
D
Spring scale: $900\text{ N}$ ; Horizontal force: $15\text{ N}$

Answer

Spring scale:

900\text{ N}

; Horizontal force:

240\text{ N}

The payload's mass is an invariant property, calculated from its Earth weight (

m = \frac{W}{g} = \frac{600}{10} = 60\text{ kg}

). On the exoplanet, the spring scale measures the local gravitational force (weight), which is mass times local gravity (

60 \times 15 = 900\text{ N}

). The horizontal force depends only on the invariant mass and the desired acceleration (

F = ma = 60 \times 4 = 240\text{ N}

Step-by-Step Solution

Determine the invariant mass of the payload using its Earth weight.

m = \frac{W_{\text{Earth}}}{g_{\text{Earth}}} = \frac{600\text{ N}}{10\text{ m/s}^2} = 60\text{ kg}

Mass is the amount of matter and remains constant regardless of location. It is required to determine both the new weight and the horizontal force.

Calculate the new weight on the exoplanet to find the spring scale reading.

W_{\text{exo}} = m \times g_{\text{exo}} = 60\text{ kg} \times 15\text{ m/s}^2 = 900\text{ N}

A spring scale measures the local force of gravity (weight), which depends on the local gravitational acceleration.

Calculate the required horizontal force using Newton's Second Law.

F = m \times a = 60\text{ kg} \times 4\text{ m/s}^2 = 240\text{ N}

Horizontal acceleration on a frictionless surface depends only on the object's mass (inertia) and the applied force, not on its weight.

Key Concept

Mass is an invariant property that determines inertia and relates to force (

F=ma

), while weight is a location-dependent gravitational force (

W=mg

) measured by spring scales.

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