A lunar exploration probe has a mass of 60\text{ kg} on Earth, where gravitational acceler… — Armed Services Vocational Aptitude Battery (ASVAB)

A lunar exploration probe has a mass of $60\text{ kg}$ on Earth, where gravitational acceleration is $9.8\text{ m/s}^2$ . The probe is transported to the Moon, where gravitational acceleration is $1.6\text{ m/s}^2$ . A thruster applies a constant horizontal net force of $180\text{ N}$ to propel the probe along a frictionless test surface. What is the mass of the probe on the Moon, and what is the magnitude of its horizontal acceleration?

A
The mass is $10\text{ kg}$ , and the acceleration is $18.0\text{ m/s}^2$ .
B
The mass is $96\text{ kg}$ , and the acceleration is $1.88\text{ m/s}^2$ .
The mass is $60\text{ kg}$ , and the acceleration is $3.0\text{ m/s}^2$ .Answer
D
The mass is $60\text{ kg}$ , and the acceleration is $1.4\text{ m/s}^2$ .

Answer

The probe's mass on the Moon is

60\text{ kg}

, and its horizontal acceleration is

3.0\text{ m/s}^2

Mass is a fundamental scalar quantity that measures an object's inertia (resistance to acceleration) and remains constant regardless of the gravitational environment. On the Moon, the probe retains its full mass of

60\text{ kg}

. By Newton's second law of motion, the horizontal acceleration is determined by dividing the net horizontal force by the mass:

a = \frac{F}{m} = \frac{180\text{ N}}{60\text{ kg}} = 3.0\text{ m/s}^2

Step-by-Step Solution

Determine the mass of the probe on the Moon

The mass remains

60\text{ kg}

Mass measures the amount of matter in an object and its inertia; it does not change with the local gravitational field strength.

Apply Newton's second law of motion (

F_{\text{net}} = ma

) to find horizontal acceleration

a = \frac{F_{\text{net}}}{m} = \frac{180\text{ N}}{60\text{ kg}} = 3.0\text{ m/s}^2

The horizontal thrust provides the net horizontal force on a frictionless surface, accelerating the object's mass.

Key Concept

Mass is an invariant intrinsic property representing inertia, whereas acceleration depends solely on the net applied force divided by that mass according to Newton's Second Law (

F = ma

Estimated Time:1m 15s

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