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Difficulty: MediumMechanics and Motion

A robotic exploration rover has a mass of 120 kg120\text{ kg} on Earth. The rover is transported to Mars, where the acceleration due to gravity is approximately 3.7 m/s23.7\text{ m/s}^2. If the rover accelerates horizontally across a flat, level surface at 2.0 m/s22.0\text{ m/s}^2, what is the magnitude of the horizontal net force acting on the rover?

  1. A
    24 N24\text{ N}
  2. 240 N240\text{ N}Answer
  3. C
    444 N444\text{ N}
  4. D
    684 N684\text{ N}

Answer

The magnitude of the horizontal net force acting on the rover is 240 N240\text{ N}.
According to Newton's Second Law of Motion (F=maF = ma), the net force acting on an object is equal to its mass multiplied by its acceleration. An object's mass is invariant across different gravitational fields. Therefore, accelerating a 120 kg120\text{ kg} rover horizontally at 2.0 m/s22.0\text{ m/s}^2 requires a horizontal net force of 120 kg×2.0 m/s2=240 N120\text{ kg} \times 2.0\text{ m/s}^2 = 240\text{ N}.

Step-by-Step Solution

1
Identify the relevant physical law and given values.
Mass m=120 kgm = 120\text{ kg}, horizontal acceleration a=2.0 m/s2a = 2.0\text{ m/s}^2, and Newton's Second Law Fnet=maF_{\text{net}} = ma.
Mass is an intrinsic scalar property that remains constant regardless of location or local gravity.
2
Calculate the horizontal net force required to accelerate the mass.
Fnet=120 kg×2.0 m/s2=240 NF_{\text{net}} = 120\text{ kg} \times 2.0\text{ m/s}^2 = 240\text{ N}.
Horizontal acceleration is governed strictly by the horizontal net force and mass, independent of vertical gravitational forces on a level surface.

Key Concept

Newton's Second Law of Motion and Independence of Mass from Gravity
Estimated Time:1m 0s
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Topics

Mechanics and Motion

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