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Difficulty: Very hardMechanics and Motion

A physicist conducts an experiment with a solid block on a perfectly frictionless horizontal track. On Earth, a constant horizontal force of 150 N150\text{ N} applied to the block produces a forward acceleration of 3 m/s23\text{ m/s}^2. If the physicist transports the exact same block and track to an exoplanet where the acceleration due to gravity is exactly one-fifth that of Earth, and applies the identical 150 N150\text{ N} horizontal force, which of the following describes the block's resulting mass and forward acceleration?

  1. The mass remains 50 kg50\text{ kg}, and the acceleration remains 3 m/s23\text{ m/s}^2.Answer
  2. B
    The mass decreases to 10 kg10\text{ kg}, and the acceleration increases to 15 m/s215\text{ m/s}^2.
  3. C
    The mass remains 50 kg50\text{ kg}, but the acceleration increases to 15 m/s215\text{ m/s}^2.
  4. D
    The mass decreases to 10 kg10\text{ kg}, but the acceleration remains 3 m/s23\text{ m/s}^2.

Answer

The mass remains 50 kg50\text{ kg}, and the acceleration remains 3 m/s23\text{ m/s}^2.
The block's mass is an intrinsic property and remains 50 kg50\text{ kg} regardless of the local gravitational field. Because the track is frictionless, the object's horizontal acceleration is determined solely by the applied horizontal force and its mass (a=F/ma = F/m). Since neither the applied force (150 N150\text{ N}) nor the mass (50 kg50\text{ kg}) changed, the acceleration remains exactly the same at 3 m/s23\text{ m/s}^2.

Step-by-Step Solution

1
Calculate the mass of the block on Earth using Newton's second law (F=maF = ma).
m=150 N/3 m/s2=50 kgm = 150\text{ N} / 3\text{ m/s}^2 = 50\text{ kg}.
Mass is the ratio of applied net force to the resulting acceleration.
2
Determine the mass of the block on the exoplanet.
The mass remains 50 kg50\text{ kg}.
Mass is an intrinsic property of an object measuring its inertia; it does not change based on the local gravitational field.
3
Calculate the horizontal acceleration on the exoplanet.
a=F/m=150 N/50 kg=3 m/s2a = F / m = 150\text{ N} / 50\text{ kg} = 3\text{ m/s}^2.
On a frictionless horizontal surface, vertical forces (weight and normal force) do not impact horizontal motion. The only horizontal force is the 150 N150\text{ N} applied force, and because the mass is unchanged, the acceleration remains identical.

Key Concept

Invariance of Mass and Independence of Horizontal Inertia from Gravity
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Topics

Mechanics and Motion

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