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Difficulty: MediumNewton's First Law (Inertia)

Two detached shipping crates, Crate X (200 kg200\text{ kg}) and Crate Y (800 kg800\text{ kg}), are gliding freely across a perfectly level, frictionless warehouse floor. Both crates are traveling in a straight line at a constant velocity of 3 m/s3\text{ m/s}. Which of the following statements is correct regarding their inertia and motion?

  1. Crate Y has four times the inertia of Crate X, meaning it requires four times as much opposing force to stop in the same amount of time.Answer
  2. B
    Crate Y has greater inertia primarily because its larger weight creates a stronger downward force against the floor.
  3. C
    The crates remain in constant motion because their forward action forces are balanced by equal and opposite reaction forces.
  4. D
    If an identical braking force is applied to both crates, Crate Y will decelerate to a stop more rapidly than Crate X.

Answer

Crate Y has four times the inertia of Crate X, meaning it requires four times as much opposing force to stop in the same amount of time.
The correct answer accurately identifies that inertia is entirely a function of mass. Because Crate Y's mass is four times greater than Crate X's mass, its inertia is proportionally larger. As a direct consequence, stopping Crate Y in the identical amount of time as Crate X requires four times the applied opposing force.

Step-by-Step Solution

1
Identify the relevant physics principle governing objects moving at a constant velocity without friction.
Newton's First Law (inertia) applies, indicating that an object's resistance to any change in its motion is entirely dependent on its mass.
The crates are coasting on a frictionless surface with no external driving forces, meaning their behavior is purely a function of inertia.
2
Evaluate and compare the physical properties of the two crates.
Crate Y (800 kg800\text{ kg}) possesses exactly four times the mass of Crate X (200 kg200\text{ kg}).
Comparing their mass establishes their relative inertia, as mass is the only measure of inertia.
3
Determine how this difference in inertia affects the external forces required to alter their state of motion.
Because Crate Y has four times the inertia, it takes four times the braking force to achieve the same rate of deceleration as Crate X.
Newton's Second Law (F=maF = ma) demonstrates that applied force must scale proportionately with mass to produce the identical acceleration or deceleration.

Key Concept

Inertia is an intrinsic property of matter that depends exclusively on mass, representing an object's natural resistance to any change in its velocity.
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Topics

Newton's First Law (Inertia)

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