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Difficulty: MediumNewton's Third Law (Action/Reaction)

A 75 kg75 \text{ kg} mechanic stands on a slick, oil-covered garage floor with negligible friction. The mechanic pushes forward horizontally against a stationary 150 kg150 \text{ kg} tool cabinet with a constant force of 200 N200 \text{ N}. Which of the following statements correctly describes the forces involved in this interaction?

  1. A
    The cabinet exerts a 100 N100 \text{ N} backward force on the mechanic, reflecting the ratio of their masses.
  2. B
    The mechanic experiences a backward reaction force only if the 200 N200 \text{ N} push fails to overcome the cabinet's inertia.
  3. The cabinet experiences a 200 N200 \text{ N} forward force, and the mechanic experiences a 200 N200 \text{ N} backward force simultaneously.Answer
  4. D
    The 200 N200 \text{ N} action force and the 200 N200 \text{ N} reaction force both act on the cabinet, preventing it from accelerating rapidly.

Answer

The statement accurately describing the interaction is that the cabinet experiences a 200 N200 \text{ N} forward force, and the mechanic simultaneously experiences a 200 N200 \text{ N} backward force.
According to Newton's Third Law, any force exerted by one object on another is accompanied by an equal and opposite force exerted back by the second object on the first. Because the mechanic pushes the cabinet with 200 N200 \text{ N} forward, the cabinet simultaneously pushes the mechanic with 200 N200 \text{ N} backward. The differing masses do not alter the force magnitudes, though they result in different accelerations.

Step-by-Step Solution

1
Identify the interacting bodies in the given scenario.
The two interacting bodies are the mechanic and the tool cabinet.
Newton's Third Law applies to the forces exerted between two interacting objects.
2
Determine the magnitude and direction of the action force.
The mechanic exerts a forward force of 200 N200 \text{ N} on the tool cabinet.
This is the initial action provided in the problem description.
3
Apply Newton's Third Law to find the reaction force.
The tool cabinet must exert an equal and opposite reaction force of 200 N200 \text{ N} backward on the mechanic.
Forces always exist in equal and opposite pairs acting on different objects, regardless of their respective masses or whether they accelerate.

Key Concept

Newton's Third Law of Motion states that when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
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Newton's Third Law (Action/Reaction)

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