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

A mechanic swings a 2 lb2 \text{ lb} hammer, striking a 100 lb100 \text{ lb} stationary steel anvil. During the brief fraction of a second of contact, the hammer rapidly decelerates to a stop while the anvil remains practically motionless. Which of the following statements correctly compares the interaction forces between the hammer and the anvil during the exact moment of impact?

  1. The force the hammer exerts on the anvil is exactly equal in magnitude to the force the anvil exerts on the hammer.Answer
  2. B
    The anvil exerts a greater force on the hammer because the hammer undergoes a much larger change in acceleration during the impact.
  3. C
    The hammer exerts a greater force on the anvil because the heavy mass and inertia of the anvil prevent it from generating an equal reaction force.
  4. D
    The forces would only be equal if both objects had the same mass; otherwise, the object with greater mass exerts the dominant force.

Answer

The force the hammer exerts on the anvil is exactly equal in magnitude to the force the anvil exerts on the hammer.
According to Newton's Third Law of Motion, forces always occur in equal and opposite pairs. When the hammer strikes the anvil, the interaction consists of the hammer pushing on the anvil and the anvil pushing on the hammer. These two forces are simultaneously created and are always perfectly equal in magnitude, regardless of the fact that the anvil is 5050 times heavier than the hammer or that the hammer is rapidly decelerating. The difference in their observed movement is due to their differing masses (Newton's Second Law), not a difference in the force applied.

Step-by-Step Solution

1
Identify the two interacting bodies in the mechanical system.
The interacting bodies are the 2 lb2 \text{ lb} hammer and the 100 lb100 \text{ lb} anvil.
Newton's Third Law always applies to the mutual interaction between exactly two distinct objects.
2
Apply Newton's Third Law to the specific moment of impact.
The force of the hammer on the anvil (FH→AF_{H \to A}) must equal the negative force of the anvil on the hammer (−FA→H-F_{A \to H}).
For every action force, there is an equal and opposite reaction force, regardless of mass or velocity.
3
Differentiate between the interaction force and the resulting acceleration.
Both objects experience the exact same magnitude of force, but the hammer decelerates rapidly because it has a much smaller mass.
Newton's Second Law (F=maF = ma) explains the differing accelerations, while Newton's Third Law dictates the equal forces.

Key Concept

Action and reaction forces between two interacting bodies are always perfectly equal in magnitude and opposite in direction, entirely independent of the objects' masses or rates of acceleration.
Estimated Time:1m 30s
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Topics

Newton's Third Law (Action/Reaction)

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