CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 2, Exercise 2 Solution
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Identifying an Action-Reaction Pair (Newton's Third Law)

PROBLEM
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A person stands on a skateboard and pushes off a wall. Using Newton's
Third Law, explain precisely which two forces are the "action" and
"reaction" pair in this scenario, and identify which object each
force acts on.

SOLUTION
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The action-reaction pair here is:

  ACTION:   The person's hands push against the wall.
            (This force acts ON THE WALL.)

  REACTION: The wall pushes back against the person's hands with an
            equal and opposite force.
            (This force acts ON THE PERSON.)

These two forces are equal in size and opposite in direction, exactly
as Newton's Third Law requires - but critically, they act on two
DIFFERENT objects (the wall and the person), not on the same object.
Because the reaction force acts on the person (who is free to move,
standing on a low-friction skateboard), that force is what actually
accelerates the person and skateboard backward, away from the wall.

ANSWER: The action is the person's push on the wall; the reaction is
the wall's equal, opposite push back on the person - and it is this
second force, acting on the person rather than the wall, that causes
the person to roll away.

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WHY THIS WORKS AS AN ANSWER

A common misconception treats action-reaction pairs as forces that
"cancel out," but they never can, because they act on two separate
objects rather than the same one. The wall does not move (it is
anchored to the building, with an enormous effective mass), so the
force on it produces no noticeable acceleration - while the same-sized
force on the much lighter, nearly frictionless person-plus-skateboard
system produces a real, visible acceleration. This is exactly the same
principle behind rocket propulsion described in the chapter: the
rocket pushes exhaust gas one way, and the exhaust gas pushes the
rocket the other way with equal force.