The Core Puzzle
A common point of confusion for students first learning Newtonian mechanics is Newton's Third Law of Motion: "For every action, there is an equal and opposite reaction." If you push a box with 10N of force, the box pushes back on you with 10N of force. So, why doesn't the system just stay still? Why does the box accelerate?
The Concept: Different Bodies, Different Forces
The reason they do not cancel out is fundamental: Action and reaction forces act on different bodies.
- Force A (Action): Force applied by Person ON Box.
- Force B (Reaction): Force applied by Box ON Person.
To determine the acceleration of an object, you must perform a Free Body Diagram (FBD) analysis. An FBD considers only the forces acting on that specific body.
Why Things Move
When you look at the Box as your system:
- The only force that matters to the box's acceleration is the force applied to it.
- The reaction force (the box pushing back on you) acts on you, not the box.
- Since the force you apply to the box is an unbalanced external force acting on the box, the box accelerates according to Newton's Second Law: $F_{net} = ma$.
Summary
- Action-Reaction pairs never cancel because they do not exist within the same Free Body Diagram.
- Equilibrium only occurs when two forces act on the same body and sum to zero.
- Always identify which object the force is acting upon before attempting to cancel forces.