The Reaction Force Does Not Cancel The Action Force Because

The interplay of action and reaction forces is a fundamental concept in physics, yet it's often misunderstood. While Newton's Third Law states that for every action, there is an equal and opposite reaction, the assertion that these forces don't cancel each other out raises a crucial point about their application and impact on different objects. Understanding why they don't cancel is vital for grasping more complex physical phenomena.

Understanding Action and Reaction Forces

Newton's Third Law of Motion is deceptively simple: For every action, there is an equal and opposite reaction. This implies that forces always come in pairs. When you push on a wall (the action), the wall pushes back on you with the same amount of force (the reaction). These forces are equal in magnitude and opposite in direction. However, they don't cancel each other out, and the reason lies in the objects on which these forces act.

To truly understand this, we must delve into what constitutes an action-reaction pair, how these forces are defined, and on what bodies they act.

Defining Action and Reaction

Action Force: The force exerted by one object on another.
Reaction Force: The force exerted by the second object back on the first.

Consider a book resting on a table. The book exerts a downward force on the table due to gravity (its weight). This is the action force. The table, in turn, exerts an upward force on the book, supporting it. This is the reaction force.

Key Characteristics of Action-Reaction Pairs

Equal in Magnitude: The force exerted by object A on object B is equal in magnitude to the force exerted by object B on object A.
Opposite in Direction: The forces act in exactly opposite directions. If the action force is downward, the reaction force is upward.
Act on Different Objects: This is the most critical point. The action force acts on one object, and the reaction force acts on a different object. This is why they don't cancel out.
Simultaneous: Action and reaction forces occur simultaneously. One doesn't happen before the other. They are inherently linked.
Same Nature: Both forces are of the same type. For instance, if the action force is gravitational, so is the reaction force.

Why Don't Action-Reaction Forces Cancel Each Other Out?

The crux of the matter lies in understanding that forces only cancel out when they act on the same object. Cancellation occurs when the net force on a single object is zero, resulting in no acceleration (Newton's First and Second Laws). Action and reaction forces, by definition, act on different objects; therefore, they cannot cancel each other's effects on those objects.

Let's illustrate this with a few examples:

Example 1: The Book and the Table

Action: The book exerts a downward force (weight) on the table.
Reaction: The table exerts an upward force on the book.

The action force acts on the table, while the reaction force acts on the book. We can analyze the forces on each object separately:

On the Book: The forces acting on the book are the upward reaction force from the table and the downward force of gravity (its weight). If the book is at rest, these forces do cancel each other out because they both act on the book. The net force on the book is zero, and it doesn't accelerate.
On the Table: The forces acting on the table are the downward force from the book and the upward force from the floor (supporting the table). If the table is also at rest, these forces cancel each other out because they both act on the table.

Example 2: A Person Pushing a Wall

Action: The person exerts a force on the wall.
Reaction: The wall exerts an equal and opposite force back on the person.

Again, the forces act on different objects:

On the Wall: The forces acting on the wall are the force from the person and the force from its foundation that keeps it in place.
On the Person: The forces acting on the person are the force from the wall and other forces like friction with the ground and possibly gravity.

The reaction force from the wall on the person can cause the person to experience a sensation of being pushed back. It can even cause acceleration if the person isn't firmly planted. The force the person exerts on the wall doesn't directly cancel the force the wall exerts on the person because they act on different entities.

Example 3: Rocket Propulsion

Action: The rocket expels exhaust gases downward.
Reaction: The exhaust gases exert an upward force on the rocket.

Here, the action force acts on the exhaust gases, and the reaction force acts on the rocket. The reaction force is what propels the rocket forward. It's crucial to note that the rocket isn't pushing against anything external (like air). It's the internal action-reaction pair between the rocket and its exhaust that generates thrust.

On the Exhaust Gases: The rocket exerts a downward force, accelerating the gases downward.
On the Rocket: The exhaust gases exert an upward force, accelerating the rocket upward.

Why It Matters: Systems and Free-Body Diagrams

The concept of action-reaction pairs acting on different objects is crucial for understanding systems and drawing free-body diagrams.

System: A system is a collection of objects that we choose to analyze together.
Free-Body Diagram: A free-body diagram is a diagram that shows all the forces acting on a single object (or system).

When analyzing a system, internal forces (forces between objects within the system) do not affect the system's overall motion. Action-reaction pairs are always internal forces within a system containing both interacting objects. Only external forces can cause the system to accelerate.

Let's revisit the book on the table example. If we consider the book and the table as a single system, the action (book on table) and reaction (table on book) forces are internal to the system. They don't contribute to the overall motion of the system. The external forces acting on the system are the force of gravity on the book and table (combined weight) and the upward force from the floor on the table.

However, if we only consider the book as our system, then the reaction force from the table is an external force, and it's essential for determining the book's motion (or lack thereof).

Common Misconceptions

Several misconceptions arise when dealing with action-reaction forces. Addressing these misconceptions is crucial for a clearer understanding.

Misconception: The stronger force "wins". Action and reaction forces are always equal in magnitude. There's no "winning" force. The effect of the forces depends on the mass and other forces acting on each object.
Misconception: The reaction force happens later. Action and reaction forces are simultaneous. They occur at the same instant.
Misconception: If action and reaction are equal and opposite, nothing can ever move. This is perhaps the most common misunderstanding. As explained above, action and reaction forces act on different objects. Movement occurs when there is a net external force on an object or system.
Misconception: Action-reaction applies only to contact forces. Action-reaction applies to all types of forces, including gravitational and electromagnetic forces, even when objects are not in direct contact. For example, the Earth exerts a gravitational force on the Moon, and the Moon exerts an equal and opposite gravitational force on the Earth.

Examples in Everyday Life

Action-reaction pairs are all around us. Recognizing them helps solidify the concept.

Walking: When you walk, you push backward on the Earth (action), and the Earth pushes forward on you (reaction), propelling you forward.
Swimming: A swimmer pushes water backward (action), and the water pushes the swimmer forward (reaction).
A bird flying: A bird pushes air downwards with its wings (action), and the air pushes the bird upwards (reaction), providing lift.
A car accelerating: The tires push backward on the road (action), and the road pushes forward on the tires (reaction), causing the car to accelerate.
Jumping: When you jump, you push down on the Earth (action), and the Earth pushes up on you (reaction), launching you into the air. While the Earth does move slightly in response to your jump, its enormous mass means the acceleration is negligible.

Deeper Dive: Mathematical Representation

We can mathematically represent action-reaction forces using vector notation:

Let FAB be the force exerted by object A on object B (the action force). Let FBA be the force exerted by object B on object A (the reaction force).

According to Newton's Third Law:

FAB = - FBA

This equation states that the force exerted by A on B is equal in magnitude but opposite in direction to the force exerted by B on A. The negative sign indicates the opposite direction.

Applying Newton's Laws

To solve problems involving action-reaction forces, it's crucial to apply Newton's Laws correctly. This involves:

Identifying all the forces acting on each object.
Drawing free-body diagrams for each object.
Applying Newton's Second Law (F = ma) to each object separately.
Using Newton's Third Law to relate the action-reaction forces.

By analyzing each object separately and considering all the forces acting on it, we can accurately predict the motion of the objects involved.

The Importance of Frames of Reference

The frame of reference also plays a role in how we perceive and analyze action-reaction pairs. An inertial frame of reference is one that is not accelerating. Newton's Laws are valid in inertial frames of reference.

If we are in an accelerating frame of reference (a non-inertial frame), we might need to introduce fictitious forces to account for the acceleration of the frame. However, the fundamental principle of action-reaction still holds true. The forces, as observed from any frame (inertial or non-inertial), will still be equal and opposite, acting on different objects.

Advanced Considerations

While the basic principle of action-reaction is straightforward, there are more complex situations where its application requires careful consideration.

Rotating Frames: In rotating frames of reference, the analysis can become more intricate due to the presence of Coriolis and centrifugal forces. However, the underlying principle of action-reaction remains valid.
Relativistic Effects: At very high speeds approaching the speed of light, relativistic effects become significant. While Newton's Laws are approximations that break down at these speeds, the principle of conservation of momentum, which is closely related to action-reaction, still holds true.
Quantum Mechanics: At the quantum level, the concept of force becomes more nuanced. However, even in quantum field theory, the fundamental principles of momentum conservation and interaction symmetry are related to the classical idea of action-reaction.

Conclusion

The idea that action and reaction forces do not cancel each other out is a cornerstone of Newtonian mechanics. Understanding this principle is essential for analyzing the motion of objects and systems. The key takeaway is that forces can only cancel each other out when they act on the same object. Action and reaction forces, by definition, act on different objects and therefore influence the motion of those separate objects. By carefully considering the forces acting on each object and drawing accurate free-body diagrams, we can apply Newton's Laws to solve a wide range of problems in physics and engineering. The seemingly simple statement of Newton's Third Law holds profound implications for understanding the world around us, from the smallest interactions to the grandest scales of the cosmos.