KAHIBARO
Table of Contents
Mutual Nature of Forces
When two objects interact, the force is never one sided. If object A pushes, pulls, attracts, or repels object B, then object B also pushes, pulls, attracts, or repels object A. These two forces are called an interaction pair, or an action reaction pair.
This idea is the heart of Newton's Third Law. The important point in this chapter is to understand the forces as part of an interaction between two different objects. A force is not something an object has by itself. A force always comes from another object.
For example, if your hand pushes on a wall, your hand exerts a force on the wall, and the wall exerts a force on your hand. If Earth pulls a book downward by gravity, the book also pulls Earth upward by gravity.
For every interaction between two objects, there are two forces:
$$\vec{F}_{A\to B} = -\vec{F}_{B\to A}$$
They are equal in magnitude and opposite in direction.
How to Identify the Two Forces
To identify an interaction pair clearly, name both objects and state who exerts the force on whom. This avoids confusion.
If object A acts on object B, write the force as $\vec{F}_{A\to B}$. The partner force is then $\vec{F}_{B\to A}$.
These forces always share three features.
First, they act on two different objects. Second, they are the same type of force, such as both gravitational or both contact forces. Third, they are equal in size and opposite in direction.
A common mistake is to think that two opposite forces on the same object are a third law pair. They are not. Third law pairs always act on different bodies.
Examples of Interaction Forces
Consider a book resting on a table. The table pushes upward on the book. The matching interaction force is the book pushing downward on the table. These two forces belong to the same interaction.
At the same time, Earth pulls the book downward by gravity. The matching force is the book pulling Earth upward. That is a different interaction pair.
This means the upward normal force on the book and the downward weight of the book are not an action reaction pair, because both act on the same object, the book.
Action reaction forces do not cancel each other, because they act on different objects.
Contact and Non Contact Interactions
Interaction forces can come from direct contact or from distance.
In contact interactions, the objects touch. Examples include pushing, friction, tension, and normal force interactions. If a rope pulls on a block, the block also pulls on the rope.
In non contact interactions, the objects do not need to touch. Gravity and electric force are examples. Earth attracts the Moon, and the Moon attracts Earth with an equal and opposite gravitational force.
Interaction Forces and Motion
Equal and opposite interaction forces do not mean the two objects must move in the same way. Their motions depend on their masses and on all the other forces acting on them.
If a small cart pushes on a large truck, the cart and truck exert equal and opposite forces on each other. But the cart may accelerate much more because its mass is much smaller.
Using Newton's Second Law for each object separately,
$$\vec{F}_{\text{net}} = m\vec{a}$$
the same interaction force can produce different accelerations.
A Simple Comparison
| Interaction | Force on first object | Force on second object |
|---|---|---|
| Hand and wall | Wall pushes hand | Hand pushes wall |
| Book and table | Table pushes book | Book pushes table |
| Earth and book | Earth pulls book | Book pulls Earth |
| Foot and ground | Ground pushes foot | Foot pushes ground |
Walking as an Interaction
Walking is a good everyday example of interaction forces. When you walk, your foot pushes backward on the ground. The ground then pushes forward on your foot. That forward force helps accelerate you forward.
The two horizontal forces are equal and opposite, but one acts on the ground and the other acts on the foot.
Force Pairs in Free Body Thinking
When studying motion, it is important to separate the objects. Draw the forces acting on only one object at a time. Then do not include the reaction force unless it acts on that same object.
For example, for a book on a table, the free body diagram of the book includes the table's upward force on the book and Earth's downward force on the book. It does not include the force of the book on the table, because that acts on the table, not on the book.
When analyzing motion, apply Newton's laws to one object at a time. Only include forces acting on that object.
A Visual Example with a Book on a Table
This picture shows two different interactions. One is between table and book. The other is between Earth and book.
Common Misunderstandings
Many beginners think that if forces are equal and opposite, they must cancel. This is only true when the forces act on the same object. Third law pairs do not cancel in the motion equation for a single object because they act on different objects.
Another common mistake is calling weight and normal force an action reaction pair. They can be equal in magnitude when the book is at rest, but they are not a third law pair because both act on the book.
Final Rule
Interaction forces are best understood as a mutual relationship between two objects. One object cannot exert a force without experiencing a partner force from the other object.
An interaction force pair always consists of two forces of the same kind, acting on two different objects, with equal magnitude and opposite direction:
$$\vec{F}_{A\to B} = -\vec{F}_{B\to A}$$
Understanding this rule makes it much easier to analyze contact, gravity, and motion correctly.