Newton's third law
Newton's Third Law
Newton's Third Law of Motion is one of the fundamental principles of classical mechanics, as described by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica. This law is often stated as:
> "For every action, there is an equal and opposite reaction."
This means that for every force exerted by one object on another, there is a force of equal magnitude but in the opposite direction exerted back on the first object by the second object.
Mathematical Formulation
The mathematical representation of Newton's Third Law is quite straightforward. If object A exerts a force $\vec{F}{A \rightarrow B}$ on object B, then object B simultaneously exerts a force $\vec{F}{B \rightarrow A}$ on object A, and these two forces are equal in magnitude and opposite in direction:
$$ \vec{F}{A \rightarrow B} = -\vec{F}{B \rightarrow A} $$
Understanding Newton's Third Law
To understand Newton's Third Law, it's important to consider the following points:
- Action and Reaction Pairs: The forces described by the third law are part of an action-reaction pair. They act on different objects and are never found acting on the same object.
- Simultaneity: The action and reaction forces occur simultaneously. When one force is applied, the other force arises at the same moment.
- Different Objects: The action and reaction forces act on different objects, which is why they do not cancel each other out.
- Same Type of Force: The forces in an action-reaction pair are of the same type (e.g., gravitational, electrical, mechanical, etc.).
Table of Differences and Important Points
| Aspect | Action Force | Reaction Force |
|---|---|---|
| Definition | The force exerted by the first object on the second object. | The force exerted by the second object on the first object. |
| Symbol | $\vec{F}_{A \rightarrow B}$ | $\vec{F}_{B \rightarrow A}$ |
| Direction | Depends on the action | Opposite to the action force |
| Magnitude | Equal to the reaction force | Equal to the action force |
| Acts on | Second object | First object |
| Result | Causes acceleration of the second object | Causes acceleration of the first object |
| Cancellation | Does not cancel with reaction force because they act on different objects | Does not cancel with action force for the same reason |
Examples
Example 1: Pushing Against a Wall
When you push against a wall with a force, the wall pushes back with an equal and opposite force. You do not move because the wall is rigid and exerts an equal force back on you.
- Action Force: Your push on the wall.
- Reaction Force: The wall's push on you.
Example 2: Walking
When you walk, your foot pushes backward against the ground. According to Newton's Third Law, the ground pushes forward on your foot with an equal and opposite force, which propels you forward.
- Action Force: Your foot pushing backward on the ground.
- Reaction Force: The ground pushing forward on your foot.
Example 3: Rocket Propulsion
A rocket propels itself forward by expelling gas out of its engines. The action is the gas being pushed backward; the reaction is the rocket being pushed forward.
- Action Force: The force on the gas pushing it backward.
- Reaction Force: The force on the rocket pushing it forward.
Conclusion
Newton's Third Law is a cornerstone of classical mechanics and is observable in everyday life. It is essential for understanding how forces interact and the concept of conservation of momentum. When studying or solving problems involving forces, always look for the action-reaction pairs to ensure a complete analysis of the situation.