Newton's Third Law and Applications in Physics

Newton's Third Law of Motion

Action and Reaction Forces

Newton's Third Law states that for every action, there is an equal and opposite reaction. This fundamental principle explains how forces always occur in pairs and is essential for understanding interactions between objects.

• Definition: If object A exerts a force on object B, then object B exerts a force of equal magnitude and opposite direction on object A.

• Mathematical Expression: $\vec{F}_{AB} = -\vec{F}_{BA}$

• Examples:

  • A swimmer pushes water backward; water pushes the swimmer forward.

  • A rocket expels gas downwards; the rocket moves upwards.

Free-Body Diagrams

Visualizing Forces

Free-body diagrams are graphical representations used to visualize the forces acting on an object. They are crucial for solving problems involving Newton's laws.

• Key Elements:

  • Represent the object as a dot or box.

  • Draw arrows for all forces acting on the object (e.g., gravity, normal force, friction, applied force).

  • Label each force clearly.

• Example: A book resting on a table experiences gravity downward and a normal force upward.

Applications of Newton's Third Law

Common Scenarios

Newton's Third Law applies to a wide range of physical situations, from everyday life to advanced engineering.

• Walking: When you walk, your foot pushes backward on the ground, and the ground pushes your foot forward.

• Jumping: Pushing down on the ground causes the ground to push you upward.

• Recoil of a Gun: When a bullet is fired forward, the gun recoils backward with equal momentum in the opposite direction.

Conservation of Momentum

Relation to Newton's Third Law

The law of conservation of momentum is closely related to Newton's Third Law. In a closed system, the total momentum before and after an interaction remains constant.

• Formula: $m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$

• Application: Collisions between objects, such as billiard balls or cars.

Sample Problem: Action-Reaction Pair

Example Calculation

Suppose a person with mass 60 kg jumps off a boat with mass 120 kg. If the person jumps with a velocity of 3 m/s relative to the water, what is the velocity of the boat after the jump?

• Solution:

  • By conservation of momentum: $m_{person} v_{person} + m_{boat} v_{boat} = 0$

  • $(60)(3) + (120)(v_{boat}) = 0$

  • $v_{boat} = -1.5$ m/s (opposite direction to the person)

Summary Table: Action-Reaction Examples

Action	Reaction
Hand pushes wall	Wall pushes hand
Earth pulls apple (gravity)	Apple pulls Earth (gravity)
Rocket expels gas	Gas pushes rocket
Swimmer pushes water	Water pushes swimmer

Additional info: Some diagrams and equations were inferred based on standard physics curriculum and the visible structure of the notes.