Newton's Third Law Lecture Notes
Fundamental Definition of Newton’s Third Law of Motion
Newton’s Third Law Statement: For every action, there is an equal and opposite reaction.
Interactions: This law describes the forces that exist between two objects when they interact with one another.
Force Pairs: Forces never exist in isolation; they always come in pairs known as action-reaction pairs.
Characteristics of the Pairs:
The two forces are always equal in magnitude.
The two forces are always opposite in direction.
Demonstrating Action-Reaction Pairs with Force Probes
The Set-up: To empirically prove the law, two force probes were connected together using a rubber band. One probe was held stationary on a ring stand while the other was pushed or pulled.
Data Collection: A software called Logger Pro was used to record the forces in real time as the probes interacted.
Observation of Motion States:
Stationary System: When one or both probes were still, the forces were equal and opposite.
Constant Velocity: When moving at a steady speed, the forces remained equal and opposite.
Acceleration: Even when the system was accelerating in a specific direction, the force readout showed perfectly mirrored, equal, and opposite values.
Universal Constant: The equality of these forces holds true regardless of the objects' mass, volume, speed, or acceleration.
Identifying Action-Reaction Pairs: The Criss-Cross Method
A reliable way to identify an action-reaction pair is to identify the two nouns involved in the interaction and swap their roles.
Example 1: Sports
Action: A baseball bat hits a ball.
Reaction: The ball hits the baseball bat.
Example 2: Walking
Action: Feet push down on the ground.
Reaction: The ground pushes up on the feet.
Example 3: Aviation
Action: An airplane propeller pushes backward on air molecules.
Reaction: Air molecules push forward on the propeller.
Example 4: High Fives
If you high five someone, both hands exert equal forces on each other in opposite directions simultaneously.
Common Misconceptions: Gravity vs. Support Force
Gravity Analysis: Gravity is the force of the Earth pulling an object (such as a person) downward.
Identifying the Reaction Force to Gravity: Following the noun-swap rule, if the Earth pulls down on a person, the reaction force is that the person pulls up on the Earth.
The Support (Normal) Force: When standing on a floor, the floor pushes up on the person. This is often mistaken for the reaction to gravity.
Why they are NOT a pair:
An action-reaction pair must involve the same two nouns (Person and Earth).
The support force involves the Person and the Floor.
The reaction force to the support force is the person pushing down on the floor.
Cardinal Rule: Two forces that act on the same object (e.g., gravity pulling you down and the floor pushing you up) cannot be an action-reaction pair.
Practical Application: The Physics of Tug of War
Scenario: A team of large, muscular individuals competes against a team of small individuals.
The Force on the Rope: Contrary to intuition, both teams exert exactly the same force on the rope. Because they are in contact with the same rope, Newton’s Third Law dictates the forces must be equal and opposite.
How a Team Wins: Winning is not determined by how hard a team pulls the rope, but by the force exerted against the ground.
If the large team wears slippers on a slick floor, they cannot exert much force on the ground and will lose.
If the small team wears boots on asphalt (providing high traction), they can exert a large force on the ground and will win.
Winning Strategy: Traction and contact with the floor are more critical than pulling strength because your feet must exert a larger force on the ground than your opponents' feet do.
Propulsion and Motion
Rockets: A rocket functions because of a chemical reaction that pushes exhaust gases out of the bottom of the engine. The reaction force is the thrust that propels the rocket upward through space.
Jet Engines: These produce thrust by moving gases backward through a turbine engine, resulting in a forward reaction force.
Defining Systems and External Forces
System Definition: A system is any collection of objects defined at will. It can consist of a single object or multiple interacting parts.
The Horse and Cart Example:
Case 1 (System = Cart): The horse is external to the system. The horse pulls the cart, providing an external force that changes the cart's motion.
Case 2 (System = Horse + Cart): Interaction between the horse and cart is internal. To move the whole system, there must be an external force from outside the system.
External Interaction: The ground provides the friction force (external force) that allows the horse-and-cart system to move forward.
Arbitrary Nature: While systems are arbitrary, they are necessary for analyzing how forces outside a defined group affect its movement.
Newton's Second and Third Laws: Why We Move
The Paradox: If every force has an equal and opposite reaction, why isn't everything in equilibrium? Why do things move?
The Solution: While forces are equal and opposite, the resulting acceleration depends on the mass of the object holding those forces ().
Inertia's Role: When you walk, you experience the same force as the building/floor. However, the building is attached to a massive structure with immense inertia, resulting in zero noticeable acceleration. You, having much less mass, experience significant acceleration.
Mathematical Case Study: Ping-Pong Ball vs. Earth
The Ball's Data:
Mass of the ball ():
Acceleration due to gravity ():
Net force on the ball ():
The Earth's Data:
Mass of the Earth ():
Reaction Force: The ball pulls up on the Earth with identical force ().
Calculating Earth's Acceleration:
Conclusion: This acceleration is essentially zero. Even if a much larger object (billions of kilograms) were dropped, the Earth's planetary scale mass ensures its acceleration remains unnoticeable. Equal forces do not result in equal motion.