Newton's Third Law and Interaction Forces

Focus Question: The primary conceptual inquiry for this lesson is: "If you push on a wall, what force does the wall exert on you?"
Definition of Newton's Third Law: This law states that all forces in the universe come in pairs. These two forces are always: * Equal in strength (magnitude). * Opposite in direction. * Acting on two different objects.
Mathematical Expression: The relationship between these forces is represented by the formula: $F_{A \text{ on } B} = -F_{B \text{ on } A}$ .
Review of Symmetry: Symmetry is defined as the condition where two or more parts of an object remain the same after undergoing a transformation, such as a reflection, flip, slide, or rotation. In the context of Newton's Third Law, symmetry appears in the subscripts of the force notation (e.g., $A \text{ on } B$ and $B \text{ on } A$ ).

Definition of an Interaction Pair: This term refers to two forces that act in opposite directions, possess equal magnitudes, and act upon different objects.
Directional Dynamics: If you (Object A) exert a force on a friend (Object B) to push them forward ( $F_{A \text{ on } B}$ ), the friend simultaneously exerts an equal and opposite force on you ( $F_{B \text{ on } A}$ ), which causes you to move backward.
Identification Requirements: To correctly identify interaction pairs, remember two critical rules: * They always occur in two different free-body diagrams (FBDs). * They always exhibit symmetry in their subscripts ( $A \text{ on } B$ and $B \text{ on } A$ ).

Scenario (Example Problem 4): A person with a mass of $55\,kg$ slips on ice and enters a state of free fall. The goal is to determine the force the person exerts on the Earth during this time.
Known Variables: * Mass of the person ( $m_{you}$ ): $55\,kg$ * Acceleration due to gravity ( $g$ ): $-9.8\,N/kg$
Unknown Variables: * Force of the person on Earth ( $F_{you \text{ on } Earth}$ ): ?
Analysis and Solution Strategy: * Draw a free-body diagram representing the person and the Earth. * Use the definition of weight to find the force Earth exerts on the person ( $F_{g} = mg$ ). * Apply Newton’s third law: The force you exert on Earth is equal in magnitude and opposite in direction to the force Earth exerts on you ( $F_{Earth \text{ on } you}$ ).

Definition of Tension: Tension is the name given to the force exerted by a string, rope, or cable.
Bidirectional Pull: At any given point along a rope or string, the tension forces are pulling equally in both directions.
Example Problem 5: Fishing Line Acceleration: * Scenario: Reeling in a fish with a mass of $6\,kg$ . The fishing line has a maximum tension threshold of $100\,N$ . * Knowns: * Mass of the fish ( $m_{fish}$ ): $6\,kg$ * Maximum Tension ( $F_{T, max}$ ): $100\,N$ * Acceleration due to gravity ( $g$ ): $-9.8\,N/kg$ * Unknowns: * Maximum acceleration during reeling ( $a_{max}$ ): ? * Solution Logic: Utilize Newton’s Second Law ( $F_{net} = ma$ ) where the net force is the difference between the upward tension and the downward weight ( $F_g = mg$ ). The calculated acceleration magnitude should be evaluated against gravity to ensure it is a reasonable physical value.

Definition: The normal force is defined as the perpendicular contact force exerted by a surface upon another object.
Relationship to Weight: It is important to note that the normal force is not always equal to the object’s weight. Its magnitude changes based on other vertical forces acting on the object or the incline of the surface.
Importance in Physics: Determining the normal force is a critical step when calculating the effects of friction between two surfaces.

Question 1: Which is the term for two forces that are in opposite directions, have equal magnitudes, and act on different objects? * Answer: A - interaction pair
Question 2: Which law states that all forces come in pairs and that the two forces are equal in strength, opposite in direction, and act on different objects? * Answer: D - Newton’s third law
Question 3: Which correctly completes the formula representing Newton’s third law? $F_{A \text{ on } B} = \text{?}$ * Answer: B - $-F_{B \text{ on } A}$
Question 4: Which is the force exerted by a string or rope? * Answer: C - tension
Question 5: Which is the perpendicular contact force exerted by a surface on another object? * Answer: C - normal force