2.3 Third law of motion
7 min read•august 21, 2024
of Motion is a cornerstone of classical mechanics. It states that for every action force, there's an equal and opposite reaction force. This principle explains countless phenomena, from to everyday interactions.
The law's applications are vast, spanning engineering, sports, and space exploration. It forms the basis for understanding force interactions in complex systems and is crucial for analyzing equilibrium, collisions, and motion in various fields of physics and engineering.
Newton's third law
- Fundamental principle in classical mechanics describing the nature of forces between interacting objects
- States that for every action force, there is an equal and opposite reaction force
- Forms the basis for understanding many physical phenomena and has wide-ranging applications in engineering and everyday life
Action-reaction pairs
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- Consist of two forces acting on different objects that are equal in magnitude and opposite in direction
- Always occur simultaneously and cannot exist in isolation
- Examples include a book pressing down on a table while the table pushes up on the book
- Action and reaction forces act on different objects, not on the same object
Equal and opposite forces
- Magnitude of the action force exactly matches the magnitude of the reaction force
- Directions of the two forces are exactly opposite to each other
- Forces act along the same line of action
- Do not cancel each other out as they act on different bodies
Examples in everyday life
- Person pushing against a wall experiences an equal push back from the wall
- Recoil of a gun when fired due to the forward force on the bullet
- Propulsion of a swimmer through water by pushing water backwards
- Birds flying by pushing air downwards with their wings
Applications of third law
- Crucial for understanding and predicting motion in various fields of physics and engineering
- Enables the design of efficient propulsion systems and the analysis of complex force interactions
- Plays a key role in biomechanics and sports science for optimizing human performance
Rocket propulsion
- Rockets expel high-speed gases backward, creating a forward thrust
- Thrust force is the reaction to the force exerted on the expelled gases
- Efficiency of rocket propulsion depends on the mass and velocity of expelled gases
- Enables space exploration and satellite deployment
Walking and running
- Legs push backward against the ground, creating a forward reaction force
- Friction between feet and ground necessary for effective locomotion
- Different gaits and running techniques utilize the third law for optimal efficiency
- Explains why it's harder to walk on slippery surfaces (reduced friction)
Collisions and impacts
- Forces during collisions always occur in pairs
- Momentum exchange between colliding objects governed by the third law
- Explains phenomena like the motion of billiard balls after collision
- Crucial in designing safety features in vehicles (crumple zones, airbags)
Forces in equilibrium
- State where the acting on an object is zero
- Results in no acceleration of the object
- Applies to both stationary objects and objects moving with constant velocity
- Understanding equilibrium is crucial for structural engineering and stability analysis
Static equilibrium
- Object at rest with all forces and torques balanced
- Sum of all forces in each direction equals zero
- Sum of all torques about any point equals zero
- Examples include a book resting on a table or a hanging chandelier
Dynamic equilibrium
- Object moving at constant velocity with balanced forces
- Net force on the object is zero, but the object is in motion
- Applies to scenarios like terminal velocity in free fall
- Crucial concept in understanding steady-state processes in physics and chemistry
Limitations and misconceptions
- While the third law is universally applicable, its interpretation can be challenging in complex systems
- Understanding these limitations helps in correctly applying the law and avoiding errors in analysis
- Important for developing a deeper understanding of force interactions in various physical scenarios
Common misunderstandings
- Mistaking the pair of forces as acting on the same object
- Assuming action and reaction forces cancel each other out
- Overlooking the role of the third law in situations involving apparent "one-way" forces
- Difficulty in identifying in complex systems
Apparent violations
- Magnetic levitation seeming to defy the third law
- Gravitational forces appearing to act without an equal reaction
- Electromagnetic forces in certain configurations
- Resolved by considering the entire system and field interactions
Mathematical representation
- Allows for precise quantification and analysis of force interactions
- Essential for solving complex problems in mechanics and engineering
- Provides a framework for computational modeling of physical systems
Vector notation
- Forces represented as vectors with magnitude and direction
- Action-reaction pair:
- Subscripts indicate the object exerting the force and the object experiencing the force
- Vector sum of all forces in a closed system equals zero:
Force diagrams
- Visual representations of all forces acting on an object
- Include magnitude, direction, and point of application for each force
- Useful for identifying action-reaction pairs and analyzing equilibrium
- Essential tool for solving problems involving multiple forces
Experimental verification
- Empirical evidence supporting the third law through various experiments
- Demonstrates the universality of the law across different scales and physical systems
- Provides historical context for the development of classical mechanics
Historical experiments
- Newton's original experiments with colliding pendulums
- Experiments by later scientists like Galileo and Huygens on impact forces
- Development of more precise measurement techniques in the 18th and 19th centuries
- Cavendish experiment indirectly verifying the third law for gravitational forces
Modern demonstrations
- High-speed camera recordings of collisions and explosions
- Force plate measurements in biomechanics and sports science
- Microgravity experiments on the International Space Station
- Atomic force microscopy for measuring nanoscale forces
Interactions between objects
- Third law applies to all types of force interactions between objects
- Understanding different types of forces crucial for applying the law correctly
- Helps in analyzing complex systems with multiple interacting bodies
Contact forces vs field forces
- Contact forces require physical touch (normal force, friction)
- Field forces act at a distance (gravity, electromagnetism)
- Both types of forces obey the third law
- Field forces explained through the concept of force-mediating particles or fields
Internal vs external forces
- Internal forces occur between parts of the same system
- External forces act between the system and its environment
- Third law applies to both, but internal forces often cancel out in whole-system analysis
- Important distinction in analyzing complex systems like machines or living organisms
Conservation principles
- Third law closely related to fundamental conservation laws in physics
- These principles provide a broader context for understanding force interactions
- Essential for analyzing systems where direct force measurements are difficult
Momentum conservation
- Direct consequence of Newton's third law
- Total momentum of a closed system remains constant
- Explains phenomena like recoil and collision outcomes
- Crucial in fields like particle physics and astrophysics
Energy conservation
- While not directly derived from the third law, often applies in force interactions
- Total energy of a closed system remains constant
- Helps in analyzing energy transfers during collisions and other force interactions
- Important in understanding efficiency of mechanical systems
Third law in complex systems
- Application of the law becomes more intricate in systems with multiple interacting objects
- Requires careful analysis to identify all relevant forces and their pairs
- Important in fields like robotics, structural engineering, and fluid dynamics
Multiple object interactions
- Forces can form complex networks in systems with many objects
- Each interaction still obeys the third law individually
- Analysis often requires breaking down the system into simpler components
- Examples include planetary systems, molecular interactions, and crowd dynamics
Distributed forces
- Forces spread over an area or volume rather than acting at a point
- Common in fluid mechanics (pressure) and elasticity (stress)
- Third law still applies but requires integration over the force distribution
- Important in analyzing phenomena like buoyancy and structural loads
Practical implications
- Third law has numerous applications in various fields of science and technology
- Understanding these applications helps in appreciating the law's relevance and importance
- Demonstrates how fundamental physics principles translate into real-world solutions
Engineering applications
- Design of propulsion systems (jets, rockets, propellers)
- Analysis of structural loads in buildings and bridges
- Development of impact-resistant materials and structures
- Optimization of mechanical systems for efficiency and stability
Sports and biomechanics
- Improving athletic performance through understanding of force interactions
- Design of sports equipment (running shoes, tennis rackets, golf clubs)
- Analysis of injury mechanisms and development of protective gear
- Optimization of prosthetics and assistive devices
Third law in different frames
- Law holds true in all inertial reference frames
- Understanding how it applies in different frames is crucial for a complete grasp of mechanics
- Important for analyzing systems involving relative motion or high velocities
Inertial vs non-inertial frames
- Third law applies directly in inertial frames
- In non-inertial frames, apparent forces must be considered
- Examples include centrifugal and Coriolis forces in rotating frames
- Important for analyzing systems like rotating machinery or geophysical phenomena
Relativistic considerations
- Third law holds in special relativity but with modified definitions
- Force concept becomes more complex at relativistic speeds
- Simultaneity of action-reaction pairs affected by relativity
- Important for understanding high-energy particle interactions and astrophysical phenomena
Key Terms to Review (20)
Action-reaction pairs: Action-reaction pairs refer to the principle that for every action, there is an equal and opposite reaction. This concept is fundamental to understanding how forces interact in nature, highlighting that forces always occur in pairs and that one force cannot exist without the other. This idea is closely tied to the way free-body diagrams are used to represent forces acting on objects and illustrates the balance of forces at play.
Collisions and impacts: Collisions and impacts refer to events where two or more objects exert forces on each other during a contact interaction, resulting in changes in their motion and energy. These events are characterized by the transfer of momentum and energy between the colliding objects, often leading to deformation, heat generation, or even breakage. Understanding these interactions is crucial for analyzing how forces operate in various systems, particularly in relation to the third law of motion, which states that for every action, there is an equal and opposite reaction.
Contact Forces vs Field Forces: Contact forces are interactions that occur when objects are physically touching each other, while field forces act at a distance without direct contact between objects. Understanding these two categories of forces is crucial in analyzing how objects interact and move, especially in the context of the third law of motion, which states that for every action, there is an equal and opposite reaction.
Dynamic Equilibrium: Dynamic equilibrium occurs when an object remains in constant motion, with all the forces acting on it balanced, resulting in no acceleration. This concept highlights that even though the object may be moving, the forces are counteracting each other, making the net force zero. Understanding dynamic equilibrium is essential as it connects motion with forces in various scenarios, showcasing how objects can be in a state of balance while in motion.
Energy Conservation: Energy conservation is the principle that energy cannot be created or destroyed, only transformed from one form to another. This concept underscores that the total energy in a closed system remains constant, which plays a crucial role in understanding various physical phenomena, including motion, potential energy, and wave interactions. By recognizing how energy shifts between kinetic and potential forms or within different systems, one can better grasp the mechanics of oscillating systems, forces acting on objects, elastic materials, and the behavior of waves.
Equal and opposite forces: Equal and opposite forces are the concept that for every action, there is an equal and opposite reaction. This principle explains how forces act in pairs, meaning that if one object exerts a force on a second object, the second object exerts a force of equal magnitude but in the opposite direction back on the first object. This relationship helps us understand motion, interactions between objects, and is foundational to the laws of physics.
Experimental verification: Experimental verification is the process of testing a hypothesis or theory through controlled experiments to determine its validity. This concept is crucial in the scientific method, as it helps establish a reliable connection between theoretical predictions and observable outcomes, ensuring that scientific claims are supported by empirical evidence.
F = -f: The equation f = -f illustrates the concept of action and reaction forces in mechanics, specifically related to Newton's third law of motion. This principle states that for every action, there is an equal and opposite reaction. In simple terms, when one object exerts a force on another, the second object exerts a force of equal magnitude but opposite direction back on the first object.
Force Diagrams: Force diagrams are visual representations that illustrate all the forces acting on an object. These diagrams help to simplify complex problems by breaking down the forces into clear vectors, allowing for a better understanding of how they interact according to Newton's laws, especially the third law of motion, which states that for every action, there is an equal and opposite reaction.
Forces in equilibrium: Forces in equilibrium occur when all the forces acting on an object are balanced, resulting in a state where there is no net force or acceleration. This means that the object will either remain at rest or continue to move at a constant velocity, highlighting the crucial relationship between forces and motion as described by Newton's laws.
Galileo Galilei: Galileo Galilei was an Italian astronomer, physicist, and mathematician who played a pivotal role in the Scientific Revolution during the Renaissance. He is best known for his contributions to motion, particularly through his studies of pendulums, his formulation of the laws of motion, and his advancements in understanding inertia, making significant connections to the principles of linear momentum and the laws of motion.
Internal vs External Forces: Internal forces are those forces that act within a system, affecting the motion of components relative to each other, while external forces are those that act on a system from outside, influencing the motion of the entire system. Understanding the difference is crucial as it helps in analyzing how systems respond to different influences, particularly in the context of interactions as outlined by the third law of motion.
Momentum conservation: Momentum conservation refers to the principle that the total momentum of a closed system remains constant over time, provided that no external forces are acting on it. This means that if two or more objects collide or interact, their combined momentum before the interaction equals their combined momentum after the interaction. This principle is crucial for understanding collisions and interactions in mechanics, where forces and motions are involved.
Net force: Net force is the overall force acting on an object after all the individual forces are combined. It determines the object's motion, whether it accelerates, decelerates, or remains at rest, depending on its magnitude and direction. Understanding net force is crucial as it relates to how objects interact in various physical scenarios, influencing momentum, frictional forces, and the response to applied forces.
Newton's Third Law: Newton's Third Law states that for every action, there is an equal and opposite reaction. This principle highlights the interactions between objects, indicating that forces always occur in pairs. When one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction back on the first object. This law is foundational in understanding motion, momentum, and the relationships between forces acting on bodies.
Rocket propulsion: Rocket propulsion is the method by which a rocket generates thrust to propel itself through space by expelling mass at high velocity. This process relies on the principles of momentum conservation, where the rocket moves in one direction as exhaust gases are expelled in the opposite direction, enabling it to overcome gravity and atmospheric resistance.
Sir Isaac Newton: Sir Isaac Newton was a renowned English mathematician, physicist, and astronomer who is best known for formulating the laws of motion and universal gravitation. His groundbreaking work laid the foundation for classical mechanics and significantly advanced our understanding of how forces interact, particularly through his articulation of the third law of motion and contributions to the understanding of elastic forces as described by Hooke's law.
Static equilibrium: Static equilibrium is a state where an object is at rest and the sum of all forces and torques acting on it is zero. In this condition, an object remains stationary, with no net force causing it to move. Understanding static equilibrium is crucial when analyzing various scenarios, such as forces on inclined surfaces, the role of normal forces, the impact of tension in strings or cables, and how to represent forces accurately using free-body diagrams.
Vector Notation: Vector notation is a mathematical representation used to denote vectors, which are quantities that have both magnitude and direction. It is essential in mechanics for visualizing and calculating forces, velocities, and accelerations, helping to analyze the interactions between objects. Vectors can be represented graphically with arrows or algebraically using coordinates, making it easier to work with multiple forces and understand their resultant effects.
Walking: Walking is a method of locomotion characterized by the movement of the body in a bipedal manner, involving the alternate lifting and placing of feet on the ground. This rhythmic movement relies on the principles of mechanics, particularly the interaction of forces, and illustrates fundamental concepts like balance, gravity, and friction in motion.