Newton's third law of motion
Intros
Lessons
Examples
Lessons
 Understanding Newton's third law and free body diagrams
A rock sits on a table. Draw complete free body diagrams for the rock and the table and highlight the actionreaction pair that includes the rock pushing down on the table.
 Calculations with Newton's second and third laws
 An 85.0 kg fireman slides down a pole with an acceleration of 2.85 $m/s^{2}$. Find the actionreaction force pair that involves the pole and calculate these forces.
 Two ice skaters stand on a frictionless ice rink and face each other, each holding the end of a rope. 50.0 kg skater A pulls on the rope, pulling 40.0 kg skater B with a force of 25.0 N.
i. Draw a free body diagram and find the acceleration of skater B.
ii. When skater A pulls on skater B, does skater A accelerate? If so, draw a free body diagram and calculate the acceleration.
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Topic Notes
Introduction to Newton's Third Law of Motion
Welcome to our exploration of Newton's third law of motion, a fundamental principle in physics that governs the way objects interact. This law, often called the actionreaction law, states that for every action, there's an equal and opposite reaction. As your friendly math tutor, I'm excited to guide you through this concept! The introduction video we're about to watch is a fantastic resource that brings this law to life. It will help you visualize how forces always come in pairs, acting on different objects. Understanding Newton's third law is crucial for grasping many everyday phenomena, from rocket propulsion to simple acts like walking. As we delve deeper, you'll see how this principle applies to countless situations in the world around us. So, let's dive in and unravel the mysteries of action and reaction together!
Understanding Newton's Third Law
Newton's Third Law of Motion is a fundamental principle in physics that describes the nature of forces between interacting objects. The law is often summarized by the famous statement: "For every action, there is an equal and opposite reaction." This concise phrase encapsulates a profound truth about the way forces operate in our universe.
To understand this law, let's break it down using a simple example: pushing a box. When you push a box, you might think you're only exerting a force on the box. However, Newton's Third Law tells us that the box is simultaneously pushing back on you with an equal force in the opposite direction. This may seem counterintuitive at first, but it's a crucial concept in understanding how forces work.
Mathematically, we can express this law as:
F_{A on B} = F_{B on A}
This equation states that the force exerted by object A on object B (F_{A on B}) is equal in magnitude but opposite in direction to the force exerted by object B on object A (F_{B on A}). The negative sign indicates the opposite direction.
The key aspects of Newton's Third Law are the concepts of "equal and opposite reaction" and "force pairs." When two objects interact, they always exert forces on each other that form a force pair. These force pairs have two critical characteristics:
 Equal Magnitude: The forces in a pair are always equal in strength or magnitude. If you push on a wall with 50 Newtons of force, the wall pushes back on you with 50 Newtons.
 Opposite Direction: The forces act in directly opposite directions. As you push forward on the wall, it pushes backward on you.
It's important to note that these force pairs act on different objects. In our box example, your push acts on the box, while the box's push acts on you. This is why the box moves (if your force overcomes friction) while you remain stationary other forces like friction and your body's reaction are at play.
The implications of Newton's Third Law are farreaching. It explains phenomena ranging from the recoil of a gun to the propulsion of rockets in space. When a rocket expels gas downwards, the gas pushes back on the rocket with an equal force upwards, propelling it into space.
Understanding force pairs is crucial in many fields, including engineering, sports science, and even everyday activities. For instance, when you jump, you're actually pushing down on the ground, and the ground pushes back up on you with an equal force, launching you into the air.
In conclusion, Newton's Third Law, with its principle of "equal and opposite reaction," provides a fundamental understanding of how forces interact in our world. By recognizing that forces always come in pairs of equal magnitude and opposite direction, we can better comprehend and predict the behavior of objects in various situations. This law remains a cornerstone of classical mechanics and continues to be essential in our understanding of physics and the world around us.
Practical Examples of Newton's Third Law
Newton's third law of motion states that for every action, there is an equal and opposite reaction. This principle might sound complex, but it's actually at work all around us in our everyday lives! Let's explore some practical examples that demonstrate this fascinating law in action.
One of the simplest examples you can try right now is pushing on a desk. Go ahead, give it a try! Place your hands on the edge of a desk and push. You'll notice that as you exert a force on the desk (the action force), you feel the desk pushing back against your hands (the reaction force). This is Newton's third law in action! The harder you push, the more forcefully the desk pushes back.
Now, let's consider a more dynamic example: kicking a soccer ball. When you kick the ball, your foot exerts an action force on it, propelling it forward. Simultaneously, the ball exerts an equal and opposite reaction force back on your foot. This is why you might feel a slight "push" against your foot when you make contact with the ball. The faster and harder you kick, the more noticeable this reaction force becomes.
Here's another everyday scenario: walking. With each step you take, you're actually pushing against the ground (action force). In response, the ground pushes back against your foot (reaction force), propelling you forward. This constant interplay of forces is what allows us to move around!
Let's look at a fun example: jumping on a trampoline. As you push down on the trampoline's surface (action force), it stretches and then springs back, pushing you upward (reaction force). The more force you apply when jumping, the higher you'll bounce due to the increased reaction force from the trampoline.
Even something as simple as sitting in a chair demonstrates Newton's third law. Your body exerts a downward force on the chair (action), and the chair pushes back with an equal upward force (reaction) to support your weight. This is why you don't sink through the chair!
Next time you're swimming, pay attention to how you move through the water. As you push water backward with your arms and legs (action force), the water pushes you forward (reaction force). This principle is what allows you to propel yourself through the pool.
Lastly, consider the act of throwing a ball. As you throw the ball forward (exerting an action force), you might notice your hand moving slightly backward. This is due to the ball exerting an equal and opposite reaction force on your hand.
These practical applications of Newton's third law are everywhere in our daily lives. Next time you're going about your day, try to spot more examples of action and reaction forces at work. Understanding this principle can give you a new appreciation for the physics that governs our world and how we interact with it. So go ahead, push that desk, kick that ball, or jump on that trampoline and feel Newton's third law in action!
Key Points to Remember About Newton's Third Law
Newton's third law of motion is a fundamental principle in physics that often challenges students' understanding. Two crucial points about this law are frequently misunderstood: the concept of force pairs and the fact that these paired forces act on different objects. Let's delve into these key aspects and address common misconceptions to enhance our grasp of this essential physics principle.
Firstly, Newton's third law states that forces always come in pairs. This means that for every action force, there is an equal and opposite reaction force. A common mistake is thinking that one force causes the other. In reality, these forces occur simultaneously. For instance, when you push against a wall, the wall pushes back on you with equal force. These forces are not cause and effect but rather two aspects of a single interaction.
The second crucial point is that each force in the pair acts on a different object. This is where many students stumble. It's easy to fall into the trap of thinking both forces act on the same object, but this is incorrect. In our wallpushing example, your force acts on the wall, while the wall's force acts on you. Understanding this distinction is vital for correctly analyzing force diagrams and solving physics problems.
A frequent misunderstanding arises when considering objects of different sizes or masses. Some mistakenly believe that a larger object exerts a greater force than a smaller one. However, Newton's third law holds true regardless of size or mass differences. When a small car collides with a large truck, the force exerted by the car on the truck is equal in magnitude to the force exerted by the truck on the car, even though the outcomes for each vehicle may differ due to their mass differences.
Another common error is confusing Newton's third law with the concept of equilibrium. While force pairs are always equal and opposite, this doesn't mean objects are always in equilibrium. The forces in a Newton's third law pair act on different objects, whereas equilibrium involves all forces acting on a single object. For example, a book resting on a table experiences an upward normal force from the table equal to its weight, keeping it in equilibrium. This is not an example of Newton's third law but rather a balance of forces on one object.
To avoid these misconceptions, always remember: force pairs in Newton's third law are simultaneous, equal in magnitude, opposite in direction, and act on different objects. By keeping these key points in mind, you'll be better equipped to apply this fundamental physics principle correctly in various scenarios, from everyday situations to complex problemsolving in physics courses.
Alternative Formulations of Newton's Third Law
Newton's third law of motion is a fundamental physics concept that describes force interactions between objects. While the traditional statement, "For every action, there is an equal and opposite reaction," is widely known, alternative formulations can provide deeper insights and practical applications. These alternative ways of expressing the law emphasize the idea of forces acting on different objects, making it easier to understand and apply correctly in various scenarios.
One alternative formulation states: "When two objects interact, they exert equal and opposite forces on each other." This version highlights the mutual nature of force interactions, emphasizing that forces always occur in pairs between distinct objects. Another way to express the law is: "Forces always come in pairs  equal in magnitude and opposite in direction." This formulation stresses the symmetry of force interactions and their bidirectional nature.
A more detailed alternative states: "If object A exerts a force on object B, then object B simultaneously exerts a force of equal magnitude but opposite direction on object A." This version explicitly identifies the objects involved and the simultaneous nature of the force interaction. These alternative formulations can be more helpful in understanding and applying the law correctly because they:
 Clarify that forces act on different objects, not a single object
 Emphasize the simultaneous nature of force pairs
 Highlight the importance of identifying both objects in an interaction
 Reduce confusion about "action" and "reaction" terminology
By focusing on these aspects, students and practitioners can avoid common misconceptions, such as thinking that one force causes the other or that the forces act on the same object. These alternative formulations also encourage a more systematic approach to analyzing force interactions in complex systems, leading to better problemsolving skills in physics and engineering applications.
Understanding these alternative ways of stating Newton's third law can significantly enhance one's grasp of force interactions and their implications in various physical phenomena. Whether studying collisions, rocket propulsion, or everyday interactions like walking or swimming, these formulations provide a more intuitive framework for applying this fundamental principle of physics, especially when considering forces acting on different objects.
Types of Forces in Newton's Third Law
Newton's third law of motion states that for every action, there is an equal and opposite reaction. This principle applies to various types of forces that occur in pairs. Understanding these different force types is crucial for grasping the full scope of Newton's third law. In this section, we'll explore applied forces, normal forces, and friction forces, using practical examples to illustrate how these force pairs interact.
Applied forces are perhaps the most intuitive type of force we encounter in everyday life. These are forces that one object directly exerts on another through physical contact. For instance, when you push a book across a table, you're applying a force to the book. According to Newton's third law, the book simultaneously pushes back on your hand with an equal and opposite force. This reciprocal action is why you feel resistance when pushing objects.
Normal forces are another common type of force pair. These forces occur when two objects are in contact with each other, and one object supports the weight of the other. The term "normal" refers to the force being perpendicular to the surface of contact. A classic example is a book resting on a table. The book exerts a downward force on the table due to gravity, and the table exerts an equal and opposite upward force on the book. This upward force is the normal force that prevents the book from falling through the table.
Friction forces are resistance forces that occur when two surfaces slide or attempt to slide against each other. These forces always act parallel to the surfaces in contact and oppose the relative motion between the objects. For example, when you push a book across a rough table surface, friction opposes the motion. The book experiences a friction force in the opposite direction of its movement, while the table experiences an equal and opposite friction force in the direction of the book's movement.
It's important to note that force pairs in Newton's third law always consist of the same type of force. For instance, if you apply a pushing force to a wall, the wall pushes back with an equal and opposite applied force. Similarly, when a book rests on a table, the normal force pair consists of two normal forces  one from the book on the table and one from the table on the book. This consistency in force types within pairs helps maintain the balance described by Newton's third law.
To further illustrate these concepts, let's consider a scenario where you're pushing a heavy box across a carpeted floor. As you apply a horizontal force to move the box, several force pairs come into play. The applied force pair consists of your push on the box and the box's push back on your hands. Simultaneously, there's a normal force pair between the box and the floor, with the floor supporting the box's weight. Friction forces also form a pair, with the carpet resisting the box's motion and the box exerting an equal and opposite friction force on the carpet.
Understanding these different types of forces and how they interact in pairs is essential for analyzing physical systems and solving problems in mechanics. Whether it's in everyday situations or complex engineering applications, recognizing applied forces, normal forces, and friction forces allows us to predict and explain the behavior of objects under various conditions. By grasping these concepts, we gain a deeper appreciation for the fundamental principles that govern motion and interaction in the physical world.
Applications and Implications of Newton's Third Law
Newton's third law of motion, which states that for every action, there is an equal and opposite reaction, has farreaching applications in various fields of physics and engineering. This fundamental principle plays a crucial role in understanding and solving complex problems, as well as in designing mechanical systems that we encounter in our daily lives.
In the realm of physics applications, Newton's third law is essential in explaining numerous phenomena. For instance, in rocket propulsion, the thrust that propels a rocket forward is a direct result of the backward expulsion of exhaust gases. This principle is also evident in the recoil of firearms, where the backward force experienced by the shooter is equal to the forward force propelling the bullet.
Engineers rely heavily on Newton's third law when designing mechanical systems. In automotive engineering, the concept is applied in the development of suspension systems, where the force exerted by the road on the tires is countered by an equal force from the suspension, ensuring a smooth ride. Similarly, in aerospace engineering, the lift generated by an aircraft's wings is balanced by the downward force on the air, allowing the plane to stay airborne.
The law's implications extend to problemsolving in various scientific disciplines. In biomechanics, researchers use this principle to analyze human movement and design prosthetics that mimic natural limb function. The study of animal locomotion, such as a bird's flight or a fish's swimming, also relies heavily on understanding the actionreaction pairs involved in their movements.
In the field of robotics, Newton's third law is fundamental in designing machines that can maintain balance and perform complex tasks. Engineers must account for the forces and counterforces at play when programming robotic arms or developing bipedal robots that can walk and run like humans.
Realworld scenarios where Newton's third law is evident are abundant. In sports, the principle explains how a swimmer propels through water by pushing it backward, or how a basketball player jumps by exerting a downward force on the ground. In construction, the stability of structures depends on balancing forces, with foundations designed to counteract the weight and external forces acting on a building.
The law also has applications in safety engineering. The design of protective gear, such as helmets and airbags, relies on the principle of distributing the force of impact over a larger area or longer time, thus reducing the potential for injury. In automotive safety, crumple zones are designed to absorb and dissipate the force of a collision, protecting the occupants.
Understanding Newton's third law is crucial in environmental engineering, particularly in the development of renewable energy technologies. Wind turbines, for example, harness the force of the wind pushing against the blades, which in turn causes the turbine to rotate and generate electricity. Similarly, hydroelectric power plants utilize the force of flowing water to turn turbines.
In the field of materials science, Newton's third law informs the development of impactresistant materials and structures. Engineers consider how forces are transmitted and distributed through materials to create stronger, more durable products, from smartphone screens to aircraft fuselages.
The law's implications also extend to more abstract applications, such as in economics, where actions and reactions in markets can be analyzed using similar principles. In social sciences, the concept of reciprocity in human interactions can be seen as a manifestation of this law in human behavior.
As we continue to push the boundaries of science and technology, Newton's third law remains a cornerstone in our understanding of the physical world. Its applications in physics and engineering continue to evolve, enabling us to solve increasingly complex problems and design more sophisticated systems that shape our modern world.
Conclusion
In summary, Newton's third law of motion states that for every action, there is an equal and opposite reaction. This fundamental physics concept is crucial for understanding the interactions between objects in our universe. The introduction video provided a clear and engaging explanation of this law, demonstrating its application through various examples. Key points discussed include the simultaneous nature of actionreaction pairs, the importance of considering both objects involved, and the law's role in explaining everyday phenomena. By grasping this concept, readers can enhance their physics understanding and apply it to realworld situations. We encourage you to observe Newton's third law in action in your daily life, from walking and swimming to rocket propulsion and recoil in firearms. By actively seeking out these examples, you'll reinforce your knowledge and gain a deeper appreciation for the underlying principles that govern our physical world.
Introduction to Newton's Third Law
What is Newton's third law?
Step 1: Understanding the Basics of Newton's Third Law
Newton's third law of motion is a fundamental principle in physics, often referred to as the actionreaction law. The law is famously stated as: "For every action, there is an equal and opposite reaction." This means that any force exerted on an object will result in a force of equal magnitude but in the opposite direction exerted back on the original object.
Step 2: RealWorld Examples of Newton's Third Law
To better understand this concept, consider a simple example: pushing a box with your hand. When you push on the box, you are exerting a force on it. According to Newton's third law, the box exerts an equal and opposite force back on your hand. If you push the box with a force of 10 newtons, the box pushes back on your hand with a force of 10 newtons in the opposite direction.
Step 3: Mathematical Representation
Newton's third law can be expressed mathematically. If we denote the force exerted by object A on object B as F_{AB}, and the force exerted by object B on object A as F_{BA}, then the law can be written as:
F_{AB} = F_{BA}
This equation signifies that the forces are equal in magnitude but opposite in direction.
Step 4: Verifying Newton's Third Law
You can easily verify Newton's third law yourself. If you are sitting at a desk, try pushing down on the desk with your hand. You will feel a pressure on your hand, which is the desk pushing back up on your hand. The harder you push, the more pressure you feel, demonstrating that the force you exert on the desk is matched by an equal and opposite force exerted by the desk on your hand.
Step 5: Key Points to Remember
There are two crucial points to keep in mind regarding Newton's third law:
 Forces always come in pairs. It is impossible to exert a force on an object without experiencing a paired reaction force.
 Each force in the pair acts on a different object. For example, if you push on a box, the force you exert is on the box, and the reaction force is on your hand. These forces do not cancel each other out because they act on different objects.
Step 6: Common Mistakes and Clarifications
A common mistake when applying Newton's third law is to assume that the action and reaction forces act on the same object. This is incorrect. The action force and the reaction force must act on two different objects. If both forces were on the same object, they would cancel each other out, resulting in no net force on the object.
Step 7: A Better Way to State Newton's Third Law
While the traditional statement of Newton's third law is wellknown, a more precise way to express it is: "If one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first object." This phrasing emphasizes that the forces are exerted on different objects, which is a critical aspect of the law.
FAQs

What is Newton's Third Law of Motion?
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object simultaneously exerts an equal force in the opposite direction on the first object.

Can you give an example of Newton's Third Law in everyday life?
A common example is walking. When you walk, you push backward on the ground with your feet (action), and the ground pushes forward on you with an equal force (reaction), propelling you forward. Another example is rowing a boat: as you push the water backward with the oar, the water pushes the boat forward.

How does Newton's Third Law apply to rocket propulsion?
Rocket propulsion is a perfect illustration of Newton's Third Law. As the rocket expels gases downward at high speed (action), the gases exert an equal force upward on the rocket (reaction). This upward force is what propels the rocket into space, demonstrating how the law works even in the absence of air or ground to push against.

Does Newton's Third Law mean that forces always cancel out?
No, Newton's Third Law doesn't mean forces always cancel out. The equal and opposite forces act on different objects. For example, when you push a box, your force on the box and the box's force on you are equal and opposite, but they act on different objects (you and the box). The box may still move if your applied force overcomes friction.

How is Newton's Third Law important in engineering and design?
Newton's Third Law is crucial in engineering and design across various fields. In automotive engineering, it's used in designing suspension systems. In aerospace, it's fundamental for aircraft lift and stability. In robotics, it's essential for balance and movement. The law is also applied in designing safety equipment like helmets and airbags, where force distribution is key to reducing impact and potential injuries.
Prerequisite Topics for Newton's Third Law of Motion
Understanding Newton's third law of motion requires a solid foundation in certain key concepts. Two crucial prerequisite topics are particularly important: operations on vectors in magnitude and direction form and Newton's first law of motion. These topics provide the necessary background to fully grasp the principles of Newton's third law and its applications in physics.
Let's start with the importance of understanding operations on vectors in magnitude and direction form. This concept is fundamental when dealing with forces, which are at the heart of Newton's third law. Forces are vector quantities, meaning they have both magnitude and direction. When studying Newton's third law, we often need to analyze multiple forces acting on objects. The ability to perform vector operations is crucial for accurately determining the magnitude and direction of forces involved in actionreaction pairs.
For instance, when two objects interact, the forces they exert on each other are equal in magnitude but opposite in direction. To fully understand this principle, students must be comfortable with vector addition, subtraction, and scalar multiplication. These operations allow for the precise calculation and representation of forces in various scenarios, from simple object collisions to complex systems involving multiple interacting bodies.
Equally important is a solid grasp of Newton's first law of motion. This law, also known as the law of inertia, sets the stage for understanding the broader context of Newton's laws of motion. It states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This concept is crucial for comprehending the nature of forces and their effects on objects, which directly relates to the principles outlined in Newton's third law.
The first law provides the foundation for understanding how forces can change an object's state of motion. When studying the third law, which deals with the interaction between two objects, it's essential to recognize how these interactions can alter the motion of both objects involved. The concept of inertia, central to the first law, helps explain why objects resist changes in their motion and how the equal and opposite forces described in the third law come into play.
By mastering these prerequisite topics, students can more easily grasp the intricacies of Newton's third law of motion. The ability to work with vectors allows for a more quantitative understanding of forces, while familiarity with the first law provides the necessary context for analyzing force interactions. Together, these concepts create a robust framework for exploring the actionreaction principle that is central to Newton's third law.
In conclusion, a thorough understanding of vector operations and Newton's first law is invaluable when studying Newton's third law of motion. These prerequisites not only facilitate a deeper comprehension of the law itself but also enable students to apply this knowledge to realworld scenarios and more advanced physics concepts. By building this strong foundation, students can confidently tackle the complexities of Newton's third law and its wideranging applications in physics and engineering.
 Newton's third law of motion
 Explaining physical phenomena using Newton's third law
 Calculations with Newton's second and third laws
Notes:
 Newton's third law: when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.
 Also stated: "for every action, there is an equal and opposite reaction."
 Each force in actionreaction force pair is located on a different object in the pair. Each force in actionreaction force pair also has the same "type."
 Example: if a wooden block slides across a floor, the floor exerts a force of friction on the block and the block exerts a force of friction that is equal in magnitude but opposite in direction on the floor. The forces in this pair are on different objects (one acts on the block, and the other acts on the floor), and both are the same type of force (friction).
For object A exerting a force on object B:
$\vec{F}_{A on B} =  \vec{F}_{B on A}$
$\vec{F}_{A on B}:$ force A is exerting on B, in newtons (N)
$\vec{F}_{B on A}:$ force B is exerting on A, in newtons (N)
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