Newton’s Third Law: Definition, Applications, Misconceptions, & Examples

Table of Contents

Introduction to Newton’s Third Law of Motion

When a person jumps from a small boat onto the shore, the boat is seen to move backward instantly. This happens because the person exerts a force on the boat, and in response, the boat exerts an equal force in the opposite direction on the person. This everyday example shows that forces always occur in pairs and act on different objects. These paired forces are known as action and reaction. Since they act on separate objects, they do not cancel each other out. This idea is summarized in the simple statement: for every action, there is an equal and opposite reaction.

Newton’s Third Law of Motion is a fundamental principle of classical mechanics that explains how objects interact with one another. As Newton’s First Law and Second Laws of Motion are used to explain and calculate the motion of objects, Newton’s Third Law is used to explain the interactions between the objects. Its importance extends from simple daily activities to advanced fields such as space exploration. Understanding this law helps us make sense of common actions like walking, swimming, rowing a boat, and the motion of vehicles and rockets, revealing how closely our everyday experiences are connected to the laws of nature.

Historical Background of the Third Law of Motion

Sir Issac Newton proposed the third law of motion in the year 1687. He had published this law in his famous book, Philosophiae Naturalis Principia Mathematica. Newton studied the motion of objects and observed that interactions between bodies always involve two forces acting on each other but in opposite directions. Newton had carefully studied collisions, forces, and interactions in nature and recognized that forces always appear in pairs.

Before Newton, ideas about motion were expressed largely in qualitative terms. Newton’s works had provided a clear mathematical and scientific foundation for mechanics. This law not only explained the movement of the Earth but also the movement of the celestial bodies. He brought together previously scattered ideas into a single, well-organized framework and systematically presented them. His ability to unify those observations and data into a logical frame transformed the study of physics and laid the foundation of major development in calculus, astronomy, and much of the physics and other branches of modern science.

Statement of Newton’s Third Law

⚖️ Statement of Newton’s Third Law
  • Newton’s Third Law of Motion: For each and every action there is equal and opposite reaction.
    • This means that when one object exerts a force on another object, the second object simultaneously exerts a force of the same magnitude but in the oppsite direction on the first object. The action and reaction forces act on different objects, which is why they do not cancel each other.

Action and Reaction Forces in Newton’s Third Law

Newton’s Third Law of Motion is expressed through a pair of forces known as action and reaction. As these forces always come in pairs, the Third Law of Motion is dual in nature, unlike Newton’s First Law and Newton’s Second Law of Motion. When an object exerts a force on another, it causes the second object to respond by exerting an equal but oppsite forces. Since action and rection acts on different objects, they do not cancel each other.

A simple way to understand this is by thinking of our everyday activities, like walking. When we walk, our foot pushes the ground backward. This is the action force that is applied by the human body. In return for that, the ground pushes our foot forward with the same amount of force. This forward push, which we are getting from the ground, is the reaction, and it makes us move ahead. Conversely, it is difficult to walk in sand because the reaction force is much less, and we cannot move forward compared to land on the sand.

Key points that show dual nature (action-reaction) forces:
  • Forces always occur in pairs.
  • The two forces are equal in magnitude.
  • They act in opposite directions.
  • They act on two different objects at the same time.

Mathematical Representation

As this law does not provide much mathematics, it is only used to explain the interactions between the objects. This law can be mathematically only visualized as;

\[\mathrm{\vec{F}_{AB}} = -\mathrm{\vec{F}_{BA}}\tag{1}\]

where,

  • \(\mathrm{\vec{F}_{AB}}\) denotes the force exerted by an object A on object B.
  • \(\mathrm{\vec {F}_{BA}}\) denotes the force object B will exert on object A.
  • The negative sign indicates that both of the forces are acting in the opposite direction.

Real-world Examples and Applications

Newton’s Third Law states that forces always occur in pairs. Below are some common examples of this law and clearly disintegrated in action and reaction forces happening in that activity.

1. Walking
  • Action: The foot pushes the ground backward.
  • Reaction: The ground pushes the foot forward, moving the person ahead.
2. Rowing a Boat
  • Action: The oars push water backward.
  • Reaction: The water pushes the boat forward.
3. Recoil of a Gun
  • Action: The gun pushes the bullet forward when fired.
  • Reaction: The bullet pushes the gun backward, causing recoil.
4. Swimming
  • Action: The swimmer pushes water backward with hands and feet.
  • Reaction: The water pushes the swimmer forward.
5. Rocket Propulsion
  • Action: The rocket expels exhaust gases downward.
  • Reaction: The exhaust gases push the rocket upward.
6. Book on the table
  • Action: Downward force (gravity) exerted by the book on the table.
  • Reaction: The upward force exerted by the table to prevent the book from falling.

Common misconceptions

Newton’s third law of motion is simple enough to remember. However, it is misunderstood in so many ways. Some of those misconceptions are explained here.

1. Action and reaction forces cancel each other

There is a misconception that action and reaction forces are equal and opposite; hence, they cancel each other. They do not cancel because they are happening on different objects.

2. Action happens first, and reaction happens later

There is a misconception that action force happens first, and then the reaction. Actually, action and reaction forces occur simultaneously without any time delay between them.

3. Action force is stronger than the reaction force

There is a misconception that action force is stronger than the reaction force, i.e., the object that acts applies the larger force. In fact, action and reaction forces are equal in magnitude, regardless of the masses of the objects involved.

4. Reaction force opposes motion.

There is a misconception that the reaction force always opposes the motion. In fact, the reaction force is the one that causes the motion, such as walking, swimming, rocket propulsion, and jumping.

5. No forces are acting on the object at rest

No forces are acting on a stationary object. The actual case is that, even at rest, the object experiences both action-reaction forces, such as a book resting on a table.

Newton’s Third Law Applications in Engineering

There are numerous applications of Newton’s third law of motion, which is widely used by various industries for force analysis, motion generation, stability, safety, and the efficient design of systems involving interacting bodies. Some of them are listed below.

1. Structural and Mechanical Engineering

Buildings, bridges, and pillars are designed by considering action-reaction forces between loads and foundations. Similarly, in the case of designing machines, gears, pistons, and engines, interacting parts exert equal and opposite forces on each other.

2. Manufacturing and Tool Design

Designing the heavy and light manufacturing tools is crucial. It is important that these tools work well without harming the person. Cutting, drilling, forging, and pressing operations rely on equal and opposite forces between these tools and the materials on which they are being operated. Understanding the mechanics helps with accurate control and application in other activities.

3. Automotive Safety-related

The safety being one of the main characteristics we look for in automotive is uncompromisable. Safety mechanisms like airbags, brakes, treads on tires, the force proportionality in the case of acceleration and braking all of these require a proper calibration of action-reaction forces when interacting with the system. Engineers work on several systems to calculate the action and reaction on all of these before finalizing the system in any automotive.

4. Aviation and Marine Engineering

Airplanes and Container vessels, which play a vital role in the transportation of goods and people around the globe, also rely on the proper application of Newton’s Third Law of Motion. The lift and thrust in aircraft are explained using the interaction forces between air and wings or engines. And the big propellers used in the vessels push the water backward and move forward in the ocean. Proper calculation of the interactions is a must to make them safe and efficient travel.

5. Robotics

In this modern world of AI and technology, it is not far from when we will have robots doing our mundane work. Understanding the action and reaction responses from the surroundings in real time and implementing them for the smooth transitions in the tasks relies highly on the balance of forces.

Newton’s Third Law and Its Significance in Aerospace Dynamics

Aerospace dynamics offers some of the clearest and most impressive illustrations of Newton’s Third Law of Motion, where motion arises due to equal and opposite force interactions.

Rocket Propulsion

Rocket engines generate motion by expelling exhaust gases at very high speeds in a downward direction. In response to this action, an equal force acts upward on the rocket, producing thrust and lifting it off the ground. There is a misconception that this propulsion requires air to push against; in reality, rocket propulsion works purely through interaction with expelled gases and therefore functions effectively even in the vacuum of space.

Mathematically, the total thrust produced by the rocket can be expressed as:

\[\mathrm{F} = \dot{m}v_e+(p_e-p_a)A_e\tag{2}\]

where,

  • \(F:\) Thrust force produced by the rocket (N).
  • \(\dot{m}:\) Mass flow rate of exhaust gases by the rocket engine (kg/s).
  • \(v_e:\) Effective exhaust velocity at which exhaust gases leave the rocket (m/s).
  • \(p_e:\) Exhaust pressure at the nozzle exit (Pa).
  • \(p_a:\) Ambient pressure– surrounding pressure of the environment (Pa).
  • \(A_e:\) Cross-sectional area at the nozzle exit where gases are expelled (\(m^2\)
Special Case (Ideal Expansion)

If the exhaust pressure equals the ambient pressure \((p_e=p_a)\), the equation simplifies to:

\[\mathrm{F} = \dot{m}v_e\tag{3}\]

In short, the thrust produced by a rocket is the sum of momentum thrust due to exhaust gases and pressure thrust due to pressure difference at the nozzle exit.

Satellite Control and Maneuvering

Satellites have small thrusters that help them to adjust their position, speed, or orientation in orbit. When the gas is released in a particular direction, the resulting reaction force causes the satellite to move or rotate in the opposite direction, allowing precise control in space.

Movement During Spacewalks

Astronauts conducting spacewalks use maneuvering units that release small jets of gas. The expelled gas creates a reaction force that pushes the astronaut in the opposite direction, enabling controlled movement in the zero-gravity environment of space.

Newton’s Third Law and Momentum Conservation

Newton’s Third Law of Motion is directly connected to the law of conservation of momentum. In a closed or isolated system, when two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction as per Newton’s Third Law of Motion. These action–reaction force pairs act for the same duration of time and therefore produce equal and opposite changes in momentum.

Consequently, any increase in momentum of one object is balanced by an equal decrease in momentum of the other. For example, when two ice skaters push away from each other on frictionless ice, each skater moves in opposite directions due to the forces they apply on one another. Although their individual momenta change, the total momentum of the system remains unchanged if it was initially zero.

Thus, momentum is conserved in all interactions because Newton’s Third Law ensures that forces always occur in pairs, keeping the total momentum of the system constant.

Summary

Like other laws of motion, Newton’s Third Law of Motion is a universal law of motion. This is simple compared to the other two; however, the applications of this law are vague, ranging from a walking phenomenon to all the way up to the launching of rockets here on earth and maneuvering the satellites in space.

The main part of the Law is to understand the action-reaction forces, and then only can we apply it in both the natural world and humand made systems. It highlights that interactions always occur as balanced, interconnected pairs. This concept extends beyond the boundaries of physics, extending to broader ideas of symmetry and cause-and-effect in nature.

As technology continues to advance rapidly, enabling exploration from outer space to the microscopic realm, Newton’s Third Law remains a fundamental principle that guides, supports, and improves scientific and technological progress.

References

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