What is External Force? Examples & Impact

An external force is a significant concept in understanding the principles governing dynamics, a field extensively studied at institutions like the Massachusetts Institute of Technology (MIT). Sir Isaac Newton, through his laws of motion, notably defines inertia as a state resistant to changes induced by any external influence. Understanding what is external force requires considering its effects on a system's momentum, which remains constant unless acted upon. Engineers often account for these forces using tools like finite element analysis software to predict structural behavior under various external conditions.

Force and motion stand as the cornerstones of classical mechanics, providing the essential framework for understanding how objects interact and behave within our universe. These concepts aren't merely abstract theoretical constructs; they are the very foundation upon which countless engineering marvels and scientific discoveries are built.

From the simplest everyday occurrences to the most complex technological advancements, force and motion dictate the rules of engagement. Understanding these principles allows us to predict, control, and harness the power of the physical world around us.

The Intertwined Dance of Force and Motion

At its core, physics seeks to describe and predict the behavior of matter and energy. Force and motion are inextricably linked in this pursuit. Force, in essence, is an interaction that, when unopposed, will change the motion of an object.

Motion, conversely, is the result of forces acting upon an object, causing it to accelerate, decelerate, or change direction. This interplay is governed by fundamental laws that provide a quantitative and qualitative understanding of how objects respond to these interactions. This forms the basis of mechanics.

Significance in Physics and Engineering

The understanding of force and motion transcends the realm of pure theoretical physics, impacting a multitude of engineering disciplines. Consider mechanical engineers designing machines, aerospace engineers developing aircraft, or civil engineers constructing bridges – all rely heavily on the principles governing force and motion.

These principles enable engineers to calculate stresses, predict structural integrity, and optimize designs for efficiency and safety. Without a firm grasp of force and motion, the creation of functional and reliable infrastructure would be impossible. Furthermore, understanding force and motion is required for designing prosthetics, or predicting the weather.

Newton's Laws: A Gateway to Classical Mechanics

Sir Isaac Newton's Laws of Motion represent a watershed moment in the history of physics. They provide a concise and powerful framework for describing the relationship between force, mass, and acceleration. These laws serve as the fundamental axioms of classical mechanics, offering a deterministic view of how objects move under the influence of external forces.

Newton's Laws offer a framework in which we can understand and analyze the world around us through clearly defined mathematical frameworks. The subsequent sections of this exposition will delve deeper into each of Newton's Laws, elucidating their implications and providing illustrative examples to solidify your understanding.

Newton's Laws of Motion: The Foundation of Mechanics

At the heart of classical mechanics lie Newton's Laws of Motion, a set of three fundamental principles that govern the behavior of objects under the influence of forces. These laws provide a deterministic framework for understanding motion and are essential for analyzing and predicting the behavior of physical systems.

A firm grasp of these laws is critical for anyone seeking to understand the physical world.

Newton's First Law: Inertia

Newton's First Law, often referred to as the Law of Inertia, states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Inertia is the tendency of an object to resist changes in its state of motion.

Understanding Inertia

Inertia is a fundamental property of matter that is directly proportional to its mass. The greater the mass of an object, the greater its inertia, and the more force is required to change its state of motion.

Inertia is not a force itself, but rather a measure of an object's resistance to acceleration.

Examples of Inertia in Everyday Life

The concept of inertia can be observed in numerous everyday scenarios. Consider a coffee cup placed on the dashboard of a car. When the car suddenly accelerates, the coffee cup tends to remain at rest, relative to the Earth, causing it to slide backward on the dashboard.

Conversely, when the car brakes suddenly, the coffee cup tends to continue moving forward, potentially spilling its contents.

Another example is the difficulty in stopping a bowling ball once it's in motion. Due to its large mass, the bowling ball possesses a significant amount of inertia, requiring a substantial force to bring it to a halt.

These examples illustrate how inertia plays a role in our daily experiences.

Newton's Second Law: Force and Acceleration

Newton's Second Law establishes a quantitative relationship between force, mass, and acceleration. It states that the acceleration of an object is directly proportional to the net force acting on it, is in the same direction as the net force, and is inversely proportional to the mass of the object.

Force as a Vector Quantity

Force is a vector quantity, meaning it has both magnitude and direction. The magnitude of a force represents its strength, while the direction indicates the way in which the force is acting.

When analyzing forces, it's crucial to consider both aspects to accurately predict the resulting motion.

The Mathematical Relationship: F = ma

The relationship between net force (F), mass (m), and acceleration (a) is expressed mathematically as F = ma. This equation is a cornerstone of classical mechanics, allowing us to calculate the acceleration of an object given the net force acting on it and its mass.

For example, if a 2 kg object is subjected to a net force of 10 N, its acceleration will be 5 m/s² in the direction of the force (a = F/m = 10 N / 2 kg = 5 m/s²).

Understanding this relationship allows us to predict and control the motion of objects by manipulating the forces acting upon them.

Net Force: The Vector Sum of Forces

In most real-world scenarios, an object is subjected to multiple forces simultaneously. The net force is the vector sum of all forces acting on the object.

To determine the net force, we must consider both the magnitudes and directions of each individual force.

For example, if two forces of equal magnitude are acting on an object in opposite directions, the net force is zero, and the object will remain in equilibrium.

However, if the forces are unequal, the object will accelerate in the direction of the larger force.

Vector addition techniques, such as resolving forces into components and using the Pythagorean theorem, are essential for calculating the net force in complex situations.

Newton's Third Law: Action and Reaction

Newton's Third Law, often referred to as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction.

This law emphasizes that forces always occur in pairs, and these pairs act on different objects.

Understanding Action-Reaction Pairs

It's crucial to understand that action and reaction forces, while equal in magnitude and opposite in direction, act on different objects. This is a key distinction that often leads to confusion.

For example, when a person pushes against a wall (the action), the wall exerts an equal and opposite force back on the person (the reaction).

The action force acts on the wall, while the reaction force acts on the person. These forces do not cancel each other out because they act on different objects.

Examples of Newton's Third Law

A common example of Newton's Third Law is a person walking. As a person walks, they push backward on the Earth (the action). In response, the Earth exerts an equal and opposite force forward on the person (the reaction), propelling them forward.

Similarly, when a rocket launches, it expels hot gases downward (the action). The gases, in turn, exert an equal and opposite force upward on the rocket (the reaction), causing it to accelerate into space.

These examples highlight the fundamental principle that forces always occur in pairs and that these pairs are essential for understanding motion and interactions in the physical world.

Exploring Different Types of Forces

Building upon the foundational principles established by Newton's Laws, it's essential to explore the diverse types of forces that govern interactions in the physical world. A comprehensive understanding of these forces is paramount for analyzing real-world scenarios and predicting the behavior of physical systems.

This section will delve into common force types: applied force, gravity, friction, normal force, and tension.

Applied Force

Applied force refers to a force exerted on an object through direct contact. It's the most intuitive type of force, representing the push or pull applied by an external agent.

Examples of applied forces abound in everyday life: pushing a lawnmower, pulling a door open, or kicking a ball. The magnitude and direction of the applied force directly influence the object's subsequent motion, in accordance with Newton's Second Law.

Gravity

Gravity is the universal force of attraction between any two objects with mass. Its influence is most apparent on a large scale, dictating the motion of planets, stars, and galaxies.

On Earth, gravity manifests as the force that pulls objects towards the planet's center, giving rise to what we perceive as weight. The magnitude of the gravitational force (Fg) between two objects is given by the formula:

Fg = G(m1m2)/r²

where:

• G is the gravitational constant (approximately 6.674 × 10^-11 Nm²/kg²)
• m1 and m2 are the masses of the two objects
• r is the distance between their centers.

A crucial consequence of gravity is the concept of weight. Weight (W) is the force exerted on an object due to gravity and is calculated as:

W = mg

where:

• m is the mass of the object
• g is the acceleration due to gravity (approximately 9.8 m/s² on Earth's surface).

Friction

Friction is a force that opposes motion between surfaces in contact. It arises from microscopic interactions between the surfaces, converting kinetic energy into thermal energy.

Friction is broadly categorized into two types: static friction and kinetic friction.

Static friction prevents an object from starting to move when a force is applied. The static friction force will increase to match an applied force, up to a maximum static friction value.

Kinetic friction opposes the motion of an object that is already moving. Kinetic friction is typically less than static friction for the same two surfaces.

Examples of friction include the force that allows us to walk without slipping, the resistance encountered by a sliding box, and the heat generated when rubbing our hands together.

Normal Force

The normal force is the force exerted by a surface perpendicular to an object in contact with it. It's a reaction force that prevents an object from passing through the surface.

The normal force adjusts its magnitude to balance other forces acting on the object, ensuring that the object remains in equilibrium in the direction perpendicular to the surface.

For instance, when a book rests on a table, the table exerts an upward normal force on the book, counteracting the downward force of gravity.

If an additional force is applied downwards on the book, the normal force will increase to maintain equilibrium.

Tension

Tension is the force transmitted through a string, rope, cable, or wire when it is pulled tight by forces acting from opposite ends.

Tension is a pulling force that acts along the length of the flexible connector. Examples of tension include the force in a rope used to lift an object, the force in a cable supporting a bridge, and the force in a string of a musical instrument.

Tension is commonly employed in pulley systems, where it allows for the redirection and multiplication of forces to lift heavy objects or perform other mechanical tasks.

Force Analysis and Equilibrium: Solving Problems with Forces

Having explored various types of forces, it's crucial to understand how to apply this knowledge to analyze real-world scenarios. This section will introduce essential problem-solving techniques centered around free body diagrams and the concept of equilibrium, providing the tools necessary to determine the motion, or lack thereof, of an object under the influence of multiple forces.

Free Body Diagrams: Visualizing Forces

The free body diagram (FBD) is an indispensable tool for visualizing and analyzing the forces acting on an object. It simplifies complex situations by isolating the object of interest and representing all external forces acting upon it as vectors.

By creating an FBD, one can more easily determine the net force acting on the object and subsequently apply Newton's Laws to predict its motion.

Constructing a Free Body Diagram: A Step-by-Step Guide

Creating an accurate and informative free body diagram requires a systematic approach:

1. Choose the Object of Interest: Clearly define the object you are analyzing. This could be a block, a car, or any other body whose motion is under investigation.
2. Identify All External Forces: Identify every force acting on the object. This includes forces such as gravity, applied forces, normal forces, friction, tension, and air resistance. Crucially, only consider forces acting on the object, not forces exerted by the object.
3. Draw the Object as a Point: Represent the object as a simple point mass. This simplifies the diagram and focuses attention on the forces.
4. Draw Force Vectors: Represent each force as a vector originating from the point mass. The length of the vector should be proportional to the magnitude of the force, and the direction of the vector should match the direction of the force. Label each vector clearly (e.g., Fg for gravity, Fa for applied force).
5. Establish a Coordinate System: Choose a convenient coordinate system (e.g., x-y axes) to resolve the force vectors into components. This simplifies the application of Newton's Second Law.

Applying Free Body Diagrams: Examples

Consider a block resting on an inclined plane. To analyze the forces acting on the block, we would:

1. Choose the block as the object of interest.
2. Identify the forces: gravity (Fg) acting downwards, the normal force (Fn) acting perpendicular to the plane, and friction (Ff) acting parallel to the plane and opposing motion.
3. Draw the block as a point.
4. Draw the force vectors Fg, Fn, and Ff, originating from the point.
5. Establish a coordinate system with the x-axis parallel to the inclined plane and the y-axis perpendicular to it.

Once the FBD is complete, you can resolve the forces into components along the chosen coordinate axes and apply Newton's Second Law to determine the block's acceleration.

Another example is a mass suspended by a cable. The forces acting are gravity (downwards) and tension in the cable (upwards). Setting these two forces equal allows for calculation of the tension.

Equilibrium: The Balance of Forces

Equilibrium is a state where the net force acting on an object is zero. This implies that the object is either at rest or moving with constant velocity (both magnitude and direction). In mathematical terms, equilibrium is expressed as:

∑F = 0

This vector equation is equivalent to:

∑Fx = 0 and ∑Fy = 0

where ∑Fx and ∑Fy represent the sum of the force components along the x and y axes, respectively.

Static vs. Dynamic Equilibrium

Equilibrium can be further divided into two categories:

• Static Equilibrium: The object is at rest (velocity = 0).

• Dynamic Equilibrium: The object is moving with constant velocity (non-zero).

In both cases, the net force is zero, but the implication for the object's motion is different.

Examples of Objects in Equilibrium

A book resting on a table is an example of static equilibrium. The gravitational force pulling the book downwards is balanced by the normal force exerted by the table upwards. Since the net force is zero, the book remains at rest.

A car traveling at a constant speed on a straight, level road is an example of dynamic equilibrium. The engine's forward force is balanced by the opposing forces of air resistance and friction. The net force is zero, so the car maintains a constant velocity.

To solve problems involving equilibrium, one typically constructs a free body diagram, resolves the forces into components, and applies the equilibrium conditions (∑Fx = 0 and ∑Fy = 0) to solve for unknown forces or angles. Careful attention to the direction of forces and consistent application of vector principles are crucial for accurate analysis.

Related Concepts: Expanding the Scope of Force and Motion

While Newton's Laws of Motion provide a robust framework for understanding forces and their effects, the study of motion extends to several interconnected concepts that offer a more complete picture of how objects interact. Momentum, impulse, work, energy, and torque are crucial extensions that deepen our understanding of force and motion.

Momentum: Inertia in Motion

Momentum is a measure of an object's mass in motion.

It is defined as the product of an object's mass (m) and its velocity (v), expressed as p = mv.

Momentum is a vector quantity, meaning it possesses both magnitude and direction.

An object with a larger mass or a higher velocity will have a greater momentum, making it more difficult to stop or change its direction.

The principle of conservation of momentum is fundamental, stating that in a closed system, the total momentum remains constant in the absence of external forces. This principle is essential in analyzing collisions and explosions.

Impulse: Changing Momentum with Force

Impulse quantifies the change in momentum of an object.

It is equal to the force (F) applied to an object multiplied by the time interval (Δt) during which the force acts: Impulse = FΔt.

Impulse is also equal to the change in momentum (Δp), leading to the relationship FΔt = Δp.

A large force applied over a short time or a smaller force applied over a longer time can produce the same impulse, and thus the same change in momentum.

This concept is vital in understanding how forces affect motion, particularly in collisions and impacts.

Work: Transferring Energy Through Force

In physics, work is defined as the energy transferred to or from an object by a force causing a displacement.

It is calculated as W = Fdcosθ, where F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and displacement vectors.

Only the component of the force acting in the direction of displacement contributes to the work done.

Work is a scalar quantity, measured in Joules (J).

Work is closely related to energy, as the work done on an object can change its kinetic or potential energy.

Energy: Kinetic and Potential

Energy is the capacity to do work.

It exists in various forms, with kinetic energy (KE) and potential energy (PE) being particularly relevant in the context of motion.

Kinetic energy is the energy of motion, given by the formula KE = (1/2)mv², where m is mass and v is velocity.

Potential energy is stored energy due to an object's position or configuration.

Gravitational potential energy (GPE) is given by GPE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above a reference point.

The law of conservation of energy states that energy cannot be created or destroyed, but can be transformed from one form to another.

Torque: The Twisting Force

Torque is a twisting force that causes rotation.

It is calculated as τ = rFsinθ, where r is the lever arm (the distance from the axis of rotation to the point where the force is applied), F is the magnitude of the force, and θ is the angle between the force and the lever arm.

Torque depends on both the magnitude of the force and the lever arm. A larger force or a longer lever arm will produce a greater torque.

Torque is a vector quantity, with its direction determined by the right-hand rule.

Understanding torque is essential for analyzing rotational motion, such as the motion of gears, wheels, and levers.

Force Sensors and Force Plates: Measuring External Forces

Force sensors and force plates are instruments used to measure forces.

Force sensors, often based on strain gauges, convert force into an electrical signal that can be measured.

Force plates measure ground reaction forces (GRF), the forces exerted by the ground on an object in contact with it.

These devices have applications in biomechanics, sports science, and engineering. They enable detailed analysis of forces exerted during walking, running, jumping, and other activities. For example, a force plate can be used to assess balance and stability in patients with neurological disorders.

Accelerometers: Measuring Acceleration

Accelerometers are devices that measure acceleration.

They can detect changes in velocity and orientation.

Accelerometers are commonly used in smartphones, automobiles, and aerospace applications.

In biomechanics and sports science, accelerometers can be used to quantify movement intensity, monitor physical activity, and assess the impact forces experienced during exercise. For example, they can measure acceleration during running to estimate the forces acting on the body.

Real-World Applications: Force and Motion in Action

The principles of force and motion, far from being abstract theoretical constructs, are constantly at play in the world around us. Examining everyday scenarios through the lens of physics reveals the profound impact of these fundamental laws on our daily experiences. By deconstructing these situations, we can reinforce our understanding of force and motion and appreciate their practical relevance.

Analyzing Everyday Scenarios

Pushing a Box: A Symphony of Forces

Consider a person pushing a box across a floor. This seemingly simple action involves a complex interplay of forces.

The applied force, exerted by the person, is the primary driver of the box's motion.

However, friction, acting between the box and the floor, opposes this motion.

The normal force, exerted by the floor on the box, counteracts the force of gravity, ensuring the box remains on the surface.

By analyzing these forces and their interactions, we can determine the net force acting on the box and, consequently, its acceleration.

The Falling Apple: Gravity's Unseen Hand

The iconic image of an apple falling from a tree perfectly illustrates the effects of gravitational force.

Gravity, the universal force of attraction between objects with mass, pulls the apple towards the Earth.

This force causes the apple to accelerate downwards, increasing its velocity until it reaches the ground.

This simple observation led Newton to formulate his law of universal gravitation, a cornerstone of classical physics.

The Accelerating Car: Force, Mass, and Acceleration

A car accelerating from rest is a direct demonstration of Newton's Second Law of Motion (F = ma).

The engine force, generated by the car's engine, propels the car forward.

The magnitude of the car's acceleration is directly proportional to the engine force and inversely proportional to the car's mass.

The greater the engine force, the faster the car accelerates. The heavier the car, the slower the acceleration for the same engine force.

The Thrown Ball: Projectile Motion Under External Influence

When a ball is thrown into the air, its motion is governed by a combination of factors.

Initially, the applied force from the thrower imparts an initial velocity to the ball.

However, once released, the ball becomes a projectile, subject primarily to the forces of gravity and air resistance.

Gravity pulls the ball downwards, causing it to follow a curved trajectory.

Air resistance opposes the ball's motion, slowing it down and affecting its range.

The Bridge: Equilibrium in Engineering

A bridge supporting the weight of vehicles exemplifies the importance of equilibrium in structural engineering.

The bridge must be designed to withstand the external forces imposed by the vehicles, wind, and its own weight.

The supporting structures of the bridge distribute these forces, ensuring that the bridge remains in static equilibrium.

If the forces are not properly balanced, the bridge could collapse.

The Sailboat: Harnessing the Power of the Wind

A sailboat propelled by the wind demonstrates the principles of fluid dynamics and the forces of lift and drag.

The wind exerts a force on the sail, which is designed to generate lift.

Lift is the force perpendicular to the wind direction that propels the boat forward.

Drag is the force opposing the boat's motion through the water and air.

The skillful sailor adjusts the sails to maximize lift and minimize drag, optimizing the boat's speed and direction.

The Rocket Launch: Overcoming Gravity with Thrust

A rocket launching into space is a spectacular demonstration of Newton's Third Law of Motion and the power of thrust.

The rocket expels hot gases downwards, creating an equal and opposite reaction force – thrust – that propels the rocket upwards.

The rocket must generate enough thrust to overcome the force of gravity and accelerate into orbit.

The Braking Car: Friction's Decelerating Effect

A car stopping due to the application of brakes illustrates the role of friction as an external force.

When the brakes are applied, friction between the brake pads and the rotors converts kinetic energy into heat, slowing the car down.

The greater the frictional force, the faster the car decelerates.

The Orbiting Satellite: A Perpetual Dance with Gravity

A satellite orbiting the Earth is constantly influenced by gravity.

Gravity provides the centripetal force that keeps the satellite in its circular or elliptical path.

Without gravity, the satellite would travel in a straight line, drifting away from the Earth.

The satellite's orbital speed and altitude are carefully chosen to maintain a stable orbit.

Influential Figures: Honoring the Pioneers of Mechanics

The field of mechanics, with its profound impact on our understanding of the physical world, owes its foundation to the brilliant minds who dared to question and quantify the phenomena around them. While many contributed to its development, Sir Isaac Newton stands as a towering figure, his work forming the bedrock of classical mechanics and shaping the course of scientific inquiry for centuries.

Isaac Newton: The Architect of Classical Mechanics

Isaac Newton (1643-1727) was an English physicist and mathematician, widely recognized as one of the most influential scientists of all time. His groundbreaking work in mechanics, optics, and calculus revolutionized our understanding of the universe and laid the groundwork for modern physics.

Newton's Laws of Motion: A Paradigm Shift

Newton's most significant contribution to mechanics is undoubtedly his articulation of the three laws of motion. These laws, first presented in his seminal work Principia Mathematica (1687), provide a concise and accurate description of how objects move and interact.

• Newton's First Law (Inertia): This law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a force. This concept of inertia fundamentally changed the way scientists viewed motion.

• Newton's Second Law (Force and Acceleration): This law quantifies the relationship between force, mass, and acceleration, expressed by the equation F = ma. It establishes that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

• Newton's Third Law (Action and Reaction): This law asserts that for every action, there is an equal and opposite reaction. This principle highlights the fundamental symmetry in interactions between objects.

Beyond Mechanics: Calculus and Optics

Newton's genius extended far beyond mechanics. He made significant contributions to mathematics, most notably through his development of calculus, a powerful tool for analyzing change and motion. Independently developed alongside Gottfried Wilhelm Leibniz, calculus became indispensable for solving complex problems in physics and engineering.

Newton also conducted groundbreaking work in optics. His experiments with prisms demonstrated that white light is composed of a spectrum of colors. He also invented the reflecting telescope, which significantly improved the clarity and magnification of astronomical observations.

Newton's Enduring Legacy

Isaac Newton's work laid the foundation for classical physics, shaping our understanding of the universe and paving the way for countless technological advancements. His laws of motion and his development of calculus continue to be essential tools for scientists and engineers today. Newton's legacy as a scientific innovator and a intellectual giant remains secure.

So, there you have it! Hopefully, you now have a solid grasp of what is external force and how it's constantly shaping the world around us. From a gentle breeze to a powerful push, it's all about understanding those influences that come from the outside. Keep an eye out for external forces in action – you'll be surprised how often you spot them!