External Forces

The Basics: External Force Definition

A force applied on an object by another object not part of the system is known as an external force. For clarity, consider a system to be the object of focus in your study.

Objects always react to these forces via Newton's Second Law of Motion, which can be summarised by the following formula:

\[ \text{force} = \text{mass} \times \text{acceleration} \]

Now you know what an external force is, let's understand how to analyse its effect on structures.

Analysing External Forces on Structure

When external forces act on a structure, they cause stress and, subsequently, deformation. The magnitude and the direction of the force, as well as the structure's properties, determine the extent of this deformation.

External forces can be visualised in a free body diagram, a tool used in physics to understand all the forces acting on a specific object or structure. The forces are typically represented as vectors pointing in the direction in which they act.

Here are some of the common external forces you might come across in classical mechanics:

• Gravitational force
• Normal force
• Air resistance
• Tension
• Friction

Impact of External Forces on Different Types of Structures

Different types of structures react differently to external forces. This behaviour is due to their unique structural properties. Think about how a wooden beam reacts compared to a steel beam when the same force is applied.

Digging Deeper: Relationship Between External and Internal Forces

In physics, understanding the interaction between external and internal forces is fundamental to analysing the behaviour of objects and structures. Let's delve into understanding these interactions.

Exploring the Interaction Between Internal and External Forces

You've already learnt about external forces, but what are internal forces? Well, these are forces that act within the object or system due to the external force. If you press your hands together, for instance, the force your right hand exerts on your left is an external force, but the forces within your hand (muscle stress, bone compression) reacting to that are internal forces.

External and internal forces work together in an object-system interplay. After an external force is applied, internal forces respond to maintain balance or to initiate movement, as per Newton's First Law of Motion, which states requires external forces to change an object's motion.

Internal forces distribute the effect of an external force throughout an object's structure. For instance, if an elevator cable exerts an upwards external force on the elevator, internal forces distribute this external force evenly across the elevator car to make it rise smoothly. This distribution of forces helps eliminate inconsistencies and asymmetric deformations.

\[ \text{{Newton's 1st Law}}: \text{{Objects at rest remain at rest, and objects in motion remain in motion in a straight line, unless acted upon by an external force.}} \]

Another crucial role of internal forces is to resist deformation caused by external forces, as per Hooke's law.

\[ \text{{Hooke's law}}: \text{{Stress}} = \text{{Modulus of Elasticity}} \times \text{{Strain}} \]

A great example is the spring. The spring's internal forces counteract the external forces trying to compress or extend it, making it an instance of Hooke's law.

Contrast Between External and Internal Forces

External forces and internal forces differ significantly but are interrelated. External forces instigate action, while internal forces resist, transfer, or react to that action. To clarify:

• Unlike external forces which stem from interaction with other objects, internal forces arise from reactions within the object or system itself.
• While external forces instigate changes in motion or state, internal forces work to maintain stability or counteract such changes.
• Unlike external forces, internal forces always occur in equal and opposite pairs as explained by Newton's Third Law of motion. But remember, external forces do not necessarily have to adhere to these conditions.

How External Forces Influence Internal Forces

So how does the application of an external force influence internal forces? The answer is two-fold.

Firstly, when an external force is applied, internal forces develop in response to prevent the system from accelerating infinitely, as per Newton's Second Law.

For example, consider a tower of bricks. If you push (external force) against the tower, the individual bricks readjust their positions relative to each other, creating a new balance of internal forces. These internal responses resist further deformation and maintain the tower's stability.

Secondly, if the external force is strong enough to exceed the internal forces' resistance, deformation or change in state occurs. The object might fracture, rupture, or substantially change form, depending on the material properties.

\[ \text{{Newton's 2nd Law}}: \text{{Force}} = \text{{mass}} \times \text{{acceleration}} \]

In a nutshell, the interplay between external and internal forces governs how every object or structure react to changes in their environment or inter-object interactions. Understanding them is crucial to various disciplines like engineering, architecture, biomechanics and even arts!

Practical Approach: External Forces Examples

Now that we've got a strong understanding of the theory of external forces, let's take a more hands-on approach by looking at some examples of external forces in the real-world environment.

Real Life Examples of External Forces

Our daily life is filled with examples of external forces in action, often without us even recognizing them. As a physics student, learning to identify and analyse these forces will not only help you understand their theoretical aspects but also apply them in practical situations.

Here are a few illustrative examples:

• Pulling or pushing: When you push a door to open it, or pull a drawer to open it, you're exerting an external force. The door or drawer responds by moving in the direction of the force.
• Gravity: When you drop an apple from a tree, it falls towards the ground. This is a result of the external force of gravity acting on the apple. Note that the acceleration of the apple is constant at \(9.8 \, \text{m/s}^2\).
• Friction: Try sliding a book across a table. You'll notice that it eventually comes to a halt. This is due to the external force of friction acting between the book and the table surface.
• Upthrust: When you submerge a ball in a bucket of water and then let go, it rises to the surface. The external force of upthrust (or buoyancy) exerted by the water on the ball causes this.

Studying External Forces in Physics through Examples

Let's take a closer look at one of the examples and break it down to understand how the external force interacts with the object of interest.

This example highlights that understanding the impacts of different external forces in action can be vital to comprehending why objects behave the way they do.

Mathematical Representation: External Force Formula

To obtain an accurate, quantifiable understanding of external forces, we rely on mathematical formulas. As pre-established, the basic equation representing force vectors is derived from Newton's Second Law of Motion:

\[ \text{force} = \text{mass} \times \text{acceleration} \]

This formula allows us to calculate external forces acting upon objects given we know the object's mass and the acceleration caused by the force. A more sophisticated analysis of external forces might also involve trigonometric functions or calculus if the direction of the force changes.

Using Formulae to Calculate External Forces

Let's see how we can use formulas to calculate external forces in a real-world scenario.

By using mathematical formulas like these, external forces can be calculated under various scenarios, aiding physicists and engineers in their investigations and designs respectively.

Further Investigation: External Force and its Impact in Physics

It's clear that external forces are a considerable cog in the vast machinery of Physics. They lay the foundation for understanding motion, changes in state, equilibrium and various other significant concepts. With your fundamental awareness of the concept, let's push the boundaries further to unravel the deeper implications and applications of external forces in Physics.

How External Forces Shape Physics

Physics as a field studies the properties, changes and interactions of matter and energy. In this space, external forces serve as vital change agents. They are the stepping stones to understanding motion, examining energy transformations and establishing the fundamental laws governing our physical world.

External forces are the catalysts for change in any physical system. Without them, objects at rest would stay at rest, and objects in motion would continue in their constant motion forever, a scenario envisioned in Newton's First Law of motion.

\[ \text{{Newton's 1st Law}}: \text{{An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.}} \]

External forces, therefore, are essential to changing an object's state of motion or its physical state in any way. They can increase or decrease velocity, impart rotation, deform substances, even tear particles asunder at micro or subatomic levels (as in fission and fusion).

Furthermore, external forces are central to understanding the concept of energy. For instance, work is done when an external force moves an object, and the energy transferred during this process is calculated as the product of the force and the distance (Work done = Force × Distance). Similarly, the concept of power, which is the rate of doing work or transferring energy, also hinges on external forces.

\[ \text{{Work Size}} = \text{{Force}} \times \text{{Distance}} \] \[ \text{{Power}} = \frac{\text{{Work Size}}}{\text{{Time}}} \]

Also, external forces provide the real-world framework to manifest the abstract mathematical notions of vectors. Since force is a vector quantity, involving both magnitude and direction, illustrating forces graphically gives students a firm grasp on vector addition, resolution and equilibrium.

Beyond mechanics, external force has implications even in the domain of electricity and magnetism, where electric and magnetic forces guide the behaviour of charged particles. In thermodynamics, forces generate pressure that causes changes in volume or state of matter. In quantum mechanics, fundamental forces dictate atomic and subatomic interactions.

Lead by these catalysts, external forces shape the foundational principles and nuanced nuances of Physics, making them an inseparable component of the discipline.

The Role of External Forces in Classical Mechanics

Delving into one of the most fundamental domains of Physics: Classical Mechanics, external forces play a significant role. This study of the motion of objects often relies on understanding how external forces lead to changes in motion, as reflected in Newton's Laws of Motion.

Newtons First Law of Motion sets the stage for our understanding of external forces. It asserts the concept of Inertia - the resistance to change. Without an external force acting on it, an object will continue in its state of rest or uniform motion. Hence, the absence or presence of an external force is what reigns over an object’s state.

Newtons Second Law of Motion gives us the relationship between force, mass and acceleration. This again places external force in the limelight, as the agent causing any change in motion (acceleration). The greater the external force applied, the greater the magnitude of acceleration produced and vice versa. This law allows physicists to calculate the external force required in various scenarios – from those happening in your high school Physics lab to those in interstellar space.

\[ \text{{Newton's 2nd Law}}: \text{{Force}} = \text{{mass}} \times \text{{acceleration}} \]

Newtons Third Law of Motion reveals another facet of forces – action and reaction. Each external force has an equal and opposite force. This is why when you jump off a boat, the boat moves in the opposite direction.

Also, classical mechanics has branches which heavily depend on the study of external forces including statics (study of forces in equilibriums), dynamics (forces causing movements) and kinematics (movements under the effect of forces)

Internal forces are also critical in Classical Mechanics, but they usually cancel each other out considering the entire system of objects, leaving external forces as the true instigators of change, which is why in a majority of Classical Mechanics problems, we often deal primarily with external forces.

Lastly, let's not forget that many everyday phenomena you encounter are governed by external forces making classical mechanics an observable reality. So next time when you kick a football or park your car, take a moment to think about the external forces at work!