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Tamim Ahmed 3 Feb 2023 (2 months ago) Araihazar, Narayanganj, Dhaka, Bangladesh

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Force – Basics Press

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Force is a physical quantity that represents an influence on an object to cause a change in its motion. In physics, force is described as a push or pull on an object resulting from interactions with other objects. Forces can cause an object to accelerate, change direction, or maintain its velocity. Some common examples of forces include gravity, friction, and electromagnetic forces.

Development of the concept

The concept of force has been developed and refined over centuries of scientific inquiry. Early civilizations such as the Greeks and Romans had rudimentary ideas about the nature of force, but it wasn’t until the advent of modern science in the 17th and 18th centuries that a more systematic understanding of force emerged.

Isaac Newton, in his laws of motion, formulated the first mathematical definitions of force in terms of its effect on motion. He defined force as the rate of change of momentum of an object, and identified the three laws of motion that describe the relationship between force and motion.

In the 19th century, the study of thermodynamics and electromagnetism further advanced the understanding of force, and the concept was incorporated into these fields of study. The development of quantum mechanics and the theory of relativity in the 20th century also had a major impact on the concept of force, leading to a deeper understanding of the nature of physical interactions and the role of force in the universe.

Pre-Newtonian concepts

Before the development of modern physics, various pre-Newtonian concepts of force existed in ancient civilizations such as the Greeks, Romans, and Chinese. These early ideas were largely qualitative and based on everyday observations and experiences.

For example, the Greek philosopher Aristotle believed that force was a necessary condition for motion, and that an object would only continue to move if it was constantly being acted upon by a force. He also believed that heavier objects fall faster than lighter ones, which was later shown to be incorrect.

The Roman engineer and inventor Archimedes is credited with the concept of force being proportional to the displacement of an object, known as the principle of virtual work. He used this principle in his designs for machines and structures.

In ancient China, the philosopher Mozi described the concept of forces acting on objects in terms of push and pull. This idea laid the foundation for the later development of the concept of force as a push or pull in physics.

These pre-Newtonian concepts laid the groundwork for the more systematic and mathematical understanding of force developed by Isaac Newton and later physicists.

Newtonian mechanics

Newtonian mechanics, also known as classical mechanics, is the study of the motion of objects under the influence of forces. It is based on the laws of motion formulated by Sir Isaac Newton in the 17th century.

Newton’s three laws of motion state that:

1. An object at rest will remain at rest, and an object in motion will continue in a straight line at a constant speed, unless acted upon by a force.
2. The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass.
3. For every action, there is an equal and opposite reaction.

These laws form the basis of Newtonian mechanics and describe the relationship between force, mass, and acceleration. Newtonian mechanics has been extremely successful in describing the motion of everyday objects and celestial bodies, and remains a cornerstone of classical physics.

However, the limitations of Newtonian mechanics become apparent at very high speeds and in the presence of very strong gravitational fields. In these cases, the theory of relativity and quantum mechanics provide a more accurate description of physical phenomena. Nevertheless, Newtonian mechanics continues to play an important role in our understanding of the physical world and remains a fundamental part of modern physics.

Special theory of relativity

The special theory of relativity is a theory of physics developed by Albert Einstein in 1905. It fundamentally changed our understanding of space and time and is considered one of the pillars of modern physics.

The theory of special relativity is based on two key postulates:

1. The laws of physics are the same for all observers in uniform relative motion.
2. The speed of light in a vacuum is constant and the same for all observers, regardless of the motion of the light source.

From these postulates, Einstein derived several important consequences, including the fact that time and length are relative to the observer and can appear to be different depending on the relative motion of the observer. This led to the idea of spacetime, a four-dimensional fabric that describes the position and time of events in the universe.

The theory of special relativity also had important implications for our understanding of the nature of space and time and their relationship to matter and energy. It showed that mass and energy are interchangeable, leading to the famous equation E=mc^2, where E is energy, m is mass, and c is the speed of light.

The special theory of relativity is a fundamental theory that has been confirmed by numerous experiments and is widely accepted as a fundamental part of modern physics. It forms the basis for our understanding of the behavior of objects traveling at high speeds and has important implications for many areas of physics, including particle physics and cosmology.

Descriptions

Equilibrium

Equilibrium is a state in which an object or a system is balanced and no net force or torque acts upon it. This means that the forces acting on the object or system are balanced and the object is not accelerating or rotating.

In physics, there are two types of equilibrium: static and dynamic.

Static equilibrium occurs when an object or system is at rest and the forces acting on it are balanced, meaning that the net force on the object is zero. For example, a book resting on a table is in static equilibrium because the gravitational force acting on it is balanced by the force of the table.

Dynamic equilibrium occurs when an object or system is in motion and the forces acting on it are balanced, meaning that the net force on the object is zero and the acceleration of the object is also zero. For example, a car driving at a constant speed on a straight road is in dynamic equilibrium because the forces acting on it, such as friction and air resistance, are balanced by the force of the engine.

In both static and dynamic equilibrium, the net force and net torque acting on an object or system are zero. The concept of equilibrium is important in many areas of physics, including mechanics, thermodynamics, and engineering, as well as in everyday life.

Static

Static refers to a state in which an object or system is not changing its position or velocity. In other words, it is not in motion.

In physics, static is used to describe a state of balance in which the net force acting on an object is zero. When an object is in static equilibrium, it is at rest and is not accelerating, meaning that its velocity is constant and equal to zero.

Static equilibrium is an important concept in mechanics and engineering, as it provides a basis for understanding the stability and balance of objects and structures. For example, the stability of a building or a bridge can be analyzed by considering the forces acting on it and determining whether the object is in static equilibrium.

In addition, the study of static equilibrium is important in fields such as thermodynamics, where it is used to understand the behavior of systems in a state of balance, and in mechanics, where it is used to study the forces acting on objects in contact with each other. The concept of static equilibrium is also important in everyday life, as it is related to the stability and balance of objects in our environment.

Dynamic

Dynamic refers to a state in which an object or system is changing its position or velocity. In other words, it is in motion.

In physics, dynamic is used to describe a state in which an object or system is subjected to a net force, leading to a change in its velocity and, as a result, its position. When an object is in dynamic motion, it is accelerating, meaning that its velocity is changing over time.

Dynamic motion can occur in a variety of ways, such as uniform acceleration, non-uniform acceleration, and oscillatory motion. The study of dynamic motion is a central part of mechanics, and is used to understand the behavior of objects and systems subjected to forces and subjected to changes in velocity.

In addition, the study of dynamic motion is important in fields such as thermodynamics, where it is used to understand the behavior of systems undergoing changes in energy, and in engineering, where it is used to design and analyze systems that are in motion. The concept of dynamic motion is also important in everyday life, as it is related to the motion of objects in our environment, such as the movement of cars, trains, and airplanes.

Forces in quantum mechanics

In quantum mechanics, forces are described by the interaction between particles, which can be modeled as the exchange of particles known as bosons. The exchange of bosons between particles leads to the transfer of momentum, which results in a force.

One of the most important forces in quantum mechanics is the electromagnetic force, which arises from the exchange of photons between charged particles. This force is responsible for phenomena such as electric and magnetic interactions, and is described by the theory of quantum electrodynamics (QED).

Another important force in quantum mechanics is the strong nuclear force, which is responsible for binding protons and neutrons together in the nucleus of an atom. This force is described by the theory of quantum chromodynamics (QCD).

The weak nuclear force, which is responsible for processes such as beta decay, is also described by a quantum mechanical theory known as the weak interaction.

In quantum mechanics, forces are described by mathematical expressions known as interaction Hamiltonians, which describe the interactions between particles in terms of their position, momentum, and other quantum mechanical properties. These Hamiltonians are used to calculate the evolution of the quantum state of a system, and to make predictions about the behavior of particles and systems subjected to forces.

Overall, the study of forces in quantum mechanics plays a central role in our understanding of the behavior of the microscopic world and provides a foundation for our understanding of the interactions between particles and systems at the quantum level.

Feynman diagrams

Feynman diagrams are graphical representations of the interactions between particles in quantum field theory. They were first introduced by physicist Richard Feynman in the late 1940s and have since become an important tool for visualizing and understanding the behavior of particles and systems at the quantum level.

A Feynman diagram is a pictorial representation of a particle interaction, where lines represent particles, and the vertices where the lines meet represent the interactions between particles. Each line in a Feynman diagram corresponds to a particle and is directed, with the direction of the arrow indicating the direction of particle flow.

Feynman diagrams are used to calculate the probability amplitudes for particle interactions, which describe the likelihood of a particular process occurring. These probabilities are used to make predictions about the behavior of particles and systems and to understand the underlying physical processes that govern particle interactions.

Feynman diagrams have proven to be a powerful tool in particle physics, and are used in the calculation of many physical quantities, such as cross sections, decay rates, and other observables. They are also used in the development of theories, such as quantum electrodynamics (QED) and quantum chromodynamics (QCD), which describe the behavior of particles and systems at the quantum level.

Overall, Feynman diagrams play a crucial role in our understanding of the behavior of particles and systems at the quantum level, and are an important tool for physicists and scientists working in the field of quantum field theory.

Fundamental forces

There are four fundamental forces in nature that govern the behavior of all matter and energy:

1. Gravitational force: This is the force that attracts any two objects with mass towards each other. It is the weakest of the four fundamental forces, but it has an infinite range and affects all objects with mass.
2. Electromagnetic force: This is the force that acts between charged particles, such as electrons and protons. It is responsible for a wide range of phenomena, including electric and magnetic interactions, and is stronger than the gravitational force.
3. Weak nuclear force: This is the force that governs the decay of particles and is responsible for processes such as beta decay. It has a very short range, only affecting particles within the nucleus of an atom.
4. Strong nuclear force: This is the force that binds protons and neutrons together in the nucleus of an atom, and is responsible for maintaining the stability of atomic nuclei. It is the strongest of the four fundamental forces, but it only acts over a very short range.

Each of these fundamental forces is described by a different theory, and the behavior of particles and systems is determined by the balance between these forces. The study of the fundamental forces plays a central role in our understanding of the universe and provides a foundation for our understanding of the behavior of matter and energy.

Non-fundamental forces

Non-fundamental forces are forces that can be explained by other fundamental forces or interactions. Unlike fundamental forces, which are irreducible and cannot be reduced to other forces or interactions, non-fundamental forces arise from more complex physical phenomena and are not considered to be basic building blocks of nature.

Examples of non-fundamental forces include:

1. Friction: This force opposes the relative motion of two objects in contact. It can be explained by the electromagnetic force between the atoms in the two objects.
2. Tension: This force is exerted by a rope or cable when it is pulled tight. It can be explained by the electromagnetic force between the atoms in the rope or cable.
3. Normal force: This force acts perpendicular to a surface and supports an object that is in contact with the surface. It can be explained by the electromagnetic force between the atoms in the surface and the atoms in the object.
4. Air resistance: This force opposes the motion of an object through a fluid, such as air or water. It can be explained by the interaction of the fluid with the object.
5. Elastic force: This force is exerted by a stretched or compressed spring. It can be explained by the electromagnetic force between the atoms in the spring.

Non-fundamental forces are forces that can be explained by other fundamental forces or interactions. Unlike fundamental forces, which are irreducible and cannot be reduced to other forces or interactions, non-fundamental forces arise from more complex physical phenomena and are not considered to be basic building blocks of nature.

Examples of non-fundamental forces include:

1. Friction: This force opposes the relative motion of two objects in contact. It can be explained by the electromagnetic force between the atoms in the two objects.
2. Tension: This force is exerted by a rope or cable when it is pulled tight. It can be explained by the electromagnetic force between the atoms in the rope or cable.
3. Normal force: This force acts perpendicular to a surface and supports an object that is in contact with the surface. It can be explained by the electromagnetic force between the atoms in the surface and the atoms in the object.
4. Air resistance: This force opposes the motion of an object through a fluid, such as air or water. It can be explained by the interaction of the fluid with the object.
5. Elastic force: This force is exerted by a stretched or compressed spring. It can be explained by the electromagnetic force between the atoms in the spring.

Overall, non-fundamental forces are important in many areas of physics and engineering, including mechanics, thermodynamics, and materials science. However, they are not considered to be basic building blocks of nature like the four fundamental forces.

Overall, non-fundamental forces are important in many areas of physics and engineering, including mechanics, thermodynamics, and materials science. However, they are not considered to be basic building blocks of nature like the four fundamental forces.

Rotations and torque

Rotation is a type of motion in which an object spins around a fixed axis. The speed and direction of rotation are described by the angular velocity and angular momentum of the object.

Torque is a measure of the force that causes an object to rotate. It is defined as the product of the force acting on an object and the lever arm, which is the perpendicular distance from the axis of rotation to the point where the force is applied. Torque has the units of Newton-meters (Nm) or pound-feet (lb-ft).

The relationship between torque and rotational motion is described by Newton’s second law for rotational motion, also known as the law of torque. This law states that the net torque acting on an object is proportional to the rate of change of its angular momentum.

In other words, if a net torque is applied to an object, it will cause the object to rotate, and the amount of rotation will depend on the magnitude and direction of the torque, as well as the object’s moment of inertia, which is a measure of its resistance to rotation.

Torques play a crucial role in many physical systems, including engines, gears, and machines. They are also important in fields such as mechanics, engineering, and physics, where they are used to analyze the behavior of objects under rotation.

Centripetal force

The centripetal force is a force that acts on an object moving in a circular path and is directed towards the center of the circle. It is the force responsible for keeping an object moving in a circular path, rather than allowing it to fly off in a straight line.

The magnitude of the centripetal force is given by the equation: F = m * v^2 / r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

The centripetal force can have various physical origins, such as gravitational forces, electrostatic forces, or tension in a rope. For example, if an object is swinging in a circular path on the end of a rope, the tension in the rope provides the centripetal force. If a car is driving in a circle, the friction between the tires and the road provides the centripetal force that keeps the car moving in the circular path.

The concept of centripetal force is important in many areas of physics, including mechanics, astronomy, and engineering. Understanding the centripetal force allows us to analyze and understand the behavior of objects moving in circular paths, and is a fundamental part of our understanding of motion.

Kinematic integrals

Kinematic integrals are mathematical tools used in the field of classical mechanics to describe the motion of an object. They provide a way to calculate position, velocity, and acceleration of an object as a function of time.

The three main kinematic integrals are:

1. Displacement: This is the change in the position of an object over time, and can be calculated as the integral of velocity with respect to time.
2. Velocity: This is the rate of change of an object’s position over time, and can be calculated as the integral of acceleration with respect to time.
3. Acceleration: This is the rate of change of an object’s velocity over time, and can be calculated as the derivative of velocity with respect to time.

These integrals can be used to solve a variety of problems in classical mechanics, such as determining the trajectory of a projectile, calculating the motion of a pendulum, or determining the motion of an object under the influence of a force.

Kinematic integrals are important in many areas of physics and engineering, and are used to analyze and understand the behavior of objects in motion. They are a fundamental part of our understanding of mechanics and the study of motion.

Potential energy

Potential energy is a type of energy that an object possesses due to its position or configuration. It is the energy stored in an object due to its position relative to other objects or forces in the system.

For example, an object lifted above the ground possesses gravitational potential energy due to its position relative to the ground. A compressed spring also possesses potential energy due to its compressed configuration.

The concept of potential energy is important because it allows us to understand and analyze the energy stored in a system, and how that energy can be transformed into other forms of energy, such as kinetic energy.

The formula for potential energy depends on the type of force involved. For example, the formula for gravitational potential energy is given by: PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

In general, the total energy in a system is equal to the sum of its potential energy and kinetic energy. This principle, known as the law of conservation of energy, states that energy cannot be created or destroyed, but can only be transformed from one form to another.

The study of potential energy is a fundamental part of classical mechanics, and is used in many areas of physics and engineering, including thermodynamics, electromagnetism, and quantum mechanics.

Conservative forces

Conservative forces are forces that can be described by a potential energy function. The work done by a conservative force is path independent, meaning that the work done depends only on the initial and final positions of an object, and not on the path taken between those positions.

For example, the force of gravity is a conservative force because it can be described by a potential energy function, and the work done by gravity depends only on the initial and final heights of an object, and not on the path taken between those heights.

The work done by a conservative force can be calculated as the negative of the change in potential energy, W = -ΔPE. This means that the work done by a conservative force can be stored as potential energy, and that the total energy of the system is conserved.

Another important characteristic of conservative forces is that they obey the principle of least action, meaning that the path taken by an object under the influence of a conservative force will be the path of least action, or the path that minimizes the total energy of the system.

Examples of conservative forces include gravity, the force exerted by a spring, the force of a tension rope, and the electromagnetic force.

The study of conservative forces is a fundamental part of classical mechanics, and is used in many areas of physics and engineering, including thermodynamics, electromagnetism, and quantum mechanics.

Nonconservative forces

Nonconservative forces are forces that cannot be described by a potential energy function. The work done by a nonconservative force is path dependent, meaning that the work done depends on both the initial and final positions of an object, as well as the path taken between those positions.

Forces such as friction, air resistance, and drag are examples of nonconservative forces. These forces do work on an object, but the work done cannot be stored as potential energy. Instead, the work done by nonconservative forces is transformed into other forms of energy, such as heat, sound, or light.

Because nonconservative forces can convert potential energy into other forms of energy, they play a crucial role in many physical processes, such as thermal conduction and diffusion, the slowing down of moving objects, and the dissipation of energy in mechanical systems.

The study of nonconservative forces is a fundamental part of classical mechanics, and is used in many areas of physics and engineering, including thermodynamics, electromagnetism, and quantum mechanics.

Units of measurement

The unit of measurement for force in the International System of Units (SI) is the Newton (N). A Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared. In other words, 1 N = 1 kg * m/s^2.

Other units of force commonly used in physics and engineering include the kilogram-force (kgf), the pound-force (lbf), and the dyne.

In addition to force, there are several other units of measurement used in mechanics and related fields, including:

• Length: meter (m)
• Mass: kilogram (kg)
• Time: second (s)
• Energy: joule (J)
• Power: watt (W)
• Velocity: meter per second (m/s)
• Acceleration: meter per second squared (m/s^2)

It is important to choose the appropriate units for a given problem in order to obtain meaningful results and to facilitate comparison with other results in the field.

Force measurement

Force measurement is the process of determining the magnitude and direction of a force acting on an object. There are various methods for measuring forces, depending on the type of force, the size and scale of the force, and the conditions under which the force is acting. Some of the most common methods of force measurement include:

1. Spring scales: Spring scales use the relationship between the applied force and the resulting change in the length of a spring to measure force. They can be used to measure forces in a variety of applications, from weighing objects to measuring the force of a muscle contraction.
2. Load cells: Load cells use strain gauges or piezoelectric sensors to measure the deformation of a material caused by an applied force. Load cells are commonly used in industrial and laboratory settings to measure weight, force, and torque.
3. Force transducers: Force transducers are electronic devices that use sensors to convert the physical force being applied into an electrical signal that can be measured and analyzed. They are commonly used in testing and calibration systems, as well as in industrial automation and control systems.
4. Balance: A balance is a device that measures the force of gravity acting on an object by comparing it to a known reference mass. Balances are used to weigh objects and measure the force of weight.
5. Force gauges: Force gauges are handheld devices that measure force by measuring the deformation of a material or the displacement of a spring. They are commonly used in manual testing applications and for measuring force in the field.

Regardless of the method used, accurate force measurement is critical in many fields, including engineering, physics, biology, and medicine. Force measurement plays a key role in the development of new technologies, the testing and calibration of equipment, and the study of the fundamental laws of nature.

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