The document discusses the four fundamental forces in the universe: gravitational, electromagnetic, weak nuclear, and strong nuclear forces. It provides details on each force, including their relative strengths and characteristics. The document then discusses applications of these fundamental forces to ordinary mechanical systems, focusing on friction forces. It outlines the laws of static and kinetic friction, defining coefficients of static and kinetic friction as the ratio of frictional force to normal force. In summary, the document provides an overview of fundamental forces and their applications to mechanical systems like friction.
There are four fundamental forces of nature: the nuclear force, electromagnetic force, gravitational force, and weak force. The nuclear force binds nucleons together in the atomic nucleus. The electromagnetic force causes interactions between charged particles and is responsible for binding atoms and molecules. The gravitational force causes attraction between all masses and is responsible for planets, stars, and galaxies. The weak force is involved in nuclear decay and neutrino interactions and is mediated by the W and Z bosons.
Besides the 4 fundamental forces established and accepted by current science community, a new force is to be added. This is the familiar mechanical force mediated by the particle 'Phonon'. A new discovery.
This document discusses the four fundamental forces in nature: gravitational, electromagnetic, weak nuclear, and strong nuclear forces. It provides details on what each force is, how it acts, examples of its effects, and the theories behind it. A key point is that physicists believe these forces may be interrelated and emerged from a single force early in the universe, as described by various grand unified theories that aim to connect fundamental forces and particles.
This presentation covers the topics of forces, types of forces, balanced and unbalanced forces, and Newton's laws of motion. It defines a force as a push or pull and describes several types of forces including gravitational, electrical, air resistance, and normal forces. It explains that balanced forces result in no change in motion, while unbalanced forces cause acceleration. Newton's three laws of motion are also summarized, including that an object at rest stays at rest unless acted on by an unbalanced force, acceleration is directly proportional to net force, and for every action there is an equal and opposite reaction.
The document describes the four fundamental forces in nature: gravitational, electromagnetic, weak nuclear, and strong nuclear forces. Gravitational force is the weakest and acts between all masses. Electromagnetic force combines electric and magnetic forces and is stronger than gravity. Weak nuclear force is responsible for beta decay and is weaker than electromagnetic force but stronger than gravity. Strong nuclear force binds quarks and nucleons in the atomic nucleus and is the strongest force.
There are four fundamental forces in nature: the strong nuclear force, electromagnetic force, weak nuclear force, and gravitational force. The strong nuclear force binds protons and neutrons together in the nucleus of an atom. The electromagnetic force is responsible for electric and magnetic effects and acts over longer distances than the strong force. The weak nuclear force causes nuclear decay and has an extremely short range. Gravity is the weakest force but acts over the greatest distances and is responsible for attraction between all objects with mass.
There are 4 main universal forces: electromagnetic, strong nuclear, weak nuclear, and gravitational. The electromagnetic force acts on charged particles like protons and electrons and is responsible for electric and magnetic forces. The strong nuclear force binds protons and neutrons together in the nucleus. The weak nuclear force is involved in nuclear decay. The gravitational force acts between all masses and is responsible for keeping planets, stars, and galaxies in orbit.
The document defines and describes the four fundamental forces in the universe: gravitational force, which causes attraction between all masses; electromagnetic force, which is associated with electric and magnetic fields and is responsible for atomic structure; strong nuclear force, which acts between quarks and keeps nucleons packed together in the nucleus; and weak nuclear force, which is responsible for beta decay within the nucleus.
There are four fundamental forces of nature: the nuclear force, electromagnetic force, gravitational force, and weak force. The nuclear force binds nucleons together in the atomic nucleus. The electromagnetic force causes interactions between charged particles and is responsible for binding atoms and molecules. The gravitational force causes attraction between all masses and is responsible for planets, stars, and galaxies. The weak force is involved in nuclear decay and neutrino interactions and is mediated by the W and Z bosons.
Besides the 4 fundamental forces established and accepted by current science community, a new force is to be added. This is the familiar mechanical force mediated by the particle 'Phonon'. A new discovery.
This document discusses the four fundamental forces in nature: gravitational, electromagnetic, weak nuclear, and strong nuclear forces. It provides details on what each force is, how it acts, examples of its effects, and the theories behind it. A key point is that physicists believe these forces may be interrelated and emerged from a single force early in the universe, as described by various grand unified theories that aim to connect fundamental forces and particles.
This presentation covers the topics of forces, types of forces, balanced and unbalanced forces, and Newton's laws of motion. It defines a force as a push or pull and describes several types of forces including gravitational, electrical, air resistance, and normal forces. It explains that balanced forces result in no change in motion, while unbalanced forces cause acceleration. Newton's three laws of motion are also summarized, including that an object at rest stays at rest unless acted on by an unbalanced force, acceleration is directly proportional to net force, and for every action there is an equal and opposite reaction.
The document describes the four fundamental forces in nature: gravitational, electromagnetic, weak nuclear, and strong nuclear forces. Gravitational force is the weakest and acts between all masses. Electromagnetic force combines electric and magnetic forces and is stronger than gravity. Weak nuclear force is responsible for beta decay and is weaker than electromagnetic force but stronger than gravity. Strong nuclear force binds quarks and nucleons in the atomic nucleus and is the strongest force.
There are four fundamental forces in nature: the strong nuclear force, electromagnetic force, weak nuclear force, and gravitational force. The strong nuclear force binds protons and neutrons together in the nucleus of an atom. The electromagnetic force is responsible for electric and magnetic effects and acts over longer distances than the strong force. The weak nuclear force causes nuclear decay and has an extremely short range. Gravity is the weakest force but acts over the greatest distances and is responsible for attraction between all objects with mass.
There are 4 main universal forces: electromagnetic, strong nuclear, weak nuclear, and gravitational. The electromagnetic force acts on charged particles like protons and electrons and is responsible for electric and magnetic forces. The strong nuclear force binds protons and neutrons together in the nucleus. The weak nuclear force is involved in nuclear decay. The gravitational force acts between all masses and is responsible for keeping planets, stars, and galaxies in orbit.
The document defines and describes the four fundamental forces in the universe: gravitational force, which causes attraction between all masses; electromagnetic force, which is associated with electric and magnetic fields and is responsible for atomic structure; strong nuclear force, which acts between quarks and keeps nucleons packed together in the nucleus; and weak nuclear force, which is responsible for beta decay within the nucleus.
The document discusses the history and development of theories attempting to unify the fundamental forces. It describes how electromagnetism was unified and the development of the electroweak theory. Efforts were made to include the strong nuclear force through grand unified theories, but requiring extremely high energies. String theory is now the leading approach to achieve a theory of everything by unifying gravity with other forces. Further experiments are still needed to fully test theories and achieve unification.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Nuclear forces keep nucleons together through powerful short-range attraction between protons and neutrons. The mass of a nucleus is less than the total mass of its constituent particles due to the nuclear mass defect. This mass defect is converted to nuclear binding energy, which is released when the nucleus forms. Nuclei with intermediate atomic weights have the greatest stability and binding energy per particle, while the lightest and heaviest nuclei are less stable.
The document discusses the four fundamental forces: gravitational, electromagnetic, nuclear, and weak. It summarizes that the nuclear force was discovered after neutrons were discovered in 1932, and holds nucleons together in the nucleus. The nuclear force is charge independent, very strong but short range, repulsive at short distances, and acts through the exchange of pions between nucleons. The document provides details on the Yukawa potential and uncertainty principle as they relate to the nuclear force. It poses a multiple choice question about identifying an incorrect statement regarding the nuclear force.
The document discusses different types of forces including gravitational, magnetic, nuclear, and muscular forces. Gravitational force causes objects to pull on each other and keeps planets orbiting the sun. Magnetic force is exerted between magnets and metallic substances. Nuclear force binds quarks together inside protons and neutrons in atomic nuclei with a power 100 times greater than electromagnetic force. Muscular force allows animals to push and pull objects.
The document outlines key concepts in astronomy and physics, including the scientific method, fundamental forces, elementary particles, and atomic structure. It discusses the four fundamental forces (gravitational, electromagnetic, strong, and weak), elementary particles like protons, neutrons, electrons, and quarks, and provides classical and modern views of atomic structure. Key terms are defined related to these topics.
1. The document discusses the nature of energy and how it relates to concepts like matter, gravity, and spacetime. It describes how opposing forces generate vibration in the form of travelling waves of energy.
2. Gravity arises when atoms or molecules form, generating rotational movement of energy known as "conveyor belts of gravity." A larger mass results in more vigorous gravitational attraction due to more conveyor belts rotating simultaneously.
3. Near a black hole, the conveyor belts rotate in a harmonized way, increasing the outward push of gravity and diminishing the inward push. This warps spacetime outward, compressing the black hole's mass into a singularity from which nothing can escape.
1. Concept of WORK
2. Concept of ENERGY
3. Different forms of energy
Mechanical (Potential & Kinetic), Heat, Light, Chemical, Atomic, Electrical, Magnetic etc
4. Detailed idea of Mechanical Energy i.e Potential and Kinetic Energy.
5. Transformation between POTENTIAL and KINETIC energy.
6. Conservation of MECHANICAL ENERGY
7. Transformation of different ENERGIES.
8. Dissipation of ENERGY
Assuming that during the “big bang” matter and anti-matter pair production and
annihilation governed the first phase before the expansion and cool down of the
universe, we would expect to find a universe consisting of both matter and anti-matter
uniformly spread apart throughout space.
That is obviously not the case as we can observe today and we expect to find some
new kind of anti-symmetry between matter and anti-matter.
In this paper we will show a paradox that leads to the conclusion that anti-matter must
have "anti-gravity". Based on this conclusion we claim that matter and anti-matter
preserve two new conservation laws: 1. Conservation of gravity, 2. Conservation of
time.
Based on these new conservation laws we predict that anti-matter is uniformly spread,
as anti-atoms or anti-elementary particles, throughout space and it’s one of the main
reasons for space expansion.
We strongly believe that future tests on the influence of anti-matter on gravity and
time will prove this theory.
The document discusses the four fundamental forces in physics - strong, weak, electromagnetic, and gravitational. It proposes that all forces originated from a single unified force that evolved over time. The forces are conveyed through exchange of force-carrying particles. It further proposes that momentum is conveyed by quasi-particles called phonons, which were originally conceptualized in solid state physics. This could fulfill Newton's conception of momentum. The document advocates representing phonons as bees or butterflies rather than balls, to capture their versatile behaviors.
JOURNEY OF THE UNIVERSE FROM BIRTH TO REBIRTH WITH INSIGHT INTO THE UNIFIED I...SURAJ KUMAR
1) The document proposes a hypothesis for the universe's life cycle from birth to death and rebirth, referring to concepts like the cosmic microwave background radiation and spiral structure of galaxies and particles.
2) It suggests that the initial spontaneous symmetry breaking that triggered the Big Bang was gravity, represented by a spiral particle structure. This led to the formation of the Higgs field and then other fundamental particles.
3) The spiral structures of these elementary particles provide a unified approach for describing their interactions through properties like the orientation and rate of change of the spiral arms. This model aims to incorporate gravity into a unified theory.
The key differences between the states of matter are the distances between particles and the strength of intermolecular forces. In solids and liquids, particles are closer together due to stronger intermolecular forces. The state of a substance depends on a balance between kinetic energy of particles and the attractions between them. There are various types of intermolecular forces including hydrogen bonding, dipole-dipole interactions, and dispersion forces. The strength of these forces influences many physical properties such as boiling point, viscosity, and surface tension.
1) Neutron stars are the remnants of collapsed stars that have a mass greater than 1.4 solar masses. They form during type II supernovae following the collapse of massive red supergiant stars.
2) Pulsars are a type of neutron star that emit beams of electromagnetic radiation and appear to pulse due to their rotation. They were first discovered by Jocelyn Bell in 1967 through detecting their regular radio pulses.
3) Gravitational waves are ripples in spacetime caused by accelerating massive objects like neutron stars and black holes. Detecting gravitational waves from binary neutron star systems could provide insights into energetic cosmic events and test Einstein's theory of general relativity.
This document provides definitions and explanations of key concepts in SPM Physics 2009, including:
1) Definitions of speed, velocity, momentum, Newton's laws of motion, balanced and unbalanced forces, work, and energy.
2) Explanations of pressure, Pascal's principle, Archimedes' principle, and Bernoulli's principle.
3) Descriptions of wave reflection, refraction, diffraction, interference, and sound waves.
4) Overviews of circuits, electromagnetism, induced current, and direct/alternating current.
5) Definitions of nucleon number, isotopes, radioactivity, nuclear fission, and nuclear fusion.
Newton observed an apple falling from a tree, which led him to discover his law of universal gravitation. The law states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Specifically, the gravitational force between two objects equals G*(m1*m2)/r^2, where G is the gravitational constant, m1 and m2 are the object masses, and r is the distance between their centers. This explained gravity and allowed prediction of orbital motion.
Anti matters gravity paradox - updated versionEran Sinbar
Assuming that during the “big bang” matter and anti-matter pair production and
annihilation governed the first phase before the expansion and cool down of the
universe, we would expect to find a universe consisting of both matter and anti-
matter uniformly spread apart throughout space.
That is obviously not the case as we can observe today and we expect to find some
new kind of anti-symmetry between matter and anti-matter.
In this paper we will show a paradox that leads to the conclusion that anti-matter
must have "anti-gravity" . Based on this conclusion we claim that matter and anti-
matter preserve two new conservation laws: 1. Conservation of gravity, 2.
Conservation of time.
Based on these new conservation laws we predict that anti-matter is uniformly
spread, as anti-atoms or anti-elementary particles, throughout space and it’s one of
the main reasons for space expansion.
We strongly believe that future tests on the influence of anti-matter on gravity and
time will prove this theory.
This document discusses various magnetic properties including magnetization, magnetic induction, magnetic field intensity, magnetic susceptibility, magnetic permeability, diamagnetism, paramagnetism, ferromagnetism, and superparamagnetism. Magnetization is defined as the magnetic dipole moment induced per unit volume. Magnetic induction is the process by which a substance becomes magnetized by an external magnetic field. Magnetic field intensity characterizes the external magnetic field excluding the material's internal field. Magnetic susceptibility is the ratio of magnetization to magnetic field intensity. Magnetic permeability is the ratio of magnetic induction to magnetic field intensity. Diamagnetism occurs in materials with paired electrons that produce an induced magnetic moment opposite to an external field. Paramagnet
Magnetic materials form magnetic domains to minimize their magnetostatic energy. Domain walls separate domains with different magnetization orientations. Bloch walls have spins rotating continuously across the wall, while Neel walls have spins rotating in the plane of the wall. The equilibrium domain size and wall thickness are determined by a balance of exchange, anisotropy, magnetostatic, and wall energies. Various techniques like SEMPA, MFM, and magneto-optical imaging are used to observe domain structures with high resolution.
1. The document discusses the nature of gravity and how it arises from the interaction of energy flows through the "arteries and veins" that make up the fabric of spacetime.
2. Gravity normally arises from the rotation of "conveyor belts of gravity" formed by the integration of energies traveling in opposite directions. However, near a black hole these conveyor belts rotate in a unique way that increases the outward push of gravity and decreases the inward push.
3. This warping of the natural energy flows near a black hole leads to gravitational lensing, time dilation, and the trapping of matter and light within the black hole's event horizon.
1) Isaac Newton formulated his law of universal gravitation in 1666, which states that any two objects attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
2) Henry Cavendish experimentally determined the proportionality constant G in 1798, which is equal to 6.67 x 10-11 N m2 / kg2.
3) Newton's law of universal gravitation explains why objects like the moon orbit the earth rather than falling straight down, and suggests that the force of gravity is universal across all masses in the universe.
The document lists character archetypes from The Simpsons television show, with Homer described as stupid, Mr. Burns as greedy with power, Bart as the problematic child, Lisa as the smart child, Marge as the housewife, and Apu as an immigrant.
Donnella's Closet is an internet fashion company that sells handbags and accessories from emerging and established designers. It gives new fashion talent the opportunity to sell their unique collections through Donnella's Closet, an established and growing brand. The company was nominated for a 2010 Rising Star in Retail award and can be found online at shopdonnella.com or emergingfashionbrands.com.
The document discusses the history and development of theories attempting to unify the fundamental forces. It describes how electromagnetism was unified and the development of the electroweak theory. Efforts were made to include the strong nuclear force through grand unified theories, but requiring extremely high energies. String theory is now the leading approach to achieve a theory of everything by unifying gravity with other forces. Further experiments are still needed to fully test theories and achieve unification.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Nuclear forces keep nucleons together through powerful short-range attraction between protons and neutrons. The mass of a nucleus is less than the total mass of its constituent particles due to the nuclear mass defect. This mass defect is converted to nuclear binding energy, which is released when the nucleus forms. Nuclei with intermediate atomic weights have the greatest stability and binding energy per particle, while the lightest and heaviest nuclei are less stable.
The document discusses the four fundamental forces: gravitational, electromagnetic, nuclear, and weak. It summarizes that the nuclear force was discovered after neutrons were discovered in 1932, and holds nucleons together in the nucleus. The nuclear force is charge independent, very strong but short range, repulsive at short distances, and acts through the exchange of pions between nucleons. The document provides details on the Yukawa potential and uncertainty principle as they relate to the nuclear force. It poses a multiple choice question about identifying an incorrect statement regarding the nuclear force.
The document discusses different types of forces including gravitational, magnetic, nuclear, and muscular forces. Gravitational force causes objects to pull on each other and keeps planets orbiting the sun. Magnetic force is exerted between magnets and metallic substances. Nuclear force binds quarks together inside protons and neutrons in atomic nuclei with a power 100 times greater than electromagnetic force. Muscular force allows animals to push and pull objects.
The document outlines key concepts in astronomy and physics, including the scientific method, fundamental forces, elementary particles, and atomic structure. It discusses the four fundamental forces (gravitational, electromagnetic, strong, and weak), elementary particles like protons, neutrons, electrons, and quarks, and provides classical and modern views of atomic structure. Key terms are defined related to these topics.
1. The document discusses the nature of energy and how it relates to concepts like matter, gravity, and spacetime. It describes how opposing forces generate vibration in the form of travelling waves of energy.
2. Gravity arises when atoms or molecules form, generating rotational movement of energy known as "conveyor belts of gravity." A larger mass results in more vigorous gravitational attraction due to more conveyor belts rotating simultaneously.
3. Near a black hole, the conveyor belts rotate in a harmonized way, increasing the outward push of gravity and diminishing the inward push. This warps spacetime outward, compressing the black hole's mass into a singularity from which nothing can escape.
1. Concept of WORK
2. Concept of ENERGY
3. Different forms of energy
Mechanical (Potential & Kinetic), Heat, Light, Chemical, Atomic, Electrical, Magnetic etc
4. Detailed idea of Mechanical Energy i.e Potential and Kinetic Energy.
5. Transformation between POTENTIAL and KINETIC energy.
6. Conservation of MECHANICAL ENERGY
7. Transformation of different ENERGIES.
8. Dissipation of ENERGY
Assuming that during the “big bang” matter and anti-matter pair production and
annihilation governed the first phase before the expansion and cool down of the
universe, we would expect to find a universe consisting of both matter and anti-matter
uniformly spread apart throughout space.
That is obviously not the case as we can observe today and we expect to find some
new kind of anti-symmetry between matter and anti-matter.
In this paper we will show a paradox that leads to the conclusion that anti-matter must
have "anti-gravity". Based on this conclusion we claim that matter and anti-matter
preserve two new conservation laws: 1. Conservation of gravity, 2. Conservation of
time.
Based on these new conservation laws we predict that anti-matter is uniformly spread,
as anti-atoms or anti-elementary particles, throughout space and it’s one of the main
reasons for space expansion.
We strongly believe that future tests on the influence of anti-matter on gravity and
time will prove this theory.
The document discusses the four fundamental forces in physics - strong, weak, electromagnetic, and gravitational. It proposes that all forces originated from a single unified force that evolved over time. The forces are conveyed through exchange of force-carrying particles. It further proposes that momentum is conveyed by quasi-particles called phonons, which were originally conceptualized in solid state physics. This could fulfill Newton's conception of momentum. The document advocates representing phonons as bees or butterflies rather than balls, to capture their versatile behaviors.
JOURNEY OF THE UNIVERSE FROM BIRTH TO REBIRTH WITH INSIGHT INTO THE UNIFIED I...SURAJ KUMAR
1) The document proposes a hypothesis for the universe's life cycle from birth to death and rebirth, referring to concepts like the cosmic microwave background radiation and spiral structure of galaxies and particles.
2) It suggests that the initial spontaneous symmetry breaking that triggered the Big Bang was gravity, represented by a spiral particle structure. This led to the formation of the Higgs field and then other fundamental particles.
3) The spiral structures of these elementary particles provide a unified approach for describing their interactions through properties like the orientation and rate of change of the spiral arms. This model aims to incorporate gravity into a unified theory.
The key differences between the states of matter are the distances between particles and the strength of intermolecular forces. In solids and liquids, particles are closer together due to stronger intermolecular forces. The state of a substance depends on a balance between kinetic energy of particles and the attractions between them. There are various types of intermolecular forces including hydrogen bonding, dipole-dipole interactions, and dispersion forces. The strength of these forces influences many physical properties such as boiling point, viscosity, and surface tension.
1) Neutron stars are the remnants of collapsed stars that have a mass greater than 1.4 solar masses. They form during type II supernovae following the collapse of massive red supergiant stars.
2) Pulsars are a type of neutron star that emit beams of electromagnetic radiation and appear to pulse due to their rotation. They were first discovered by Jocelyn Bell in 1967 through detecting their regular radio pulses.
3) Gravitational waves are ripples in spacetime caused by accelerating massive objects like neutron stars and black holes. Detecting gravitational waves from binary neutron star systems could provide insights into energetic cosmic events and test Einstein's theory of general relativity.
This document provides definitions and explanations of key concepts in SPM Physics 2009, including:
1) Definitions of speed, velocity, momentum, Newton's laws of motion, balanced and unbalanced forces, work, and energy.
2) Explanations of pressure, Pascal's principle, Archimedes' principle, and Bernoulli's principle.
3) Descriptions of wave reflection, refraction, diffraction, interference, and sound waves.
4) Overviews of circuits, electromagnetism, induced current, and direct/alternating current.
5) Definitions of nucleon number, isotopes, radioactivity, nuclear fission, and nuclear fusion.
Newton observed an apple falling from a tree, which led him to discover his law of universal gravitation. The law states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Specifically, the gravitational force between two objects equals G*(m1*m2)/r^2, where G is the gravitational constant, m1 and m2 are the object masses, and r is the distance between their centers. This explained gravity and allowed prediction of orbital motion.
Anti matters gravity paradox - updated versionEran Sinbar
Assuming that during the “big bang” matter and anti-matter pair production and
annihilation governed the first phase before the expansion and cool down of the
universe, we would expect to find a universe consisting of both matter and anti-
matter uniformly spread apart throughout space.
That is obviously not the case as we can observe today and we expect to find some
new kind of anti-symmetry between matter and anti-matter.
In this paper we will show a paradox that leads to the conclusion that anti-matter
must have "anti-gravity" . Based on this conclusion we claim that matter and anti-
matter preserve two new conservation laws: 1. Conservation of gravity, 2.
Conservation of time.
Based on these new conservation laws we predict that anti-matter is uniformly
spread, as anti-atoms or anti-elementary particles, throughout space and it’s one of
the main reasons for space expansion.
We strongly believe that future tests on the influence of anti-matter on gravity and
time will prove this theory.
This document discusses various magnetic properties including magnetization, magnetic induction, magnetic field intensity, magnetic susceptibility, magnetic permeability, diamagnetism, paramagnetism, ferromagnetism, and superparamagnetism. Magnetization is defined as the magnetic dipole moment induced per unit volume. Magnetic induction is the process by which a substance becomes magnetized by an external magnetic field. Magnetic field intensity characterizes the external magnetic field excluding the material's internal field. Magnetic susceptibility is the ratio of magnetization to magnetic field intensity. Magnetic permeability is the ratio of magnetic induction to magnetic field intensity. Diamagnetism occurs in materials with paired electrons that produce an induced magnetic moment opposite to an external field. Paramagnet
Magnetic materials form magnetic domains to minimize their magnetostatic energy. Domain walls separate domains with different magnetization orientations. Bloch walls have spins rotating continuously across the wall, while Neel walls have spins rotating in the plane of the wall. The equilibrium domain size and wall thickness are determined by a balance of exchange, anisotropy, magnetostatic, and wall energies. Various techniques like SEMPA, MFM, and magneto-optical imaging are used to observe domain structures with high resolution.
1. The document discusses the nature of gravity and how it arises from the interaction of energy flows through the "arteries and veins" that make up the fabric of spacetime.
2. Gravity normally arises from the rotation of "conveyor belts of gravity" formed by the integration of energies traveling in opposite directions. However, near a black hole these conveyor belts rotate in a unique way that increases the outward push of gravity and decreases the inward push.
3. This warping of the natural energy flows near a black hole leads to gravitational lensing, time dilation, and the trapping of matter and light within the black hole's event horizon.
1) Isaac Newton formulated his law of universal gravitation in 1666, which states that any two objects attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
2) Henry Cavendish experimentally determined the proportionality constant G in 1798, which is equal to 6.67 x 10-11 N m2 / kg2.
3) Newton's law of universal gravitation explains why objects like the moon orbit the earth rather than falling straight down, and suggests that the force of gravity is universal across all masses in the universe.
The document lists character archetypes from The Simpsons television show, with Homer described as stupid, Mr. Burns as greedy with power, Bart as the problematic child, Lisa as the smart child, Marge as the housewife, and Apu as an immigrant.
Donnella's Closet is an internet fashion company that sells handbags and accessories from emerging and established designers. It gives new fashion talent the opportunity to sell their unique collections through Donnella's Closet, an established and growing brand. The company was nominated for a 2010 Rising Star in Retail award and can be found online at shopdonnella.com or emergingfashionbrands.com.
The document compares past and present US presidents to movie and TV characters. Bush and Cheney are likened to the Dukes of Hazard due to getting into trouble. Abraham Lincoln is placed on the movie poster for Liar Liar due to his honesty. Bill Clinton is compared to James Bond for his ability to talk his way out of scandals. Obama and Biden are portrayed as an 80s cop flick, with Obama as the new rookie and Biden the experienced chief. Ronald Reagan is imagined as Obi-Ron Kenobi from Star Wars due to his fondness for the series.
Apresentação Câmara Técnica Áreas Verdes 2016copelli
O documento descreve o Programa de Monitoramento da Cobertura Vegetal do Rio de Janeiro, que mapeia as áreas de floresta remanescente na cidade utilizando sensoriamento remoto e levantamentos de campo. O programa identificou que 29% da área da cidade ainda possui cobertura vegetal nativa, enquanto as áreas urbanizadas correspondem a 66% do território. As principais transformações entre 2010-2014 incluíram a conversão de florestas e brejos para uso urbano e solo exposto.
Humidity refers to the amount of water vapor in the air, measured as a percentage. Dew point is the temperature at which water vapor condenses. Clouds form when the air reaches the dew point temperature. Different types of clouds like cirrus, cumulus and stratus form at different levels and produce different types of precipitation.
The document discusses the creation of logos, propaganda posters, and visuals for political parties. It includes sections from multiple students. One student created a green party focused on environmental issues with a simple name-based logo in green and blue. Another created a capitalist party with propaganda posters to attract voters and change views. A third created an international neutral party promoting equality with a logo and posters sending that message.
This document discusses capitalism, mercantilism, and their implications. It begins by defining capitalism as a private economic system where individuals and businesses exchange goods and services through complex market transactions. It then defines mercantilism as Europe's 16th-18th century economic policy focused on acquiring gold and silver. It questions if capitalism is the new mercantilism since both aim to expand production and trade. It also discusses how mercantilism drove European expansion through the slave trade and search for resources like gold. Finally, it summarizes how capitalism faced crises in the 20th century from wars and ideologies but ultimately emerged as the dominant victorious system.
ACK Travel is a leading corporate travel management company in India that provides integrated travel solutions. Their global technology infrastructure allows corporations to analyze travel data and maximize efficiency and return on investment. ACK Travel aims to anticipate customer needs and respond with excellence in their people, processes, and technologies. They were founded in 2006 and have experienced consistent growth through their customer-focused and service-oriented approach. Services include domestic and international air, rail, bus, taxi, hotels, visas, holidays, and foreign exchange. Special offers provide additional value to customers.
The document discusses the expansion of western civilization and global trade networks from the 15th century onward. It describes how technological developments like the compass and mapmaking enabled longer ocean voyages. Countries like Portugal sought to protect their commercial interests by establishing forts along trade routes. Explorers like Columbus and Magellan opened up sea routes connecting Europe, Africa, Asia, and the Americas, integrating these regions into a growing global economy. Over time, more areas and peoples around the world were incorporated into the expanding webs of trade, leading to profound cultural and economic changes on a global scale.
ACK Travel is a leading corporate travel management company in India that provides integrated travel solutions. Their global technology infrastructure allows corporations to analyze travel data and maximize efficiency and return on investment. ACK Travel aims to anticipate customer needs and respond with excellent service. They were founded in 2006 and have experienced consistent growth through their customer-focused and service-oriented approach. Services include domestic and international air, rail, bus, taxi, hotels, visas, holidays, and foreign exchange. Special offers provide additional value to customers. ACK Travel ensures the best rates through direct connections with airlines and well-trained staff.
Existen dos tipos principales de bailes: bailes en pareja como el tango, paso doble y vals, y bailes individuales como el hip-hop, funky y danza del vientre. Algunos ejemplos comunes de bailes en pareja son el tango, salsa y rock and roll, mientras que el hip-hop, street dance y danza del vientre son bailes individuales más populares.
The document discusses several dying languages:
- The Tsoa language spoken in Botswana is being replaced by Setswana.
- Several languages in Australia such as Martuthunira are extinct, while others like Nukunu have less than 10 speakers remaining.
- The document also mentions languages such as Livonian (spoken in Latvia), Tibetan, and the ancient English language as examples of dying languages.
Hurricanes form over warm ocean waters and require specific conditions including warm temperatures, low pressure, high humidity, and the Coriolis effect. They can produce dangerous storm surges that are the most damaging part of a hurricane. Thunderstorms form from cumulus clouds and can produce tornadoes, hail, lightning and heavy rain. Flash floods occur when rainwater cannot drain quickly from an area, while river floods happen when a river overflows its banks due to heavy rainfall.
The document discusses different types of forces including contact forces, normal force, tension force, spring force, frictional force, air resistance force, applied force, buoyant force, gravitational force, magnetic force, electrical forces, strong force, electromagnetic force, weak force, and gravitational force. It provides definitions and examples for each force and describes their characteristics such as how they are generated and their relative strengths. Key formulas related to these forces are also presented.
The sand increases the coefficient of friction between the tires of a car and the road, making it safer to drive on icy roads. Therefore, the correct answer is 2.
This document discusses the four fundamental forces in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. It provides details on each force, including a definition, examples of effects, examples of applications, and key properties like range and relative strength. The gravitational force acts over infinite distances and causes attraction between masses. The electromagnetic force acts via electric and magnetic fields between charged particles over infinite distances. The strong nuclear force binds quarks within protons and neutrons over very short distances, while the weak nuclear force is responsible for radioactive decay over an extremely short range.
Physics is related to other sciences through concepts like:
- Mathematics studies physical variables that led to calculus.
- Chemistry uses concepts like X-rays and radioactivity from Physics.
- Astronomy uses telescopes and discoveries enabled by Physics.
- Biology applies concepts like pressure measurements and imaging from Physics.
- Meteorology uses discoveries about pressure changes from Physics.
The four fundamental forces that govern all phenomena are the gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Conservation laws state that certain physical quantities like energy, mass, linear momentum, and angular momentum remain constant over time in closed systems.
The document discusses different types of forces including air resistance, applied, spring, frictional, gravitational, electrical, normal, and magnetic forces. It provides brief definitions and explanations of each force. For example, it states that air resistance is friction between an object and air caused by molecules bumping into moving objects. Frictional forces result from molecular adhesion and surface roughness when two materials are in contact. Gravitational force is defined by Newton's law of universal gravitation. Magnetic force differs from gravitational and electrical forces in that its potential energy comes from an electrical field over time.
- A force is any influence that causes an object to change its motion, either by starting to move, changing speed, or changing direction. The newton is the SI unit used to measure force.
- Electrostatic force results from stationary or slow-moving electrical charges and holds together electromagnetic fields created by particles like electrons and protons.
- Friction is a force that opposes the relative motion between two objects in contact. It allows us to walk, sit, climb stairs, and use devices that require movement.
This document discusses different types of forces and energy. It defines force as a push or pull on an object and lists nine common types of forces: frictional, normal, magnetic, air resistance, applied, spring, gravitational, electrical, and tension. It then defines energy as the ability to make things happen or cause change. The document outlines six main types of energy: sound, wind, light, kinetic, potential, and heat. Brief descriptions are provided for each type of force and energy.
This document defines different types of forces and energy. It describes 9 types of forces: frictional, normal, magnetic, air resistance, applied, spring, gravitational, electrical, and tension. It explains that force is a push or pull on an object. It then defines 7 types of energy: sound, wind, light, kinetic, potential, and heat. Force and energy allow things in the world to function and change. Force causes motion or tries to stop motion while different forms of energy underlie everyday phenomena and power technologies.
Physics is the study of natural phenomena in the physical world. It aims to understand and describe nature at its most fundamental level by making observations, performing experiments, and developing theories to explain experimental results. Some key ideas discussed are:
- Physics studies both macroscopic phenomena visible to the naked eye and microscopic phenomena at atomic and nuclear scales.
- The scientific method involves systematic observation, experimentation, and mathematical modeling to understand natural phenomena.
- Major forces that govern physical interactions are gravitational, electromagnetic, strong nuclear, and weak nuclear forces. The electromagnetic force is the strongest at atomic and molecular scales.
This document discusses the concept of forces in physics. It defines a force as a push or pull on an object and explains that forces are vectors that have both magnitude and direction. There are four main forces in nature: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. Dynamics and statics are introduced as areas of study related to forces and motion. Newton's three laws of motion are outlined. Common ways of measuring mass and examples of force problems are provided, including free body diagrams, friction, inclined planes, and pulleys.
First, describe what a force is and what effects forces have on obje.pdfkostikjaylonshaewe47
First, describe what a force is and what effects forces have on objects. Provide one or two
examples of forces operating at a macroscopic scale to help you form analogies to describe
atomic phenomena. Then describe the forces involved in holding matter together at the atomic
level. Describe what would happen if various atomic forces disappeared? Also, provide a
description of some of the forces between atoms that result in molecules and larger collections of
atoms, and how these forces are important
Solution
Force changes the state of motion and state of rest , Force is a push or pull which creats
acceleration , forces changes direction of the objects moving . force change shape of the objects,
force is the capacity to do work.
Forces work at the macroscopic level prmarly is gravity which is responsible for the whole mass
in the universe to stay in tact with out getting fly away , the same gravity makes stars , solar
systems and helps the formation of planets.
The fource basic forces of nature are , Gravity , Electromagnetic , strong nuclear forces and weak
nuclear forces, out of which gravitational forces works at macroscopic scale and rest of the
threee works in microscopic scale on matter.
Electromagnetic force is responsible for holding all the atoms in molecules to gether ,and also
the same force behind all the chemical reactions. the stong nuclear and weak nuclear forces are
the backbone behind the binding of nucleons in nucleus.
Strong and weak nuclear force play key role in the formation of heavy nucleus from individual
protons, electromagnetic forces are responsible for the formation of atoms , with out either stong
nuclear and EM force atoms may not exist in our universe , and gravity plays the leed role for the
formation of stars where the systhesis of all the nucleus takes places, with out gravity the
universe may left with individual protons and electrons .
The residual attractive or repulsive forces between atoms, molecules, and surfaces, as well as
other intermolecular forces are called vander waals forces, which arise due to electromagnetic
fields, van der Waals forces are weaker than normal covalent ionic bonds which are short-range
forces and should be considered only if the molecules are closer , these forces are important in
the formation of macrosizd molecules in the formation fo liquids and protein stuctures and DNA..
Forces can be categorized as either contact forces or non-contact forces. Contact forces require physical contact between objects and include applied forces, normal forces, friction, tension, and spring forces. Non-contact forces do not require physical contact and include gravitational, magnetic, and electrostatic forces. Pressure is defined as the force applied per unit area and is measured in Pascals. Factors like magnitude of force and contact area determine the level of pressure, with high pressure applications including hydraulic systems and low pressure applications including building foundations and snow shoes.
Grand unified field theory a predator prey approach corroboration dissipation...Alexander Decker
The document discusses the four fundamental interactions in nature: gravitation, electromagnetism, strong nuclear force, and weak nuclear force. It describes how each interaction is mediated by different bosons being exchanged between fermions. The strong nuclear force binds quarks together via gluon exchange. The document also discusses how gravitation, while the weakest force on small scales, becomes important on large macroscopic scales due to its infinite range and inability to be shielded against.
The document discusses different types of forces including frictional, gravitational, magnetic, muscular, electrostatic, and normal forces. It defines each force and provides relevant formulas. Frictional force opposes motion between two surfaces in contact. Gravitational force is due to the attraction between masses and equals an object's weight. Magnetic force is exerted by magnets. Muscular force results from muscle action. Electrostatic force acts between charged bodies. Normal force supports contact between surfaces. Balanced forces do not cause acceleration while unbalanced forces do. The three laws of motion are also summarized.
1. Gravity arises from the rotation of "conveyor belts of gravity" between atoms and molecules. These conveyor belts are formed from the rotational movement of energies traveling through the "arteries and veins" that make up spacetime.
2. In a black hole, these conveyor belts rotate in a unique way where energies in the arteries accelerate while energies in the veins decelerate, greatly increasing the outward push of gravity near the black hole.
3. This intense gravitational force near a black hole causes effects like gravitational lensing, where light bends as it approaches the black hole, and time dilation, where time passes more slowly near the black hole.
The document discusses elementary particles and their classification. It describes how elementary particles are divided into two main groups: fermions and bosons. Fermions include quarks and leptons, which have half-integer spin and obey the Pauli exclusion principle. Bosons have integer spin and obey Bose-Einstein statistics, carrying the fundamental forces. The standard model of particle physics describes three of the four fundamental forces and all known elementary particles.
This document discusses the key concepts of gravitation, including:
1) Isaac Newton discovered the law of universal gravitation after observing an apple fall from a tree, realizing all objects attract each other with a gravitational force.
2) Newton's law of universal gravitation states that every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
3) The gravitational force between two objects follows Newton's third law of motion, with equal but opposite forces between the objects.
1. 1
Chapter No. 05
Mohd Yousuf Soomro ( Lecturer )
Applications Of Newton’s Laws Institute of Physics
5-1 Force laws:
To understand the effects of forces a detailed microscopic understanding of interaction
of objects with their environment is necessary.
All of known forces in the universe can be grouped into four types.
1- The Gravitational forces
2- The Electromagnetic forces
3- The Weak Nuclear forces
4- The Strong Nuclear forces.
1- The Gravitational forces:
It originates with the presence of matter. The gravitational force between two protons
just touching their surfaces is about 10-38 of the strong force between them.
The principal difference between gravitation & other forces is that, on the practical
scale, gravity is cumulative and infinite in range. Gravity is the weakest of the four
fundamental forces, yet it is the dominant force in the universe for shaping the large
scale structure of galaxies, stars, etc.
The gravitational force between two masses m1 and m2 is given by the relationship:
This is often called the "universal law of gravitation" and G the universal gravitation
constant. It is an example of an inverse square law force. The force is always attractive
and acts along the line joining the centers of mass of the two masses. The forces on the
two masses are equal in size but opposite in direction, obeying Newton's third law.
Viewed as an exchange force, the mass less exchange particle is called the graviton.
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2. 2
The gravity force has the same form as Coulomb's law for the forces between electric
charges, i.e., it is an inverse square law force which depends upon the product of the
two interacting sources.
2- The Electromagnetic forces:
Electromagnetism is important in the structure & the interaction of fundamental particle.
It is also responsible for the binding of atoms & the structure of solids. the
electromagnetic force manifests itself through the forces between charges.
The electromagnetism force between two neighboring protons is about 10-2 of the strong
force. The electromagnetic force is a force of infinite range which obeys the inverse
square law, and is of the same form as the gravity force.
3- The Weak Nuclear forces:
The weak force is responsible for certain radioactive process & other similar decay
processes involving fundamental particles. The weak force between two neighboring
protons is about 10-7 of strong force between them. One of the four fundamental forces,
the weak interaction involves the exchange of the intermediate vector bosons, the W and
the Z. Since the mass of these particles is on the order of 80 GeV, the uncertainty
principle dictates a range of about 10-18 meters which is about 0.1% of the diameter of a
proton.
It is crucial to the structure of the universe in that
1. The sun would not burn without it since the weak interaction causes the transmutation
p ≥ n so that deuterium can form and deuterium fusion can take place.
2. It is necessary for the buildup of heavy nuclei.
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3. 3
It was in radioactive decay such as beta decay that the existence of the weak interaction
was first revealed.
4- The Strong Nuclear force:
A force which can hold a nucleus together against the enormous forces of repulsion of
the protons is strong indeed. However, it is not an inverse square force like the
electromagnetic force and it has a very short range.
It is responsible for the binding of the nuclei, is the dominant force in the reaction &
decays of most of the fundamental particles.
The relative strength b/w two neighboring protons is 1. the strong force is 1038 times
greater than gravitational force.
Fundamental Forces
Unification for forces:
In 19th century James Clerk Maxwell united the separate electric & magnetic fields into
a single electromagnetism force.
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4. 4
In 1967 a theory was proposed by “Dr. Abdus Salam”, “Stephen Weinberg”.
According to this theory the weak & electromagnetism forces could be regarded a part
of a single force called electroweak force.
Theories called GUTs (Grand Unification Theories) predicts about the unification of
strong and electroweak forces.
Other theory called TOE ( Theory of everything ) which unified the Strong,
electroweak & gravitational forces.
Prediction of TOE:
One prediction of these theories is that proton should not be a stable particle but should
decay on a time scale greater than 1031 years.
One way to test this theory is to which collection of 5.3 X 10 33 protons from a year to if
one of proton decays.
Electroweak Unification
The discovery of the W and Z particles, the intermediate vector bosons, in 1983 brought
experimental verification of particles whose prediction had already contributed to the
Nobel prize awarded to Weinberg, Salam, and Glashow in 1979. The photon , the
particle involved in the electromagnetic interaction, along with the W and Z provide the
necessary pieces to unify the weak and electromagnetic interactions. With masses
around 80 and 90 GeV, respectively, the W and Z were the most massive particles seen
at the time of discovery while the photon is mass less.
The discovery of the W and Z particles in 1983 was hailed as a confirmation of the
theories which connect the weak force to the electromagnetic force in electroweak
unification
Grand Unification
Grand unification refers to unifying the strong interaction with the unified electroweak
interaction.
One prediction of the grand unified theories is that the proton is unstable at some level.
In the 1970's, Sheldon Glashow and Howard Georgi proposed the grand unification of
the strong, weak, and electromagnetic forces at energies above 1014 GeV. If the ordinary
concept of thermal energy applied at such times, it would require a temperature of 1027K
for the average particle energy to be 1014 GeV.
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5. 5
The unification of the strong force is well beyond our reach at the present time, and the
unification of gravity with the other three is out of reach for earthbound experiments.
This has led to greater cooperation between high-energy particle physicists and
astrophysicists as each group realizes that some of their answers can only come from the
other.
Ordinary Mechanical Systems:
Ordinary mechanical system involves only two forces.
(1)Gravity
(2) Electromagnetism
The gravitational force is apparent property in the Earth’s attraction for objects, which
gives them weight.
All other forces are electromagnetism in origin.
I. Contact forces
II. Viscous forces
III. Tensile forces
IV. Elastic forces
I. Contact forces:
There are two kinds of contact forces:
a. Normal Force
b. Frictional Force
a. Normal force:
Normal force is produced in bodies when one body pushes on another.
The normal force is defined as the net force compressing two parallel surfaces together;
its direction is perpendicular to the surfaces.
b. Frictional force:
Frictional force Produced b/w bodies when one surface rubs against another.
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6. 6
II Viscous forces:
Air resistance.
III Tensile forces:
Tensile forces are produced in a stretched rope or string.
Tension is a reaction force applied by a stretched string (rope or a similar object) on the
objects which stretch it. The direction of the force of tension is parallel to the string, away
from the object exerting the stretching force. So if an object hangs from a rope due to
gravity, the gravitational force on the object points downward, and there is an equal
tension force in the rope point upward, making the net force on the object equal to zero.
Tension exists also inside the string itself: if the string is considered to be composed of
two parts, tension is the force which the two parts of the string apply on each other. The
amount of tension in the string determines whether it will break, as well as its vibrational
properties, which are used in musical instruments.
IV Elastic forces:
Elastic forces are that kind of forces arising from the deformation of a solid body which
depends only on the body's instantaneous deformation and not on its previous history,
and which is conservative. These are produced in a spring
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7. 7
6.2 FRICTIONAL FORCES:
When one body slides over the surface of another body, an opposing force is set up to
resist the motion. This force which opposes the motion is called “force of friction” or
friction.
Friction is the resistive force acting between bodies that tends to oppose and damp out
motion. Friction is usually distinguished as being either
1. static friction (the frictional force opposing placing a body at rest into motion)
and
2. Kinetic friction (the frictional force tending to slow a body in motion).
3. In general, static friction is greater than kinetic friction.
The friction force is electromagnetic in origin: atoms of one surface "stick" to atoms of
the other briefly before snapping apart, causing atomic vibrations, and thus transforming
the work needed to maintain the sliding into heat.
The study of friction is called tribology.
The frictional forces on each body are in a direction opposite to its motion relative to the
other body.
Frictional forces automatically oppose this relative motion and never aid it even when
there is no relative motion, frictional forces may exist b/w surfaces.
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8. 8
Factors on which force of friction depends:
1- Normal reaction forces
2- Nature of surface
1- Normal reaction ( R ):
Force of friction is directly proportional to normal reaction “ R “ which acts in upward
direction against the weight of the body sliding on a surface.
The normal force is defined as the net force compressing two parallel surfaces together;
its direction is perpendicular to the surfaces.
In the simple case of a mass resting on a horizontal surface, the only component of the
normal force is the force due to gravity, where FN=mg. In this case, the magnitude of the
friction force is the product of the mass of the object, the acceleration due to gravity,
and the coefficient of friction. However, the coefficient of friction is not a function of
mass or volume; it depends only on the material. For instance, a large aluminum block
will have the same coefficient of friction as a small aluminum block. However, the
magnitude of the friction force itself will depend on the normal force, and hence the
mass of the block.
If an object is on a level surface and the force tending to cause it to slide is horizontal,
the normal force N between the object and the surface is just its weight, which is equal
to its mass multiplied by the acceleration due to earth's gravity, g.
If the object is on a tilted surface such as an inclined plane, the normal force is less,
because less of the force of gravity is perpendicular to the face of the plane. Therefore,
the normal force, and ultimately the frictional force, is determined using vector analysis,
usually via a free body diagram. Depending on the situation, the calculation of the
normal force may include forces other than gravity.
2-Nature of surface:
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9. 9
Force of friction also depends on the nature of two surfaces in contact with each other.
And it is constant for various pair of surfaces in contact and its value is known as
Co-efficient of friction.
Friction is very important in our daily lives.
Advantages of frictional forces:
1- In the absence of frictional forces b/w ground & our feet we can not walk.
2- The frictional force b/w the roads & the driving wheels propel an automobile the
frictional force prevents the tier from slipping & provides the necessary propelling
force.
3- Proper forces of frictional are maintained in the joints of the body to facilitate
running or rapid movement of joints in the absence of friction we can not stand
upright.
Disadvantages of frictional forces:
In a car engine oil under pressure is supplied continuously to all bearing surfaces.
Absence of oil will allow metal to metal contact & the resulting friction will raise the
temperature and cause the bearing and position to seize up.
Force Law for Frictional Forces:
Now if we want to know the force law for frictional forces or we want to know how to
express frictional forces in terms of the properties of the body and its environment.
The force law for dry, sliding friction is empirical in character & approximate in their
predictions. They do not have the elegant simplicity and accuracy as for the
gravitational force law & for the electrostatic force law.
Consider a block at rest on a horizontal table ( a ) attach a spring to it to measure the
horizontal force ( F ) required to set the block in motion.
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10. 10
We find that the block will not move even though we apply a small force fig ( b ).
It means that applied force is balanced by an opposing frictional force “ f “ exerted on
the block by the table, acting along the surface of contact.
As we increase the applied force fig (c) (d) then there is a definite force at which the
block will “brake away “from the surface & begins to accelerate. Fig ( e ).
By reducing the force once motion has started, it is possible to keep the block in
uniform motion without acceleration. Fig ( f ).
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11. 11
TYPES OF FRICTION:
1- Static friction
2- Kinetic friction
1- Static friction:
The frictional forces existing b/w surfaces at rest with respect to each other are called
forces of static friction.
A motionless body is subject to static friction. The direction of the static friction force
can be visualized as directly opposed to the force that would otherwise cause motion,
were it not for the static friction preventing motion. In this case, the friction force
exactly cancels the applied force, so the net force given by the Vector sum, equals zero.
It is important to note that in all cases, Newton's first law of motion holds.
2-Kinetic friction:
The forces acting b/w surfaces in relative motion are called forces of kinetic friction.
The friction force is directed in the opposite direction of the Resultant force acting on a
body.
In the case of kinetic friction, the direction of the friction force may or may not match
the direction of motion: a block sliding atop a table with rectilinear motion is subject to
friction directed along the line of motion; an automobile making a turn is subject to
friction acting perpendicular to the line of motion (in which case it is said to be 'normal'
to it).
LAWS OF Static FRICITION:
These laws were discovered experimentally by Leonardo da vinci. (1452- 1519)
Two laws of friction about the maximum force of Static friction b/w any pair of dry un-
lubricated surfaces.
1. It is approximately independent of the area of contact over wide limits.
2. It is proportional to the normal force.
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12. 12
Normal force / loading force:
It is the force which arises from the elastic properties of the bodies in contact.
For a block resting on a horizontal table or sliding along it, the normal force is equal in
magnitude to the weight of the block.
Laws of Kinetic Friction:
Two laws of friction about of kinetic friction fk b/w dry un-lubricated surfaces:
1. It is approximately independent of the area of contact over wide limits.
2. It is proportional to the normal force
Coefficient of friction
The coefficient of friction is a dimensionless quantity used to calculate the force of
friction (static or kinetic).
While it is often stated that the coefficient of friction (COF) is a "material property," it
is better categorized as a "system property." Unlike true material properties (such as
conductivity, dielectric constant, yield strength), the COF for any two materials depends
on system variables like temperature, speed, atmosphere, as well as on geometric
properties of the interface between the materials.
For example, a copper pin sliding against a thick copper plate can have a COF that
varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds
when the copper surface begins to melt due to frictional heating. The latter speed, of
course, does not determine the COF uniquely; if the pin diameter is increased so that the
frictional heating is removed rapidly, the temperature will drop, the pin remains solid
and the COF rises to that of a 'low speed' test.
1. Coefficient of Static friction
2. Coefficient of kinetic friction
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13. 13
1. Coefficient of Static friction
The coefficient of static friction is defined as the ratio of the maximum static
friction force (F) between the surfaces in contact to the normal (N) force.
Co-efficient of Static friction: ( μs ):
The ratio of magnitude of the maximum force of static friction to the magnitude of the
normal force is called the co-efficient of static friction for the surfaces involved.
f S ≤ µS N −−−−−− →(1)
fS
µS =
N
Where
f S = magnitude of the force of static friction
µS = co-efficient of static friction
N = magnitude of normal force
NOTE :
The equality sign hold only when fS has its maximum value.
substance
wood on wood 0.25-0.50
steel on steel 0.58
glass on glass 0.9-1.0
Muhammad Yousuf Soomro (Lecturer) Institute of Physics
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14. 14
2. Coefficient of kinetic friction
The ratio of the magnitude of the force of kinetic friction to the magnitude of the normal
force is called the co-efficient of kinetic friction.
f K = µ K N − − − − − − → (2)
fK
µK =
N
Where
f K = magnitude of the force of kinetic friction
µK = co-efficient of kinetic friction
N = magnitude of the normal force
NOTE :
The force of the kinetic friction is also reasonably impendent of the relative speed with
which the surfaces move over each other.
Some values for common substances are given in the following table
substance T( )
hickory on dry snow -- 0.08
ice 0 0.020
ice -10 0.035
brass on ice 0 0.020
NOTE :
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Equations (1) & equation (2) are relations b/w the magnitude only of the normal &
frictional forces these forces are always directed perpendicularly to one another
IMPORTANT :
1- Both µS , µK ,are dimensionally constant , each being the ratio of ( magnitude)
two forces.
2- Usually for a given pair of surfaces µS > µK
3- The actual values of µS & µK depend on the nature of both the surfaces in
contact.
4- Both µS , µK can exceed unity, although commonly they are less than 1.
NOTE :
1. Both static and kinetic coefficients of friction depend on the pair of surfaces in
contact.
2. Their values are usually determined experimentally.
3. For a given pair of surfaces, the coefficient of static friction is larger than that of
kinetic friction.
A free-body diagram of a block resting on a rough inclined plane, with its weight (W),
normal force (N) and friction (F) shown.
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16. 16
Sliding Coefficient of Friction
when the tangential force F overcomes the frictional force between two surfaces
then the surfaces begins to slide relative to each other. In the case of a body
resting on a flat surface the body starts to move. The sliding frictional
resistance is normally different to the static frictional resistance.
The coefficient of sliding friction is expressed using the same formula as the
static coefficient and is generally lower than the static coefficient of friction..
Rolling Friction
When a cylinder rolls on a surface the force resisting motion is termed rolling
friction. Rolling friction is generally considerably less than sliding friction. If W is
the weight of the cylinder converted to force, or the force between the cylinder and the
flat surface, and R is radius of the cylinder and F is the force required to overcome the
rolling friction then.
W
F =f ×
R
“ f “ is the coefficient of rolling friction and has the same unit of length as the radius R.
Typical values for f are listed below
Surfaces Rolling Friction f
Steel on Steel 0,0005m
Wood on Steel 0,0012m
Wood on Wood 0,0015m
Iron on iron 0,00051m
Iron on granite 0,0021m
Iron on Wood 0,0056m
Polymer of steel 0,002m
Hardrubber on Steel 0,0077m
Hardrubber on Concrete 0,01 -0,02m
Rubber on Concrete 0,015 -0,035m
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17. 17
Factors affecting the friction between
surfaces
Dry surfaces
1. For low surface pressures the friction is directly proportional to the
pressure between the surfaces. As the pressure rises the friction factor
rises slightly. At very high pressure the friction factor then quickly
increases to seizing
2. For low surface pressures the coefficient of friction is independent of
surface area.
3. At low velocities the friction is independent of the relative surface velocity.
At higher velocities the coefficient of friction decreases.
Well lubricated surfaces
1. The friction resistance is almost independent of the specific pressure
between the surfaces.
2. At low pressures the friction varies directly as the relative surface speed
3. At high pressures the friction is high at low velocities falling as the velocity
increases to a minimum at about 0,6m/s. The friction then rises in
proportion the velocity 2.
4. The friction is not so dependent of the surface materials
5. The friction is related to the temperature which affects the viscosity of the
lubricant
Muhammad Yousuf Soomro (Lecturer) Institute of Physics
University of Sindh Jamshoro
17
18. 18
6-3 The Dynamics Of Uniform Circular Motion
If a particle moves at constant speed in a circular path both the velocity and acceleration
are constant in magnitude but both change their direction continuously this motion is
called uniform circular motion.
Examples of uniform circular motion:
1- In atoms, the electrons move in circular orbits around the nucleus.
2- The earth and others plants keep as moving around the sun in fixed orbits.
3- Computer disks.
If a body is moving at uniform speed “ v ” in a circle or a circular arc of radius “r” it
v2
experience a centripetal acceleration “a” whose magnitude is .
r
The direction of centripetal acceleration is always radially inward towards the center of
circle. This centripetal acceleration is a vector because even though its magnitude
remains constant, its direction changes continuously as the motion progresses.
If a body undergoing uniform circular motion, then a net force must be acting on it &
the magnitude of net force
mv 2
∑ F = ma = r
The direction of net force acting at any instant must be the direction of centripetal
acceleration “a“ at that point, radially inward.
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19. 19
Example :
A disk is moving with uniform circular motion & it moving on the end of a string in a
circle on a frictionless horizontal table as shown in figure.
The net force on the disk is provided by the tension “T“in the string. It string accelerates
the disk by constantly changing the direction of its velocity so that the disk moves in s
circle.
The direction of T is always towards the pin at the center, and its magnitude must equal
mv 2
to
r
mv 2
T=
R
If the string were to be cut where it joins the disk, there would be no net force exerted
on the disk. The disk would then move with constant speed in a straight line along the
direction of the tangent to the circle at the point at which the string was cut.
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20. 20
Centripetal Forces:
Forces responsible for uniform circular motion are called centripetal forces because they
are directed towards the center of the circular motion. So
1- for the revolving disk , the centripetal force is a tensile provided by the string.
2- For the Moon revolving around the earth the centripetal force is the
gravitational pull of the earth on the Moon.
3- For an electron circulating about an atomic nucleus the centripetal force is
electrostatic.
Examples of Centripetal forces:
The Conical Pendulum:
Consider a small body of mass “ m “ revolving in a horizontal circle with constant speed
“ v” at the end of a string of length “ L “. As the body swings around, the string sweeps
over the surface of an imaginary cone. This device is called a Conical Pendulum.
We want to find the time required for one complete revolution of the body.
If the string makes an angle θ with the vertical, the radius of the circular path is
R = L sin θ
20
21. 21
The forces acting on the body of mass “ m “ are its
( i ) Weight mg
( ii ) Tension T
Of the string.
Apply Newton’s second law of motion
∑F = T + mg
∑ F = mg ∴g = a
Or ∑F = ma
We can resolve T at any instant into a radial and vertical components
Tr = −T sin θ (Radial component)
Tr = T cos θ (Vertical component)
The radial component is –ve because if radial direction to be positive outward from axis.
21
22. 22
As there is no vertical acceleration in body so Z- component of Newton’s second law of
motion
∑ F = T − mg = 0
z z
Or T cos θ =mg −−−−−−→(1)
The radial acceleration is
V2
ar =−
R
It is –ve because it acts radially inward.
Radial acceleration is supplied by Tr which provides the centripetal force acting
on “m “.
From the radial component of Newton’s second law of motion
∑F r = Tr = mar
V2
∑ F = −T sin θ = m(− R )
mV 2
−T sin θ = −
R
mV 2
T sin θ = − − − − − − → (2)
R
Muhammad Yousuf Soomro (Lecturer) Institute of Physics
University of Sindh Jamshoro
22
23. 23
Dividing equation ( 2 ) by equation ( 1 )
T sin θ mV 2 R
=
T cos θ mg
sin θ
=V 2 R
cos θ g
V2
tan θ =
Rg
V 2 =tan θRg
V = Rg tan θ
This equation gives the constant aped of the body.
Period of Motion:
Now if t represents the time for one complete revolution of the body
.
23
24. 24
2π R
V =
t
or
2π R
t =
V
2π R
t =
Rg tan θ
Squaring both sides
4π R 2
2
t 2
=
Rg tan θ
4π R
2
t 2
=
g tan θ
4π R2
t 2
=
g tan θ
R
t = π
2
g tan θ
As R =l sin θ
24
25. 25
L sin θ
t =π
2
g tan θ
L sin θ
t =π
sin θ
2
g( )
cos θ
L cos θ
t =π
2
g
Note :
This equation gives the relation b/w t, L, θ.
T is called period of motion and it does not depend on mass m.
6-4 Equations & Motion
Constant and non constant forces
Constant forces:
Forces that dose not depend on time, velocity or position.
Examples :
1. Object falling near the earth surface.
2. Braking car
If force is constant, then the acceleration is constant, and for constant acceleration
the solution in one dimensional for V(t) & x(t) are easily obtained.
Constant forces demonstrate the applications of Newton’s law and they are certainly
easier to work with than non constant forces.
25
26. 26
Many particle problems often include forces that remain constant under many
circumstances.
Examples :
1 Gravity near the earth surface
2 Frictional forces
3 Tension forces in a strings
Find V(t) for constant force:
Let “ a “ represent constant acceleration & an object starts with velocity “ Vo “ at
time t = 0 & at time “ t “ later it has velocity V.
V2 − V1 ∆V
a= =
t2 − t1 ∆t
Or
26
27. 27
∆V V − V0
a= =
∆t t −0
V − V0
a=
t
at = V − V0
V = V0 + at − − − − − − → (1)
This important result allows us to find the velocity at all later times. This equation
No. 01 shows the velocity as a function of time, and it can be written as V(t).
Note :
Equation 01 is in the form of Y= mx+b, which describes the graph a straight line.
Non-Constant forces:
Forces that depends on time, velocity & position.
Examples :
1 Swinging pendulum bob
2 Rocket blasting toward earth’s orbit
3 A rain drop falling against air resistance.
27
28. 28
When the force is not constant then we can not use constant acceleration formulae to
find V(t) & x(t).
Methods of solving problems:
1 Analytical method
2 Numerical method
1 Analytical method:
This method involving integral calculus.
Find V( t ):
As
V
a =
t
or
dv
a =
dt
a.dt =dv
dv = .dt
a
Take integration both sides with limits of velocity V as follows
Vo at time t = 0 &
V at time t = t
Limits of time from 0 to t
28
29. 29
V 1
∫ dv =∫a.dt
Vo 0
V 1
∫ dv =a ∫dt
Vo 0
[V ]Vo =a [ t ] 0
V 1
Appling limits
V − Vo = a (t − 0)
V − Vo = at
V = Vo + at
or
V (t ) = Vo + at
29
30. 30
Find x ( t ):
As
S
V = S =x
t
or
x
V =
t
dx
V =
dt
dx = V .dt
dx = (Vo + at )dt
dx = Vo.dt + a.t.dt
Integrate with limits from position xo at time 0 to position x at time t
x t t
∫ dx = ∫V
xo 0
0 dt + ∫ at dt
0
x t t
∫ dx = V ∫ dt + a ∫ tdt
x0
0
0 0
t
t 2
[ x] x = V0 [ t ] 0 + a
x t
0
2 0
30
31. 31
Apply limits
( x − x0 ) = V0 (t − 0) + a( 1 t 2 )
2
x − x0 = V0 t + 1 at 2
2
x = x0 + V0 + 1 at 2
2
or
x(t ) = x0 + V0 t + 1 at 2
2
Physical phenomenon involving non-constant forces:
1. Forces depending on the time
2. Forces depending on the velocity
3. Forces depending on the position
2-Numerical methods:
In this method we use a computer to evaluate the integrals, obtaining not the analytic
functions V( t ) & x( t ) but instead the numerical values of V & x at any time t this
can be done to any desired level of precision.
Muhammad Yousuf Soomro (Lecturer) Institute of Physics
University of Sindh Jamshoro
31
32. 32
Time-Dependent Forces: (analytical methods)
When the forces is time dependent, we can obtain an acceleration a(t) using Newton’s
laws of motion.
Find V( t ):
Find the velocity by direct integration.
V
as a=
t
dv
a=
dt
dv = a (t ) dt
Integrate with limits from
Time t = 0 , when the initial velocity is Vo , to time t when velocity is V
V t
∫ dv= ∫a(t)dt
V0 0
t
[ V]V = ∫a(t)dt
V
0
0
t
V-V0 = ∫a(t)dt
0
t
V=V0 + ∫a(t)dt
0
or
t
V(t)=V0 + ∫a(t)dt
0
32
33. 33
Find x ( t ):
as V = dx
dt
dx = V dt
or dx = V (t ) dt
Integrate with limits time t = 0 when the particle is located at xo, to time t = t, when the
position is x .
x t
∫ dx= ∫V (t)dt
x0 0
t
[ x] x = ∫V (t)dt
x
0
0
t
x-x 0 = ∫V (t)dt
0
t
x=x 0 + ∫V (t)dt
0
or
t
x (t)=x 0 + ∫V (t)dt
0
33
34. 34
x t
x t
∫ dx = ∫ V (t )dt
x0 0
∫ dx =∫V (t )dt
x0 0
t t
[ x] x = ∫ V (t )dt
x
[ x ] x =∫V (t ) dt
x
0 0
0 0
t t
x − x0 = ∫ V (t ) dt x −x0 = ∫V (t ) dt
0 0
t t
x = x0 + ∫ V (t ) dt x = x0 +∫V (t ) dt
0 0
or or
t t
x (t ) = x0 + ∫ V (t ) dt x (t ) = x0 +∫V (t ) dt
0
0
Chapter No. 07 Mohd Yousuf Soomro
WORK & ENERGY Institute of Physics
Work:
When force acts upon a body and if it causes displacement also, then work is said to be
done by the force upon the body.
Or
Dot product of two vector quantities (force & displacement) is called work.
Work is a scalar quantity.
rr
W = F .d
Where
F = force
d = displacement moved by the body in the direction of force.
NOTE :
Sometimes the force and displacement may not be in the same direction.
Examples:
34
35. 35
A wooden block is pulled by means of a rope, it moves in the horizontal direction, but
the force acts along the rope. If the force makes an angle “ θ “ with the direction of
motion then work done can be found by the production of the component of the force
along the direction of motion and the displacement “ S “ moved by the block.
We can express work done by the force analytically as
W = F . d cosθ
Where r
F = magnitude of the vector F
r
d = magnitude of the vector d
r r
θ = angle b/w F and d
Work is an algebraic quantity.
It can be positive, negative , zero depending upon the value of angle b/w force ( F ) and
displacement ( d ).
Cases of work done:
( i ) case:
When the components of force is in the same direction of the displacement ( θ = 0 ) then
the work is positive.
35
36. 36
r r
W = F . d cos θ
if θ =0
W = F .d cos 0
W = F .d (1)
cos00 = 1
W = F .d
Example :
When a spring is stretched, then work done by the stretched ( stretching force ) is
positive.
( ii ) case:
When the direction of the force is opposite to the direction of the displacement ( θ =1800 )
the work done is negative.
36
37. 37
rr
W = F .d cos θ
if θ = 1800
W = F .d cos1800 cos1800 = − 1
W = F .d (− 1)
W = − F .d
Example :
Work done by the “gravitational force “on the body being lifted is negative.
When a body is lifted against gravity at very slow speed , the angle b/w gravity and
displacement is 1800.
( iii ) case:
When the force acts at right angle to the displacement ( θ = 900 ) THEN THE WORK
done is zero.
It means that force does not produce work.
37
38. 38
rr
W = F .d cos θ
if θ =0
W = F .d cos 900
W = F .d X 0 cos 900 = 0
W =0
Example :
work done by the centripetal force is zero because the centripetal force is always at right
angles to the direction in which the body moving.
Units:
SI System: (MKS System)
In the S.I system the unit of work is Newton-meter which is commonly known as
Joule(J ).
1 Newton. meter = 1 Joule
38
39. 39
1N. m = 1 J
The work of 1 joule is said to be done if a force of 1 Newton acts on a body and if it
moves through a distance of 1 meter in the direction of force.
CGS system: ( centimeter , gram , second system )
In CGS system the unit of work is erg.
1 erg = 1 dyne 1 cm
1 erg = 10-7 J
The work of 1 erg is said to be done if a force of 1 dyne acts on a body and if it moves
through a distance of 1 centimeter in the direction of force.
FPS System ( foot, pound , second system ) / British Engineering
System :
In FPS System the unit of work is Foot . Pound ( ft-lb ).
1 ft. lb = 1.355 joule
Relationships b/w units:
1 Joule = 105 dynes X 102 cm
1 Joule = 107 ( dynes .cm )
1 Joule =107 Joule
1055 Joule = 1 Btu (Btu= British thermal unit)
NOTE :
In the physics of molecules , atoms , and elementary particles a much smaller unit is
used , it is called electron volt ( e.V )
39
40. 40
1eV = 1.60 X 10−19 J
Multiples of the electron volts:
1 million eV = 1 M eV = 106 eV
1 billion eV = 1 B eV = 1012 eV
Muhammad Yousuf Soomro Lecturer Institute of Physics
University of Physics Jamshoro
Physical dimension of Work:
As
Work = force. displacement
W = F . d − − − − − −− → (1)
Since F = ma
Or
F = mass × acceleration
L
F = M × ( ) M = mass
T2
a = acceleration
L = length
T = time
So equation ( 1 ) becomes
40
41. 41
L
W = M× ( 2
)( L)
T
ML2
W = 2
T
W = M L2 T −2
7.1 Constant Force on a Particle:
Suppose a particle of mass “m “is subjected to a constant force “ F “. We assume the
motion of a particle along x- axis.
41
42. 42
W = F .d
or
W = F .dx − − − −− → (∗)
As we know from Newton’s second law of motion
F = ma
dv
F =m
dt
So equation ( * ) becomes
dv
F . dx = m .dx − − − − − (1)
dt
Suppose the particle is displaces from “Xo” to “X”.
Let the velocity at “ Xo” be “ Vo” and velocity at “ X “ be “ V “.
Applying these conditions on equation (1) and integrate it.
x v
dv
∫ F .dx = ∫ m
x0 V0
dt
.dx
Since the force “ F “ and mass “ m “ are constants so we may take these constants out of
the integral sign.
x v
dv
F ∫ dx = m ∫ .dx
x0 V0
dt
x v
dx
F ∫ dx = m ∫ .dv
x0 V0
dt
42
43. 43
x v
dx
F ∫ dx = m ∫ Vdv V=
x0 V0
dt
2 v
v
F [ x] x = m
x
0
2 v0
Appling the limits
2
v 2 v0
F ( x − x0 ) = m( − )
2 2
F ( x − x0 ) = 1 mv 2 − 1 mv0 − − − − → (2)
2 2
2
2
We call 1 mv as the Kinetic energy of the body. The R.H.S of equation ( 2 ) is the
2
change in the K.E of the particle when it changes its position from “xo” to “x”.
Thus
“The work done by a force is equal to the change in K.E of the particle. “
7.2 Work Done by a Variable Force:
The work done by a variable force can not be calculated by the direct use of formula
W= F.d for the entire displacement “ d” because the force is continuously changing with
the displacement.
So to calculate the work done by a variable force , we make two assumptions.
(1) The direction of force is along positive X-axis and its magnitude is changing with
displacement.
(2) The body is constrained to move in positive X-axis direction only.
Suppose a body of mass “ m “ is moving under a variable force “ f “.
The value of force “ f” is different at different positions.
43
44. 44
We assume that the body moves from its initial position “ A “ to the final position “ B “
in the direction of the variable force.
If the body has moved from position “ A “ to the position “ B “ then we divide the total
displacement “ AB “ into small interval each of width “Δr “ .
During any short displacement interval “Δr “the force remains almost constant. Thus the
force for any one displacement interval = dot product of “F “and “Δr “.
The total work done for the displacement “ AB “
WA→ B = F1∆r1 + F2 ∆r2 + F3∆r3 + ........
or
B
W A→ B = ∑ F ( r ) ∆ r
A
The constant force is taken to be the force which acts at the beginning of each interval.
Let the total number of intervals from “A” to “ B “ be “ N “.
Now if the number of intervals are made infinite ( N → ∞ ) and the width “ Δr “ is made
so small that it tend to zero ( ∆r → 0 )
44
45. 45
B
WA→ B = ∆r → 0∑ F .∆r
A
Now
B B
∆r → 0 ∑ F .∆r = ∫ F .dr
A A
therefore the total force
B
WA→B = ∫ F .dr − − − −− → (1)
A
As we known that F=ma
dv dv
F=m a=
dt dt
So equation ( 1 ) becomes
B
dv
WA→B = ∫ m dr − − − −− → (2)
A
dt
Since “ m “ mass is constant so we may take it out of the ingral sign
B
dv
WA→B = m ∫ dr
A
dt
B
dr
WA→B = m ∫ dv
A
dt
B
WA→B = m ∫ Vdv − − − − → (3)
A
Integrate equation ( 3 ) with respect to ”v”
45
46. 46
B
2
V
=m
2 A
B
1
= mV 2
2 A
Applying limits
1 1
mVB2 − mVA
2
2 2
It means
K .E at B =K .E at A
1 1
mVB2 = mVA −− −− → (4)
2
2 2
Example :
An example of a variable force involving in the motion of spring.
We consider a spring that acts on a particle of mass “m “ . The particle moves in the
horizontal direction with the origin ( x = 0 ).
46
47. 47
Let the particle be displaced a distance “ x “ from its original position x = 0 , as the
agent exerts a force “ F “ on the particle , the spring exerts an opposing force “ F “.
We know from the Hook’s law that
“Force acting on the body is directly proportional to the displacement of the
body”.
F = − kx
Where
K= force constant or spring constant.
Let us consider the work done on the particle by the spring when the particle moves
from initial position “ xi “ to “ xf”.
F = −k x
W = F .d
W = ( −kx ).dx
xf
W = ∫ ( −kx ).dx
xi
As k is constant so we may take it out of the integral sign.
xf
W = k ∫ (− x).dx − − − − → (1)
xi
Integrating equation ( 1 ) with respect to “ x”.
47
48. 48
xf
x 2
W = k −
2 xi
Now applying limits
kx 2
kxi2
f
W =− +
2 2
2
kxi2 kx f
W= − − − − − → (2)
2 2
7-4 Work Energy & The Work Energy Theorem:
Work energy theorem:
The net work done by the forces acting on a particle is equal to the change in the Kinetic
energy of the particle.
Wnet = K f − Ki = ∆ K
Explanation :
Consider a net work done (W net) on a particle not by single force but all the forces that
act on the particle.
Ways to find Net Work:
There are two ways to find the net work.
1- Find the net force:
It means the vector sum of all the forces that acts on the particle.
Fnet = F1 + F2 + F3 + .......
48
49. 49
Then treat this force as a single force in calculating the net work by following equation.
xf
W = ∫ F ( x)dx (One dimension)
xi
f f
W = ∫ F .ds = ∫ F cos φ ds (Many dimensions)
i i
Muhammad Yousuf Soomro Lecturer Institute of Physics
University of Sindh Jamshoro
2- Calculate the work done by each of the forces that acts on the
particle:
W1 = ∫ F1.ds
W2 = ∫ F2 .ds
W3 = ∫ F3 .ds
Wn = ∫ Fn .ds
To find net work, add the work done by each of the individual forces.
Wnet = W1 + W2 + W3 + .........
We know that a net unbalanced force applied to a particle will change its state of
motion by accelerating it from initial velocity “ Vi “ to final velocity “ Vf “.
Under the influence of constant force , the particle moves from Xi to Xf & it
accelerates uniformly from Vi to Vf. The work done is
49
50. 50
Wnet =Fnet ( x f −xi )
Wnet =ma ( x f −xi )
Because acceleration is constant we use the equation
V 2 = V02 + 2a ( x − x0 )
or
V f2 = Vi 2 + 2a ( x f − xi )
1 1
Wnet = mv 2 − mv
f
2 2
It means:
“The result of the net work on the particle has been to bring about a change in the
value of quantity 1 mv 2 from point “ i “ to point “ f “. This quantity is called the Kinetic
2
energy K of the particle.
K = 1 mv 2
2
NOTE :
Work energy theorem holds for both constant forces as well as non constant forces:
The work energy theorem does not represent a new independent law of classical
mechanics. It is useful for solving problems in which the net work done on a particle by
external forces is easily computed and in which we are interested in finding the
particle’s speed at certain positions.
General Proof of Work-Energy Theorem:
50
51. 51
Let Fnet represent the net forces acting on the particle. The net work done by all the
external forces that act on the particle is
Wnet = ∫ Fnet dx − − − −− ⇒ (1)
Fnet = ma
As
dv dv
Fnet = m ∴a=
dt dt
By using chain rule
dv dx
Fnet = m
dx dt
dv
Fnet = m v
dx
dv
Fnet = mv − − − −− ⇒ (2)
dx
Put equation ( 2 ) in equation ( 1 )
51
52. 52
Wnet = ∫ Fnet dx
or
dv
Wnet = ∫ mv dx
dx
Wnet = ∫ mv dv
Integrate from initial velocity “Vi” to final Velocity “Vf”
vf
Wnet = ∫ mvdv
vi
vf
Wnet = m ∫ vdv
vi
2 vf
v
Wnet = m
2 vi
52
53. 53
Applying limits
Wnet = m( 1 v 2 − 1 vi2 )
2 f 2
Wnet = 1 m(v 2 − vi2 )
2 f
or
Wnet = 1 mv 2 − 1 mvi2
2 f 2
This shows that the work – energy theorem holds also for non constant forces.
7-5 Power
“The work done in unit time called power”.
Or
“The rate of doing work is called power “.
F .d
Power =
t
W
Power = ∴ W = F .d
t
d
Power = F .V ∴ =V
t
Kinds of Power:
53
54. 54
1. Average power
2. Instantaneous power
1. Average Power:
If “Δw“ is the work done in a time “ Δt “ the power is called average power and it is
written as Pav.
∆W
P =
av
∆ t
2. Instantaneous power:
∆W
If ∆t → 0 the limiting value of is called Instantaneous power at time “ t “.
∆t
∆W
P = lim − − − −− → (1)
∆t →0 ∆t
As we know that
W = F .d
So equation ( 1 ) becomes
dr
P = lim F .
∆t →0 dt
P = F .V
It means power is equal to the dot product of force and velocity.
Units:
SI System:
54
55. 55
The S.U unit of power is Joule per Second (J/s) which is also called Watt (W).
This unit is named in honor of James Watt (1736-1819)
1 W = 1 J / s = 1 Kg.m2 / s3
Watt:
One watt is defined as:
“The rate of doing work or using energy at Joule per Second”.
Bigger Units:
The bigger units of power are Kilowatt ( kW) Mega watt ( MW) and Giga Watt ( Gw )
1 kW= 103 watt = 1000 w
1 Mw=106 watt=1000000w=1000 Kw
1 Gw= 109 watt=1000000000w
FPS System:
In British Engineering system the unit of power is ft-lb / sec (foot. Pound / second ).
Since this unit is quite small, therefore a bigger unit called Horse Power (hp) is used.
1 horsepower = 745.7 watts
The term "horsepower" was coined by the engineer James Watt (1736 to 1819) in 1782
while working on improving the performance of steam engines.
Horse Power:
“One horse power (hp) is the power of an agency which does work at the rate of
550 ft-lb/sec or 33000 ft-lb per minute.
550 ft-lb/sec = 33000 ft-lb / min
1 horsepower = 745.7 watts
Or
1 hp = 746 watt
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56. 56
1 min = 60 seconds
1 ft = 0.3048 m and
1 lb = 0.45359237 kg
Relationship b/w Kilowatt hour & Joule:
The term kilowatt hour (KWh ) is originated from the unit of work.
One Kilo watt is defined as the work done in one hour by an agency working at the
constant rate of 1 Kw that is 1000 Joule per Second.
1 hour = 3600 seconds
1 Kwh = 1000 X 3600 = 3.6 X 106 Joules
Relationship b/w Horse power & Watt:
1 hp= 550 ft –lb / sec
We know that
1 ft = 0.3048 m
1 lb = 4.448 N
So 1 hp = 550 X 1.351 X 4.448
= 550 X 1.351 N.m / sec
= 550 X 1.351 Joules / sec
1 hp = 746 watt
Some Important Units of Energy
MECHANICAL ENERGY:
56
57. 57
Metric Units: SI: Joule (J) 1 J = 1 N-m
English Units: foot-pound (ft-lbs) 1 ft-lbs = 1.356 J
HEAT ENERGY:
Calorie (Cal) 1 Cal = 4.186 J
British Thermal Unit (BTU) 1 BTU = 1,055 J
ELECTRICAL & ATOMIC ENERGY:
Electron Volt (eV) 1 eV = 1.6x10-19 J
Kilowatt-hour (kWh) 1 kWh = 3.6x10+6 J
Muhammad Yousuf Soomro Lecturer Institute of Physics
University of Sindh Jamshoro
57