This document discusses vectors and scalars in physics. It defines a scalar as a quantity that has magnitude but no direction, while a vector has both magnitude and direction. Vectors are represented by arrows to show both magnitude and direction. The document provides examples of applying vectors to problems involving addition, subtraction, and resolving perpendicular components using trigonometry. It demonstrates solving vector problems for displacement, velocity, and other physical quantities.
The document discusses the astronomical contributions of Eudoxus, a Greek astronomer from the 4th century BCE. Eudoxus developed the first mathematical model to explain the motions of the sun, moon, and planets. His model assigned multiple spheres to each celestial object, with the inner spheres rotating at different rates and angles than the outer spheres. This system could reproduce the observed retrograde motion of planets and was an important early step in developing mathematical astronomy.
The document discusses motion in two and three dimensions. It explains that displacement, velocity, and acceleration vectors can be divided into their x, y, and z components. Position functions can be written for each dimension as a function of time. Examples are provided to demonstrate calculating position, velocity, acceleration, distance traveled, and maximum height using these concepts and component vector equations.
Getting vector resultant using polygon methodsalvie alvaro
The document describes different methods for calculating the resultant vector of multiple displacements or forces, including:
1) The polygon method, which involves drawing vectors representing each displacement on a scale diagram and connecting them to find the resultant.
2) The component method, which breaks vectors down into their x and y components to calculate the resultant.
3) The pythagorean theorem method, which uses the theorem to calculate the magnitude of the resultant when its components are at right angles to each other.
MOVEMENT OF PLATES AND FORMATION OF FOLDS AND.pptxmarionboyka
This document discusses various types of rock deformation processes including metamorphism, plate tectonics, folds, faults, and joints. It describes contact and regional metamorphism, the four main types of stresses that cause rock deformation, and plate tectonic theory including the three types of plate boundaries. The document also defines common geological structures such as anticlines, synclines, monoclines and the four basic types of folds. Finally, it explains joints, faults, and the four main fault types.
This document discusses ray diagrams for concave mirrors. It explains that rays parallel to the principal axis will be reflected through the principal focus, rays passing through the principal focus will be reflected parallel to the principal axis, and rays passing through the center of curvature will be reflected back along their own path. The document constructs ray diagrams to show the nature of the image formed for objects placed at different positions relative to the focal point and center of curvature of the concave mirror.
The document describes several methods for finding the vector sum (resultant) of two or more vectors, including:
1. The parallelogram method draws the vectors to form a parallelogram, with the resultant being the diagonal.
2. The cosine method uses a formula involving the magnitudes of the vectors and the angle between them.
3. The polygon method connects the vectors tip to tail to form a polygon, with the resultant connecting the initial and final points.
4. The analytic method resolves the vectors into their x and y components, sums the respective components, and determines the resultant's magnitude and direction from the sums and a formula.
This document discusses vectors and scalars in physics. It defines a scalar as a quantity that has magnitude but no direction, while a vector has both magnitude and direction. Vectors are represented by arrows to show both magnitude and direction. The document provides examples of applying vectors to problems involving addition, subtraction, and resolving perpendicular components using trigonometry. It demonstrates solving vector problems for displacement, velocity, and other physical quantities.
The document discusses the astronomical contributions of Eudoxus, a Greek astronomer from the 4th century BCE. Eudoxus developed the first mathematical model to explain the motions of the sun, moon, and planets. His model assigned multiple spheres to each celestial object, with the inner spheres rotating at different rates and angles than the outer spheres. This system could reproduce the observed retrograde motion of planets and was an important early step in developing mathematical astronomy.
The document discusses motion in two and three dimensions. It explains that displacement, velocity, and acceleration vectors can be divided into their x, y, and z components. Position functions can be written for each dimension as a function of time. Examples are provided to demonstrate calculating position, velocity, acceleration, distance traveled, and maximum height using these concepts and component vector equations.
Getting vector resultant using polygon methodsalvie alvaro
The document describes different methods for calculating the resultant vector of multiple displacements or forces, including:
1) The polygon method, which involves drawing vectors representing each displacement on a scale diagram and connecting them to find the resultant.
2) The component method, which breaks vectors down into their x and y components to calculate the resultant.
3) The pythagorean theorem method, which uses the theorem to calculate the magnitude of the resultant when its components are at right angles to each other.
MOVEMENT OF PLATES AND FORMATION OF FOLDS AND.pptxmarionboyka
This document discusses various types of rock deformation processes including metamorphism, plate tectonics, folds, faults, and joints. It describes contact and regional metamorphism, the four main types of stresses that cause rock deformation, and plate tectonic theory including the three types of plate boundaries. The document also defines common geological structures such as anticlines, synclines, monoclines and the four basic types of folds. Finally, it explains joints, faults, and the four main fault types.
This document discusses ray diagrams for concave mirrors. It explains that rays parallel to the principal axis will be reflected through the principal focus, rays passing through the principal focus will be reflected parallel to the principal axis, and rays passing through the center of curvature will be reflected back along their own path. The document constructs ray diagrams to show the nature of the image formed for objects placed at different positions relative to the focal point and center of curvature of the concave mirror.
The document describes several methods for finding the vector sum (resultant) of two or more vectors, including:
1. The parallelogram method draws the vectors to form a parallelogram, with the resultant being the diagonal.
2. The cosine method uses a formula involving the magnitudes of the vectors and the angle between them.
3. The polygon method connects the vectors tip to tail to form a polygon, with the resultant connecting the initial and final points.
4. The analytic method resolves the vectors into their x and y components, sums the respective components, and determines the resultant's magnitude and direction from the sums and a formula.
The document summarizes several historical models of the universe:
1) Eudoxus of Cnidus proposed a geocentric model in the 4th century BC with concentric spheres and the first systematic explanation of planetary motion.
2) Aristotle also proposed a geocentric model, believing Earth was stationary at the center and composed of four elements.
3) Aristarchus proposed the first heliocentric model in the 3rd century BC, placing the Sun at the center with the Earth and planets orbiting it.
4) Ptolemy proposed a refined geocentric model in the 2nd century AD explaining planetary motions with epicycles and deferents.
5) Copernicus published his he
There are two types of forces: non-fundamental and fundamental. The four fundamental forces are gravitational, electromagnetic, strong nuclear, and weak nuclear. Gravitational force causes attraction between objects due to mass. Electromagnetic force causes attraction or repulsion between charged bodies. Strong nuclear force holds atomic nuclei together, while weak nuclear force plays a role in radioactive decay. Contact forces require direct physical contact while non-contact forces do not. Mass is a measure of matter and weight is the force on an object due to gravity, related by the equation W=mg, where W is weight, m is mass, and g is acceleration due to gravity.
This document provides an overview of key topics in General Chemistry II to be covered in weeks 3-4. These include:
1) Expressing the concentration of solutions using various units like percent by mass, molarity, molality, etc.
2) Performing stoichiometric calculations for reactions in solution.
3) Describing how concentration affects colligative properties of solutions.
4) Differentiating colligative properties of nonelectrolyte and electrolyte solutions.
5) Calculating properties like boiling point elevation and freezing point depression from concentration.
This document provides an overview of early Greek astronomy from Plato to Ptolemy. It discusses how Plato and Aristotle viewed the universe, with Plato believing in uniform circular motion and Aristotle recognizing lunar phases and arguing that the moon reflects sunlight. It then covers how later Greek astronomers like Hipparchus made important advances, including developing star catalogs and discovering precession. The document concludes with Claudius Ptolemy, who synthesized the knowledge in his influential book "The Almagest," establishing the geocentric Ptolemaic system as the standard model for over 15 centuries.
The document discusses orbital motion and the forces that allow Earth to remain in orbit around the sun. It explains that Earth orbits due to a balance of forces - the gravitational pull from the sun acts as an inward force while Earth's inertia acts as an outward force, allowing it to travel in a constant orbit. Friction from air or ground contact would cause Earth to slow if in motion on the surface, but in the vacuum of space there is no friction to slow Earth's orbital motion.
This document is the learner's material for precalculus developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools. The document contains the copyright notice and details that it is the property of the Department of Education and may not be reproduced without their permission. It provides the table of contents that outlines the units and lessons covered in the material.
This document discusses how Tycho Brahe's accurate astronomical observations and data collection paved the way for Johannes Kepler's discovery of the laws of planetary motion. Brahe made extensive measurements of the positions of planets and stars. Kepler used Brahe's data to discover that planets move in elliptical orbits with the sun at one focus, that they sweep out equal areas in equal times, and that the squares of their orbital periods are proportional to the cubes of their average distances from the sun.
The document outlines the learning outcomes and steps for communication for academic purposes, which includes writing and presenting academic papers using the proper tone, style, conventions and reference styles. It discusses communicating ideas through oral, audio-visual and web-based presentations for different audiences. The document also defines communication for academic purposes as sharing, informing or presenting ideas, products or research results. It mentions developing a research plan and conducting a final project in groups of 5 members.
This document is a science lesson plan for teaching 9th grade students about projectile motion. It outlines the objectives, content, learning resources, tasks, and assessments for a week of lessons on motion in two dimensions. The lessons cover uniformly accelerated motion in the horizontal and vertical planes, as well as projectile motion, including how the angle of release relates to the height and range of a projectile. Students will perform activities and solve problems to explore these concepts in physics. The lesson plan provides guidance for teachers to elicit, engage, explore, explain, elaborate, and evaluate student understanding of motion concepts.
This document provides information about earthquakes. It begins by defining key earthquake terms like epicenter, hypocenter, foreshocks, aftershocks, and magnitude. It then explains that earthquakes are caused by the sudden slipping of fault blocks within the earth, as the plates of the earth's crust shift. The document discusses how seismographs are used to measure and locate earthquakes by recording seismic waves. It also describes the different scales used to measure earthquake size and intensity. Finally, it provides references for additional information.
This document summarizes a physics lecture on electrical charges and Coulomb's law. It discusses the structure of atoms and how they can become charged by gaining or losing electrons. Coulomb's law is then introduced, stating that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Several example problems are worked through applying Coulomb's law to calculate the electrostatic force between charged objects at varying distances.
• THEMES OF LIFE:
o BIOLOGICAL SYSTEMS
o THE CELLULAR BASIS OF LIFE
o STRUCTURE AND FUNCTION
o REPRODUCTION AND INHERITANCE
o ENVIRONMENTAL INTERACTIONS
o ENERGY AND LIFE
o REGULATION
o EVOLUTION AND DIVERSITY
o SCIENTIFIC INQUIRY
o SCIENCE, TECHNOLOGY AND SOCIETY
The document differentiates the universe, galaxy, and solar system. The solar system consists of the sun and everything bound to it by gravity, including 8 planets, moons, asteroids, dwarf planets, and other objects. A galaxy is a large system of stars held together by gravity, isolated from other galaxies by vast space. The Milky Way galaxy is about 100,000 light years across and contains 200 billion stars. The universe is defined as the totality of all known objects and phenomena in space. Regarding what makes Earth unique, it notes that Earth is the only planet with an atmosphere containing 21% oxygen, it likely has the only ozone layer, and it is the only planet that is known to have life.
The document discusses different types of lenses including convex and concave lenses. It describes key lens features such as focal length and principal plane. Characteristics of images formed by convex and concave lenses are provided, including whether images are real or virtual, upright or inverted, and enlarged or reduced. Examples of optical instruments that use lenses like cameras, telescopes, microscopes and projectors are outlined. Defects in vision and lenses are also summarized.
The document compares Aristotle and Galileo's concepts of horizontal and vertical motion. Aristotle believed horizontal motion required a continuous force, while Galileo believed objects in motion stay in motion due to inertia unless acted on by an external force. For vertical motion, Aristotle believed heavier objects fall faster, while Galileo demonstrated that all objects accelerate at the same rate when in free fall, defined as motion only due to gravity. The document also discusses projectile motion, quantities used to describe motion, and examples of motion concepts.
This teaching guide provides lessons on physical science for senior high school students. It discusses the formation of elements in the universe through both the Big Bang and stellar evolution. Students will learn about the historical development of ideas regarding the atom and chemical elements from ancient Greek philosophers to modern theories. Specific scientists discussed include J.J. Thomson, Ernest Rutherford, Henry Moseley, Niels Bohr, and John Dalton. The guide aims to give students an understanding of how elements form and are distributed in the universe, as well as how modern atomic theory evolved from ancient ideas.
Polarization occurs when light vibrates in only one direction, rather than in all planes. There are several methods to polarize unpolarized light, which vibrates in all directions, including selective absorption using polarizing materials like Polaroid. Polarization experiments showed that light waves are transverse, not longitudinal, with electric and magnetic fields oscillating perpendicular to the direction of propagation. Polarized light has many applications like 3D movies, sunglasses, and improving contrast in microscopes.
This document discusses lenses and their properties. It defines convex and concave lenses, and explains that convex lenses converge light rays while concave lenses diverge them. It then describes the six cases of image formation by a convex lens depending on the object's position, including real/virtual and inverted/upright properties. Sign conventions for thin lens equations are also provided. The document contains questions related to identifying lens types, drawing ray diagrams, and calculating thin lens image characteristics.
Lenses have several important uses. Concave lenses diverge light rays, while convex lenses converge light rays. Lenses are used in cameras, telescopes, and eyeglasses. Cameras use lenses to admit more light and create a brighter, more focused image on film. Eyeglasses use lenses to correct nearsightedness and farsightedness by refocusing light rays onto the retina. Telescopes also employ lenses to magnify distant objects.
The document discusses equations for calculating velocity, acceleration, displacement, and time for objects moving with constant velocity or uniform acceleration. It provides the key equations:
1) For constant velocity, average velocity (v) equals displacement (Δx) over time (Δt), and displacement equals velocity times time.
2) For uniform acceleration, final velocity (vf) equals initial velocity (v0) plus acceleration (a) times time (Δt), and displacement equals initial velocity times time plus one-half acceleration times time squared.
3) A single equation relates displacement, initial velocity, final velocity, and acceleration, which can be rearranged to solve for any of those variables.
Newton's laws of motion by Mphiriseni Khwandamkhwanda
Newton's Laws of Motion document summarizes Newton's three laws of motion. It discusses Newton's first law, stating that objects at rest stay at rest and objects in motion stay in motion with constant velocity unless acted upon by an unbalanced force. It addresses misconceptions about the first law. Newton's second law states that acceleration is directly proportional to net force and inversely proportional to mass. Problems are provided applying the laws, including drawing free-body diagrams and solving equations of motion. Newton's third law is not discussed.
Newton's first and second laws applicationsmkhwanda
This document discusses Newton's laws of motion and their applications. It contains examples of problems involving Newton's first law regarding inertia and an object's motion when the net force is zero. Newton's second law relating force, mass and acceleration is explained. Free body diagrams are demonstrated as a problem solving tool. Examples are provided of calculating acceleration from forces using Newton's second law for objects on an inclined plane and connected objects on pulleys. Friction forces are also discussed.
The document summarizes several historical models of the universe:
1) Eudoxus of Cnidus proposed a geocentric model in the 4th century BC with concentric spheres and the first systematic explanation of planetary motion.
2) Aristotle also proposed a geocentric model, believing Earth was stationary at the center and composed of four elements.
3) Aristarchus proposed the first heliocentric model in the 3rd century BC, placing the Sun at the center with the Earth and planets orbiting it.
4) Ptolemy proposed a refined geocentric model in the 2nd century AD explaining planetary motions with epicycles and deferents.
5) Copernicus published his he
There are two types of forces: non-fundamental and fundamental. The four fundamental forces are gravitational, electromagnetic, strong nuclear, and weak nuclear. Gravitational force causes attraction between objects due to mass. Electromagnetic force causes attraction or repulsion between charged bodies. Strong nuclear force holds atomic nuclei together, while weak nuclear force plays a role in radioactive decay. Contact forces require direct physical contact while non-contact forces do not. Mass is a measure of matter and weight is the force on an object due to gravity, related by the equation W=mg, where W is weight, m is mass, and g is acceleration due to gravity.
This document provides an overview of key topics in General Chemistry II to be covered in weeks 3-4. These include:
1) Expressing the concentration of solutions using various units like percent by mass, molarity, molality, etc.
2) Performing stoichiometric calculations for reactions in solution.
3) Describing how concentration affects colligative properties of solutions.
4) Differentiating colligative properties of nonelectrolyte and electrolyte solutions.
5) Calculating properties like boiling point elevation and freezing point depression from concentration.
This document provides an overview of early Greek astronomy from Plato to Ptolemy. It discusses how Plato and Aristotle viewed the universe, with Plato believing in uniform circular motion and Aristotle recognizing lunar phases and arguing that the moon reflects sunlight. It then covers how later Greek astronomers like Hipparchus made important advances, including developing star catalogs and discovering precession. The document concludes with Claudius Ptolemy, who synthesized the knowledge in his influential book "The Almagest," establishing the geocentric Ptolemaic system as the standard model for over 15 centuries.
The document discusses orbital motion and the forces that allow Earth to remain in orbit around the sun. It explains that Earth orbits due to a balance of forces - the gravitational pull from the sun acts as an inward force while Earth's inertia acts as an outward force, allowing it to travel in a constant orbit. Friction from air or ground contact would cause Earth to slow if in motion on the surface, but in the vacuum of space there is no friction to slow Earth's orbital motion.
This document is the learner's material for precalculus developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools. The document contains the copyright notice and details that it is the property of the Department of Education and may not be reproduced without their permission. It provides the table of contents that outlines the units and lessons covered in the material.
This document discusses how Tycho Brahe's accurate astronomical observations and data collection paved the way for Johannes Kepler's discovery of the laws of planetary motion. Brahe made extensive measurements of the positions of planets and stars. Kepler used Brahe's data to discover that planets move in elliptical orbits with the sun at one focus, that they sweep out equal areas in equal times, and that the squares of their orbital periods are proportional to the cubes of their average distances from the sun.
The document outlines the learning outcomes and steps for communication for academic purposes, which includes writing and presenting academic papers using the proper tone, style, conventions and reference styles. It discusses communicating ideas through oral, audio-visual and web-based presentations for different audiences. The document also defines communication for academic purposes as sharing, informing or presenting ideas, products or research results. It mentions developing a research plan and conducting a final project in groups of 5 members.
This document is a science lesson plan for teaching 9th grade students about projectile motion. It outlines the objectives, content, learning resources, tasks, and assessments for a week of lessons on motion in two dimensions. The lessons cover uniformly accelerated motion in the horizontal and vertical planes, as well as projectile motion, including how the angle of release relates to the height and range of a projectile. Students will perform activities and solve problems to explore these concepts in physics. The lesson plan provides guidance for teachers to elicit, engage, explore, explain, elaborate, and evaluate student understanding of motion concepts.
This document provides information about earthquakes. It begins by defining key earthquake terms like epicenter, hypocenter, foreshocks, aftershocks, and magnitude. It then explains that earthquakes are caused by the sudden slipping of fault blocks within the earth, as the plates of the earth's crust shift. The document discusses how seismographs are used to measure and locate earthquakes by recording seismic waves. It also describes the different scales used to measure earthquake size and intensity. Finally, it provides references for additional information.
This document summarizes a physics lecture on electrical charges and Coulomb's law. It discusses the structure of atoms and how they can become charged by gaining or losing electrons. Coulomb's law is then introduced, stating that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Several example problems are worked through applying Coulomb's law to calculate the electrostatic force between charged objects at varying distances.
• THEMES OF LIFE:
o BIOLOGICAL SYSTEMS
o THE CELLULAR BASIS OF LIFE
o STRUCTURE AND FUNCTION
o REPRODUCTION AND INHERITANCE
o ENVIRONMENTAL INTERACTIONS
o ENERGY AND LIFE
o REGULATION
o EVOLUTION AND DIVERSITY
o SCIENTIFIC INQUIRY
o SCIENCE, TECHNOLOGY AND SOCIETY
The document differentiates the universe, galaxy, and solar system. The solar system consists of the sun and everything bound to it by gravity, including 8 planets, moons, asteroids, dwarf planets, and other objects. A galaxy is a large system of stars held together by gravity, isolated from other galaxies by vast space. The Milky Way galaxy is about 100,000 light years across and contains 200 billion stars. The universe is defined as the totality of all known objects and phenomena in space. Regarding what makes Earth unique, it notes that Earth is the only planet with an atmosphere containing 21% oxygen, it likely has the only ozone layer, and it is the only planet that is known to have life.
The document discusses different types of lenses including convex and concave lenses. It describes key lens features such as focal length and principal plane. Characteristics of images formed by convex and concave lenses are provided, including whether images are real or virtual, upright or inverted, and enlarged or reduced. Examples of optical instruments that use lenses like cameras, telescopes, microscopes and projectors are outlined. Defects in vision and lenses are also summarized.
The document compares Aristotle and Galileo's concepts of horizontal and vertical motion. Aristotle believed horizontal motion required a continuous force, while Galileo believed objects in motion stay in motion due to inertia unless acted on by an external force. For vertical motion, Aristotle believed heavier objects fall faster, while Galileo demonstrated that all objects accelerate at the same rate when in free fall, defined as motion only due to gravity. The document also discusses projectile motion, quantities used to describe motion, and examples of motion concepts.
This teaching guide provides lessons on physical science for senior high school students. It discusses the formation of elements in the universe through both the Big Bang and stellar evolution. Students will learn about the historical development of ideas regarding the atom and chemical elements from ancient Greek philosophers to modern theories. Specific scientists discussed include J.J. Thomson, Ernest Rutherford, Henry Moseley, Niels Bohr, and John Dalton. The guide aims to give students an understanding of how elements form and are distributed in the universe, as well as how modern atomic theory evolved from ancient ideas.
Polarization occurs when light vibrates in only one direction, rather than in all planes. There are several methods to polarize unpolarized light, which vibrates in all directions, including selective absorption using polarizing materials like Polaroid. Polarization experiments showed that light waves are transverse, not longitudinal, with electric and magnetic fields oscillating perpendicular to the direction of propagation. Polarized light has many applications like 3D movies, sunglasses, and improving contrast in microscopes.
This document discusses lenses and their properties. It defines convex and concave lenses, and explains that convex lenses converge light rays while concave lenses diverge them. It then describes the six cases of image formation by a convex lens depending on the object's position, including real/virtual and inverted/upright properties. Sign conventions for thin lens equations are also provided. The document contains questions related to identifying lens types, drawing ray diagrams, and calculating thin lens image characteristics.
Lenses have several important uses. Concave lenses diverge light rays, while convex lenses converge light rays. Lenses are used in cameras, telescopes, and eyeglasses. Cameras use lenses to admit more light and create a brighter, more focused image on film. Eyeglasses use lenses to correct nearsightedness and farsightedness by refocusing light rays onto the retina. Telescopes also employ lenses to magnify distant objects.
The document discusses equations for calculating velocity, acceleration, displacement, and time for objects moving with constant velocity or uniform acceleration. It provides the key equations:
1) For constant velocity, average velocity (v) equals displacement (Δx) over time (Δt), and displacement equals velocity times time.
2) For uniform acceleration, final velocity (vf) equals initial velocity (v0) plus acceleration (a) times time (Δt), and displacement equals initial velocity times time plus one-half acceleration times time squared.
3) A single equation relates displacement, initial velocity, final velocity, and acceleration, which can be rearranged to solve for any of those variables.
Newton's laws of motion by Mphiriseni Khwandamkhwanda
Newton's Laws of Motion document summarizes Newton's three laws of motion. It discusses Newton's first law, stating that objects at rest stay at rest and objects in motion stay in motion with constant velocity unless acted upon by an unbalanced force. It addresses misconceptions about the first law. Newton's second law states that acceleration is directly proportional to net force and inversely proportional to mass. Problems are provided applying the laws, including drawing free-body diagrams and solving equations of motion. Newton's third law is not discussed.
Newton's first and second laws applicationsmkhwanda
This document discusses Newton's laws of motion and their applications. It contains examples of problems involving Newton's first law regarding inertia and an object's motion when the net force is zero. Newton's second law relating force, mass and acceleration is explained. Free body diagrams are demonstrated as a problem solving tool. Examples are provided of calculating acceleration from forces using Newton's second law for objects on an inclined plane and connected objects on pulleys. Friction forces are also discussed.
- A force is a push or pull on an object due to its interaction with other objects. Common forces include gravity, normal force, tension, friction, electromagnetic force, and contact force.
- Forces are represented by arrows, with the length proportional to the magnitude. Forces can be added vectorially to find the net/resultant force. If the net force is nonzero, the object will accelerate. If it's zero, the object will maintain a constant velocity or remain at rest.
- For every action there is an equal and opposite reaction. The forces due to interactions between two objects are always equal in magnitude and opposite in direction.
This document discusses key concepts in engineering mechanics including units, dimensions, Newton's laws of motion, and vector representations of forces. It covers topics like the parallelogram law, triangle law, vector operations of addition, subtraction, dot and cross products. It also discusses concepts like coplanar forces, rectangular components, particle equilibrium, equivalent force systems, and the principle of transmissibility.
The document discusses rotational kinetic energy and rotational inertia. It defines rotational kinetic energy as 1/2Iω2, where I is the rotational inertia and ω is the angular velocity. Rotational inertia, analogous to mass in linear motion, is a measure of an object's resistance to changes in its rotational motion. It provides an example of calculating the rotational kinetic energy of a uniform disk rotating about a fixed axis, given its moment of inertia, angular acceleration, and time.
An introduction to the module is given, including forces, moments, and the important concepts of free-body diagrams and static equilibrium. These concepts will then be used to solve static framework (truss) problems using two methods: the method of joints and the method of sections.
Equilibrium and Equation of Equilibrium:2Drasel2211
This presentation discusses the concept of equilibrium in 2 dimensions. Equilibrium occurs when the net force and net torque on an object are both zero. This allows the object to remain at rest or in uniform motion. The key equations of equilibrium in 2D are: the sum of the horizontal forces equals 0 (ΣFx=0), the sum of the vertical forces equals 0 (ΣFy=0), and the sum of torques about the z-axis equals 0 (ΣMz=0). Examples are provided to demonstrate how to apply these equations to solve for unknown forces by drawing a free body diagram and setting up the appropriate equilibrium equations.
Equilibrium and Equation of Equilibrium:2Drasel2211
This presentation discusses the concept of equilibrium in 2 dimensions. Equilibrium occurs when the net force and net torque on an object are both zero. This allows the object to remain at rest or in uniform motion. The key equations of equilibrium in 2D are: the sum of the horizontal forces equals 0 (ΣFx=0), the sum of the vertical forces equals 0 (ΣFy=0), and the sum of torques about the z-axis equals 0 (ΣMz=0). Examples are provided to demonstrate how to apply these equations to solve for unknown forces by drawing a free body diagram and setting up the appropriate equilibrium equations.
This document discusses equilibrium of particles and free body diagrams (FBD) in statics. It begins by defining equilibrium of a particle as having zero net external force. A particle is a model of a real body where all forces act at a single point. The document then discusses how to draw FBDs by showing all forces and moments acting on a body. It provides examples of drawing FBDs for various systems involving spheres, rings, and cables. It also discusses applying the equations of equilibrium to solve for unknown forces using the FBD approach.
This document provides information about the recruitment exam guide and handbook for junior engineers. It includes the following sections: engineering mechanics and strength of materials, theory of machines and machine design, thermal engineering, fluid mechanics and machinery, and production engineering. It also provides information on different engineering mechanics concepts like forces, force systems, equilibrium, moments, friction, kinematics, dynamics, and Newton's laws of motion. Additionally, it covers topics like stress, strain, stress-strain relationships, shear stress, and strain tensor. Examples of stress analysis for different structural components are also given.
- Newton's laws of motion describe the relationship between an object and the forces acting upon it.
- The first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
- The second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
The document describes a train initially moving at 48 km/h that needs to stop within a certain distance without causing crates loaded on the train's flatcar floor to slide. The crates have a coefficient of static friction of 0.25 with the floor. Using equations for static friction and kinematics, the minimum stopping distance is calculated to be 36.26 meters.
With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize the Alchemist's dream of turning 'base metal' into 'gold'.
Forces can cause objects to deform, speed up, slow down, or change direction. A free-body diagram represents all the forces acting on an object with arrows pointing in the direction of each force. Newton's Second Law states that the acceleration of an object is proportional to the net force acting on it. Newton's Third Law states that for every force there is an equal and opposite reaction force.
1) Work is defined as the product of the force applied and the distance moved in the direction of the force. Work can cause a change in energy but the total energy in a system remains constant.
2) There are four types of work depending on whether the force and/or distance is constant or variable. Work by a conservative force depends only on the start and end points and not the path taken.
3) Kinetic energy is the energy of motion while potential energy is stored energy due to an object's position or state. Mechanical energy is the sum of an object's kinetic and potential energies.
This document outlines key concepts in 2D and 3D force systems. It begins by defining forces and force components in rectangular coordinate systems. It discusses concepts like concentrated vs distributed forces, and contact vs body forces. It also covers moments, couples, and resultants of force systems. Several example problems are provided to demonstrate calculating forces, moments, and resultants for 2D systems.
Gravitational field and potential, escape velocity, universal gravitational l...lovizabasharat
What is Escape Velocity-its derivation-examples-applications
Universal Gravitational Law-Derivation and Examples
Gravitational Field And Gravitational Potential-Derivation, Realation and numericals
Radial Velocity and acceleration-derivation and examples
Transverse Velocity and acceleration and examples
Presentation on Equilibrium and Equilibrium equation 2DToufiq Rifath
This document provides an overview of equilibrium and equilibrium equations in two dimensions (2D). It defines equilibrium as a state of balanced opposing forces, and describes static and dynamic equilibrium. It outlines the key equations of equilibrium for 2D systems - that the sum of the horizontal forces equals zero, the sum of the vertical forces equals zero, and the sum of the moments about any point equals zero. An example problem is shown to demonstrate applying these equations to a 2D frame with multiple forces to solve for unknown reaction forces.
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdfGetInData
Recently we have observed the rise of open-source Large Language Models (LLMs) that are community-driven or developed by the AI market leaders, such as Meta (Llama3), Databricks (DBRX) and Snowflake (Arctic). On the other hand, there is a growth in interest in specialized, carefully fine-tuned yet relatively small models that can efficiently assist programmers in day-to-day tasks. Finally, Retrieval-Augmented Generation (RAG) architectures have gained a lot of traction as the preferred approach for LLMs context and prompt augmentation for building conversational SQL data copilots, code copilots and chatbots.
In this presentation, we will show how we built upon these three concepts a robust Data Copilot that can help to democratize access to company data assets and boost performance of everyone working with data platforms.
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Discussion on Vector Databases, Unstructured Data and AI
https://www.meetup.com/unstructured-data-meetup-new-york/
This meetup is for people working in unstructured data. Speakers will come present about related topics such as vector databases, LLMs, and managing data at scale. The intended audience of this group includes roles like machine learning engineers, data scientists, data engineers, software engineers, and PMs.This meetup was formerly Milvus Meetup, and is sponsored by Zilliz maintainers of Milvus.
1. PHYSICS 13 & 11A
GENERAL PHYSICS 1
MARLON FLORES SACEDON
Dynamics of Motion:
Application of Newton’s Laws of Motion
2. Friction 𝑓 - refers to actual forces that are exerted to oppose motion
- a resistance that opposes every effort to slide or roll a body over another
Kinds of Friction:
1. Static friction - force that will just start the body.
2. Kinetic friction - force that will pull the body uniformly.
APPLICATION OF NEWTON’S LAWS OF
MOTION
Friction
Coefficient of friction 𝜇 - the ratio of the force necessary to move one surface over the other with uniform velocity to
the normal force pressing the two surfaces to other.
𝜇 =
𝑓
𝑁
Where: N is the normal force exerted by the contact surface to the object. Normal force is
always acting against and perpendicular to the surface in contact.
m
𝑁
𝑃
𝑤
𝑓
𝜃
𝑦
𝑥
𝜃
𝑓 = 𝜇𝑁
4. Free-Body Diagram (FBD)
FBD of Furniture
𝑦
𝑥
𝜮𝑭
𝒂
𝑷
𝒘 = 𝒎𝒈
N
𝒇 = 𝝁𝑵
Σ 𝐹𝑦 = 𝑁 − 𝑤 = 0 (for static equilibrium)
Σ 𝐹𝑥 = 𝑃 − 𝑓 (Net External force)
𝜮𝑭 = 𝑃𝑥 − 𝑓
Net external force
Note: If pulling force 𝑃 is less than friction 𝑓 then furniture is at
rest otherwise it will move to the right..
APPLICATION OF NEWTON’S LAWS OF
MOTION
FBD is a vectors diagram showing all forces acting on the body.
5. Free-Body Diagram (FBD)
N
P
𝒘 = 𝒎𝒈
𝑦
𝑥
𝑷 𝒙
𝑷 𝒚
FBD of box
Σ 𝐹𝑦 = 𝑁 + 𝑃𝑦 − 𝑤 = 0 (for static equilibrium)
𝒇 = 𝝁𝑵
Σ 𝐹𝑥 = 𝑃𝑥 − 𝑓 (Net External force)
𝜮𝑭 = 𝑃𝑥 − 𝑓
Note: If Σ 𝐹𝑦 is not equal to zero then box didn’t touch the ground
surface. Therefore Net external force is not equal to Σ 𝐹𝑥.
Net external force
𝜮𝑭
𝒂
APPLICATION OF NEWTON’S LAWS OF
MOTION
FBD is a vectors diagram showing all forces acting on the body.
6. Free-Body Diagram (FBD)
Exercise Problem: Construct the free-body diagram (FBD)
𝒘 = 𝒎𝒈
FBD of box
𝒘 𝒚
𝒘 𝒙
20 𝑜
APPLICATION OF NEWTON’S LAWS OF
MOTION
7. 𝑠
𝑡 = 2𝑠
𝑚 𝐴
𝑚 𝐵
Figure:
𝑚 𝐴
𝑚 𝐵
𝑚 𝐵
𝑚 𝐴
𝑠
𝑡 = 2𝑠
APPLICATION OF NEWTON’S LAWS OF
MOTIONProblem: A horizontal cord is attached to a 6.0-kg body in a horizontal table whose coefficient of kinetic friction 𝜇 𝑘 = 0.25. The cord passes
over a pulley at the end of the table and to this end is hung a body of mass 8 kg. What is the acceleration of the system and tension in the cord?
Find the distance the two bodies will travel after 2s, if they start from rest.
8. Problem: A horizontal cord is attached to a 6.0-kg body in a horizontal table whose coefficient of kinetic friction 𝜇 𝑘 = 0.25. The cord passes
over a pulley at the end of the table and to this end is hung a body of mass 8 kg. What is the acceleration of the system and tension in the cord?
Find the distance the two bodies will travel after 2s, if they start from rest.
𝑚 𝐵
𝑚 𝐴
𝑠
𝑡 = 2𝑠
𝑚 𝐴
𝑚 𝐵
Figure:
𝑚 𝐴
𝑚 𝐵
𝑠
𝑡 = 2𝑠
𝑦
𝑥
𝑦
𝑥𝑚 𝐴
𝑦
𝑥
𝑚 𝐵
+𝑇𝑐𝑜𝑟𝑑
−𝑇𝑐𝑜𝑟𝑑
−𝑤 𝐴= 𝑚 𝐴 𝑔
𝑤 𝐵 = 𝑚 𝐵 𝑔
𝑁
Σ 𝐹𝐴
Σ 𝐹𝐵
𝑎
𝑎
FBD of 𝑚 𝐴 FBD of 𝑚 𝐵
Σ 𝐹𝑥 = +𝑇𝑐𝑜𝑟𝑑 − 𝑓
Σ 𝐹𝑦 = 𝑁 − 𝑤 𝐴 = 0 (static equilibrium)
Σ 𝐹𝐴 = 𝑚 𝐴 𝑎
From Second law
𝑇𝑐𝑜𝑟𝑑 − 𝑓 = 𝑚 𝐴 𝑎
Σ 𝐹𝑦 = 0 (static equilibrium)
Σ 𝐹𝑥 = −𝑇𝑐𝑜𝑟𝑑+𝑚 𝐵 𝑔
Σ 𝐹𝐵 = 𝑚 𝐵 𝑎From Second law
−𝑇𝑐𝑜𝑟𝑑+𝑚 𝐵 𝑔 = 𝑚 𝐵 𝑎
Substi. 𝐸𝑞 2 in 𝐸𝑞. 1 to eliminate
𝑇𝑐𝑜𝑟𝑑 then solve Acceleration 𝑎.
𝑎 =
𝑔(𝑚 𝐵 − 𝜇 𝑘 𝑚 𝐴)
𝑚 𝐴 + 𝑚 𝐵
𝑎 =
9.81(8 − 0.25(6)
6 + 8
= 4.55 𝑚/𝑠2
Net external force
Net external force
APPLICATION OF NEWTON’S LAWS OF
MOTION
−𝑓
𝑇𝑐𝑜𝑟𝑑 = 𝑚 𝐵 𝑔 − 𝑚 𝐵 𝑎 Eq.2
= 𝑇𝑐𝑜𝑟𝑑 − 𝜇 𝑘 𝑚 𝐴 𝑔
𝑇𝑐𝑜𝑟𝑑 − 𝜇 𝑘 𝑚 𝐴 𝑔 = 𝑚 𝐴 𝑎
Eq.1
9. 𝑚 𝐵
𝑚 𝐴
𝑠
𝑡 = 2𝑠
𝑚 𝐴
𝑚 𝐵
Figure:
𝑚 𝐴
𝑚 𝐵
𝑠
𝑡 = 2𝑠
𝑦
𝑥
𝑦
𝑥
a) Solve for tension in the cord 𝑇𝑐𝑜𝑟𝑑 using Eq.1
𝑇𝑐𝑜𝑟𝑑 = 6 4.55 + 0.25(6)(9.81)= 42.08 N ANSWER
b) Solve for the distance 𝑠 of two bodies after travelling 2
Given:
𝑣𝑖 = 0
𝑡 = 2 𝑠
𝑎 = 4.55 𝑚/𝑠2
From kinematics: 𝑠 = 𝑣1 𝑡 +
1
2
𝑎𝑡2
𝑠 = 0 2 +
1
2
4.55 22
= 9.10 𝑚 ANSWER
APPLICATION OF NEWTON’S LAWS OF
MOTION
𝑇𝑐𝑜𝑟𝑑 − 𝑓 = 𝑚 𝐴 𝑎 Eq.1
𝑇𝑐𝑜𝑟𝑑 = 𝑚 𝐴 𝑎 + 𝜇 𝑘 𝑚 𝐴 𝑔
Problem: A horizontal cord is attached to a 6.0-kg body in a horizontal table whose coefficient of kinetic friction 𝜇 𝑘 = 0.25. The cord passes
over a pulley at the end of the table and to this end is hung a body of mass 8 kg. What is the acceleration of the system and tension in the cord?
Find the distance the two bodies will travel after 2s, if they start from rest.
10. 𝒎 𝟏
Atwood Machine
𝑤1 = +𝑚1 𝑔
−𝑇𝑐𝑜𝑟𝑑
Σ 𝐹1
𝑎
FBD of 𝑚1
𝑦
+𝑥
Σ 𝐹𝑥 = +𝑤1 − 𝑇𝑐𝑜𝑟𝑑
Net external force
Σ 𝐹1 = 𝑚1 𝑎
From Second law
+𝑤1 − 𝑇𝑐𝑜𝑟𝑑 = 𝑚1 𝑎
𝒎 𝟐
−𝑤2= 𝑚2 𝑔
+𝑇𝑐𝑜𝑟𝑑
Σ 𝐹2
𝑎
FBD of 𝑚2
𝑦
+𝑥
Σ 𝐹𝑥 = −𝑤2 + 𝑇𝑐𝑜𝑟𝑑
Net external force
Σ 𝐹2 = 𝑚2 𝑎
From Second law
−𝑤2 + 𝑇𝑐𝑜𝑟𝑑 = 𝑚2 𝑎
𝑇𝑐𝑜𝑟𝑑 = 𝑚2 𝑎 +𝑤2 𝑚1 𝑔 − 𝑇𝑐𝑜𝑟𝑑 = 𝑚1 𝑎 Eq.1
Substi Eq.2 in eq.1
𝑚1 𝑔 − (𝑚2 𝑎 +𝑚2 𝑔) = 𝑚1 𝑎
𝑇𝑐𝑜𝑟𝑑 = 𝑚2 𝑎 +𝑚2 𝑔 Eq.2
𝑎 =
𝑔(𝑚1 − 𝑚2)
𝑚1 + 𝑚2
11. Problem: Two blocks connected by a cord passing over a small, frictionless pulley rest on a double inclined plane. Block A whose mass is 𝑚 𝐴 =
100 𝑘𝑔 is on left side and Block B with mass 𝑚 𝐵 = 50 𝑘𝑔 is on the right side inclined plane.. The coefficient of kinetic frictions between
block and inclined plane on the right and left side are 𝜇 𝐴 = 0.30 and 𝜇 𝐵 = 0.25 respectively. The angles of the inclined plane are 𝜃 =
30 𝑜 (left side) and 𝛽 = 53.1 𝑜 (right side). (a) Calculate the acceleration "𝑎" of the system, (b) calculate also the tension in the cord 𝑇𝐶.
𝜃 𝛽
12. . Given:
m = 10 kg
h = 5 m
L = 10m
S1 = 2m
Ø =44o
𝜇 = 0.06 coef. of kinetic friction
Note:
Particle “m” is release from rest at pt. A and moves
to pt. B, then to pt.C, and finally to pt.D.
Neglect the effect of the change in velocity direction at pt.B.
The same value of coef. friction, from pt.A to pt.C.
Projectile motion from pt.C to pt.D.
Required:
a. Free-body diagram of the particle at inclined plane AB.
b. Free-body diagram of the particle at horizontal plane BC.
c. Unbalanced force of the particle along the inclined plane AB.
d. Unbalanced force of the particle along the horizontal plane BC.
e. acceleration, a1 of the particle along the inclined plane AB.
f. acceleration, a2 of the particle along the horizontal plane BC.
g. velocity of the particle at pt.B.
h. velocity of the particle at pt.C.
i. Range, (S2)
j. Total time of travel of particle from pt A to pt. D.
ASSIGNMENT
Figure: