Chapter 3
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This document summarizes projectile motion in two dimensions. It explains that a projectile's curved motion can be analyzed as the combination of horizontal and vertical linear motion. In the horizontal direction, the motion is at a constant speed due to the lack of acceleration. In the vertical direction, gravity causes acceleration, resulting in parabolic motion. The document provides an example problem of analyzing the motion of a cannon ball fired at an angle, solving for variables like time, distance, and the equation of its parabolic path. It also gives another example of determining how far a ball will land after rolling off a table.
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A projectile moves under the influence of gravity in two dimensions along a parabolic path. The horizontal and vertical components of the projectile's motion can be described using equations that include the initial velocity, launch angle, and gravitational acceleration. These equations show that the trajectory of a projectile forms a parabolic curve and can be used to calculate the maximum height, total time, and total horizontal range of the projectile's motion.
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The document discusses projectile motion and provides sample problems to illustrate the concepts. It begins by defining projectile motion and describing the forces acting on a projectile. It then presents the kinematic equations for the horizontal and vertical motion of a projectile. Several sample problems are worked out applying these equations to calculate values like minimum launch speed, projectile impact location and time, and velocity at impact.
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Projectile motion can be thought of as the combination of horizontal and vertical motion. The horizontal motion is unaffected by gravity and follows the equation x=u*cosθ*t, while the vertical motion is affected by gravity and follows the equation y=u*sinθ*t - 0.5*g*t^2. The path of a projectile forms a parabolic curve. Factors like the launch angle and initial velocity determine the time of flight, maximum height, and horizontal range of the projectile. Projectile motion has applications in various sports to calculate the optimal angle for maximum distance.
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This document discusses projectile motion and provides examples. It can be analyzed as independent horizontal and vertical motion components. Projectile paths can be modeled using hanging beads on a ruler. Example problems calculate the time and speed of a ball rolling off a table and the maximum speed of a tennis ball clearing a net within the court boundaries, showing that mass does not affect projectile motion.
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The document summarizes key concepts in kinematics including displacement, velocity, acceleration, and motion under constant acceleration. It defines displacement as the difference between an object's initial and final positions, and average velocity as the displacement divided by the time elapsed. Acceleration is defined as the rate of change of velocity with respect to time. Examples are provided to demonstrate calculations of displacement, velocity, acceleration, and motion under gravity. Key equations of motion are also summarized.
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A projectile moves under the influence of gravity in two dimensions along a parabolic path. The horizontal and vertical components of the projectile's motion can be described using equations that include the initial velocity, launch angle, and gravitational acceleration. These equations show that the trajectory of a projectile forms a parabolic curve and can be used to calculate the maximum height, total time, and total horizontal range of the projectile's motion.
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The document discusses projectile motion and provides sample problems to illustrate the concepts. It begins by defining projectile motion and describing the forces acting on a projectile. It then presents the kinematic equations for the horizontal and vertical motion of a projectile. Several sample problems are worked out applying these equations to calculate values like minimum launch speed, projectile impact location and time, and velocity at impact.
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Projectile motion can be thought of as the combination of horizontal and vertical motion. The horizontal motion is unaffected by gravity and follows the equation x=u*cosθ*t, while the vertical motion is affected by gravity and follows the equation y=u*sinθ*t - 0.5*g*t^2. The path of a projectile forms a parabolic curve. Factors like the launch angle and initial velocity determine the time of flight, maximum height, and horizontal range of the projectile. Projectile motion has applications in various sports to calculate the optimal angle for maximum distance.
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This document discusses projectile motion and provides examples. It can be analyzed as independent horizontal and vertical motion components. Projectile paths can be modeled using hanging beads on a ruler. Example problems calculate the time and speed of a ball rolling off a table and the maximum speed of a tennis ball clearing a net within the court boundaries, showing that mass does not affect projectile motion.
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Physics by Younes Sina
1) A wave is a disturbance that transfers energy through a medium without permanent transfer of matter. This document discusses mechanical and electromagnetic waves, their characteristics such as wavelength and frequency, and how waves behave in different media like strings and pipes.
2) Resonance occurs when an object vibrates at its natural frequency, causing large oscillations. Standing waves can form in pipes and strings, with nodes and antinodes depending on boundary conditions and wavelength.
3) The Doppler effect describes the change in frequency heard by an observer due to relative motion between the source and observer. The pitch is higher if approaching and lower if receding due to the change in wavelength reaching the observer each second.
Chapter 14
This document discusses the expansion of gases and the relationships between pressure, volume, temperature, and number of moles in gases. It introduces the ideal gas law (PV=nRT) and describes some key gas processes including isobaric (constant pressure), isothermal (constant temperature), and isometric (constant volume) processes. Examples are provided to demonstrate how to use the ideal gas law and gas equations of state to calculate pressure, volume, temperature, or number of moles given values of the other variables.
Chapter 12
The document discusses temperature, heat, and phase changes. It defines temperature as a measure of the average kinetic energy of particles in an object. Temperature scales like Fahrenheit, Celsius, and Kelvin are introduced. Heat is a form of energy that transfers between objects due to temperature differences. Equations are provided to calculate heat transfer during temperature changes and phase changes using values like specific heat and latent heat. Examples demonstrate using the equations to solve heat and temperature problems involving substances like water, ice, and metals.
Chapter 11
This document contains examples and solutions related to fluid statics concepts such as pressure, density, buoyancy, and Pascal's principle. It begins with examples calculating the mass, weight, density, and pressure using given values. Later examples apply concepts like buoyancy, pressure at depths, and pressure transmission using hydraulic jacks. Key formulas introduced include pressure (p=F/A), fluid pressure (p=hρg), and buoyancy (B=Vfluidρfluid). Overall, the document provides practice problems and solutions for understanding fundamental fluid statics principles.
Chapter 9
This document provides examples and explanations of concepts related to rotational kinetics, including:
- Torque is calculated as the product of a force and its perpendicular distance from the axis of rotation. Net torque is the sum of all torques acting on an object.
- Rotational equilibrium occurs when the net torque on an object is zero, meaning the sum of clockwise and counterclockwise torques are equal.
- The center of mass of a uniformly distributed object is located at its geometric center. For rotational problems involving uniform objects, the center of mass can be treated as the axis of rotation.
- Newton's second law for rotational motion states that the net torque equals the product of the object's moment
Chapter 8
This chapter discusses rotational kinematics, including angular displacement (θ), angular velocity (ω), angular acceleration (α), and time (t). Key relationships are developed between these rotational variables and their linear motion counterparts. Examples are provided to demonstrate calculating angular acceleration, angular displacement, angular velocity, tangential acceleration, centripetal acceleration, and tangential and centripetal forces for objects undergoing rotational motion. Homework problems 1 through 5 at the end of the chapter are assigned.
Chapter 6
This document discusses work, energy, and power. It defines work as the product of parallel force and distance. Kinetic energy and gravitational potential energy are forms of mechanical energy. The work-kinetic energy theorem states that work done by net force equals change in kinetic energy. The law of conservation of energy says energy cannot be created or destroyed, only converted from one form to another. Power is defined as work done per unit time. Examples calculate work, kinetic energy, potential energy, efficiency, and power for various situations.
Chapter 5
This document summarizes key concepts about uniform circular motion including:
- Radians are the SI unit for measuring angles where 1 radian is the central angle that spans an arc equal to the circle's radius.
- Formulas relate angular quantities like speed (ω) and displacement (θ) to linear quantities like speed (v) and arc length (s) using the radius (R).
- Centripetal force (Fc) is required to cause circular motion and is given by Fc = Mv2/R, where M is the object's mass and v is its speed.
- Banked roads allow vehicles to safely take curved portions faster by providing tilt that replaces needed friction with
Chapter 4
Force may cause motion or deformation of an object. Newton's second law relates the net force on an object to its acceleration. An example calculates the engine force needed to accelerate a car based on its mass, acceleration, and frictional force. The document provides additional examples applying Newton's laws to calculate accelerations, forces, distances, and times for objects undergoing different motions.
Chapter 1
This document discusses fundamental units, vectors, and trigonometry. It begins by defining basic units like length, time, and velocity. It then explains that vectors require both a magnitude and direction, while scalars only require a magnitude. The document provides examples of adding vectors graphically using the head-to-tail method and analytically using trigonometric functions. It also discusses solving for unknown sides of triangles using trigonometric functions like sine, cosine, and tangent.
ICDIM 2012 presentation
This study investigated the implantation of sapphire by zirconium and zirconium plus oxygen ions. Important factors that influence amorphization during ion implantation include temperature, ion mass, energy, and fluence. Rutherford backscattering spectrometry was used to determine the threshold fluence for amorphization in sapphire by zirconium implantation and examine the effect of additional oxygen implantation. Optical absorption and photoluminescence measurements provided information about induced color centers and defects from the ion irradiation.
Phase Diagram, ZrO2 and Al2O3 System
This document discusses the Al2O3-ZrO2 phase diagram through several figures and studies:
1) It presents experimental and calculated Al2O3-ZrO2 phase diagrams showing the different phases like tetragonal ZrO2, monoclinic ZrO2, and liquid present at different temperatures and compositions.
2) Studies found the eutectic composition to be around 42.5% ZrO2 with a eutectic temperature of around 1910°C.
3) One study using solar furnace and electron microprobe analysis examined 17 compositions between 0-100% ZrO2 and identified phase transitions between tetragonal, monoclinic,
Electron irradiation effect on Al2O3
1. Electron irradiation of sapphire (Al2O3) results in both electronic and nuclear damage.
2. Electronic damage includes electron excitation and ionization via interactions between the incident 1 MeV electrons and the aluminum and oxygen atoms in Al2O3.
3. Nuclear damage, or displacement damage, occurs when electrons transfer sufficient energy to atomic nuclei to displace them from their lattice sites, calculated using models of electron-atom cross sections and displacement thresholds.
Line Spectra (Rydberg’s Constant)
The document describes an experiment to measure Rydberg's constant using the emission spectrum of hydrogen. Electrons in hydrogen atoms absorb energy and transition to higher energy levels. When they drop down, they emit photons of specific wavelengths according to Planck's law. By measuring the wavelengths of photons emitted during transitions from higher to lower energy levels in the Balmer series, Rydberg's constant can be calculated and verified. Measurements of hydrogen's spectral lines will be used to calculate Rydberg's constant and compare to the accepted value.
Nuclear Radiation, the chart of nuclides
This document provides information about nuclear radiation and the chart of nuclides. It defines key terms like thermal neutrons and fast neutrons. It also summarizes how nuclear reactors work through the fission of U-235 when it absorbs a neutron, and the concept of critical mass. The bulk of the document provides a guide to reading and understanding the chart of nuclides, defining various symbols and indicators on the chart.
Ion implantation effects in sapphire-Poster for advisory meeting at utk
This document discusses a study on the effects of ion implantation in sapphire. Zirconium and boron ions were implanted into sapphire single crystals at room temperature. For zirconium implantation, an amorphous layer was formed at fluences above 4x10^16 Zr+/cm^2. RBS-C, XRD, and other analysis found zirconium formed clusters in the amorphous region. For boron implantation, a high defect density was found without complete loss of crystallinity for fluences up to 1x10^17 B+/cm^2. The study aims to identify the nature of defects introduced and how implanted species interact with the material.
RBS
This document discusses backscattering spectrometry, which uses elastic scattering of ions to determine the elemental composition of materials. It describes how Rutherford scattering can be used for low energy particles, while higher energies require solving the Schrodinger equation. Examples are given of using kinematic factors to identify elements in a spectrum and calculating stopping power and cross sections. The document outlines approaches for thin film analysis using peak integration and mean energy calculations to determine areal densities and stoichiometry.
Younes Sina, Ion implantation and thermal annealing of α-Al2O3 single crystals
This document describes an experiment involving ion implantation and thermal annealing of chromium ions in alpha aluminum oxide single crystals. Chromium ions were implanted at energies of 280-300 keV and doses of 1016-1017 ions/cm2. Backscattering spectroscopy measurements showed the implantation caused damage in the aluminum and oxygen sublattices but did not amorphize the surface region. Thermal annealing from 800-1600°C led to damage recovery and incorporation of chromium into substitutional lattice sites. Angular scans and calculations determined the chromium was substituting into sites in the aluminum sublattice rather than the oxygen sublattice.
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Chapter 3
- 1. Chapter 3 Motion in Two Dimensions Younes Sina
- 2. Curved motion of a projectile is a motion in two dimensions. For example, if an object is to move along a curve as shown in the following figure, its position and its velocity at any given time ( t ) can be determined by its two coordinates ( x ) and ( y ). This parabolic motion can be replaced by a constant speed motion in the horizontal direction (x-axis) and an accelerated motion in the vertical direction (y-axis).
- 3. The package falling from the plane is an example of projectile motion. An accelerated motion in the vertical direction constant speed motion in the horizontal direction (x-axis)
- 4. The path of motion of the ball in air (neglecting air resistance) is a parabola.
- 5. The reason for the constant speed motion along the x- axis is that there is no gravitational pull horizontally to accelerate the ball and, neglecting air resistance, there is no force to slow it down. In the y-direction, because of the gravitational pull, it first slows down as it goes upward, and then speeds up as it returns to the ground.
- 6. In the x-direction: In the y-direction: x = (1/2) ax t2 + vix t y = (1/2) g t2 + viy t Since ax = 0, g = (vfy -viy )/ t x = vix t vfy 2 - viy 2 = 2 g y
- 8. Example : A cannon ball is fired at an initial speed of 250m/s through a 27o angle. Determine (a) its horizontal and vertical components of velocity, (b) the time it takes to reach the highest point, (c) the highest elevation it reaches, (d) the time it spends in air before landing, (e) the farthest horizontal distance it travels before landing (f) the equation of its path.
- 9. In the x-direction: In the y-direction: x = (1/2) ax t2 + vix t y = (1/2) g t2 + viy t Since ax = 0, g = (vfy -viy )/ t x = vix t vfy 2 - viy 2 = 2 g y Vix = v0cos(θo) Viy=v0cos(θo) Vfy = 0 x = vix t
- 10. Solution: (a) Vix = 250cos(27o) = 223m/s Viy = 250sin(27o) = 113m/s. (b) At the highest point, Vfy = 0 ; from g = (Vfy - Viy) / t t = (Vfy - Viy) /g = (0 - 113 ) / -9.8 = 12s (c) At the highest point, Vfy = 0 ; from (Vfy)2 - (Viy)2 = 2 g y 02 - 1132 = 2(-9.8)y ; y = 650m (d) Using the result of Part (b), ttotal = 2(12s) = 24s. (e) Using the only x-equation, x = Vix t, x = ( 223 m/s)( 24s ) = 5400m (f) To find the equation of the path (a parabola), the common variable or the common parameter ( t ), must be eliminated between the x- and y-components of motion. To do this, let us first write down the equations of motion in the x- and y- directions. In the y-direction, y = (1/2) g t2 + Viyt y = -4.9t2 + 113t In the x-direction, x = Vix t x = 223 t or t = x / 223 Substituting for ( t ) in the y-equation, yields: y = -4.9( x / 223)2 + 113 ( x / 223) y = -0.000099 x2 + 0.51 x (A parabola)
- 11. Example : A small ball is rolling at a speed of 5.0m/s on a horizontal table 1.2m high with respect to the floor. How far from the edge of the table does it land after rolling off the table? V= 5.0m/s h=1.2m θ= 0o
- 13. Homework problems 1 through 3 chapter 3