Linear Impulse and Momentum
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On the History of the Radiation Reaction1 Kirk T
On the History of the Radiation Reaction1 Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (May 6, 2017; updated March 18, 2020) 1 Introduction Apparently, Kepler considered the pointing of comets’ tails away from the Sun as evidence for radiation pressure of light [2].2 Following Newton’s third law (see p. 83 of [3]), one might suppose there to be a reaction of the comet back on the incident light. However, this theme lay largely dormant until Poincar´e (1891) [37, 41] and Planck (1896) [46] discussed the effect of “radiation damping” on an oscillating electric charge that emits electromagnetic radiation. Already in 1892, Lorentz [38] had considered the self force on an extended, accelerated charge e, finding that for low velocity v this force has the approximate form (in Gaussian units, where c is the speed of light in vacuum), independent of the radius of the charge, 3e2 d2v 2e2v¨ F = = . (v c). (1) self 3c3 dt2 3c3 Lorentz made no connection at the time between this force and radiation, which connection rather was first made by Planck [46], who considered that there should be a damping force on an accelerated charge in reaction to its radiation, and by a clever transformation arrived at a “radiation-damping” force identical to eq. (1). Today, Lorentz is often credited with identifying eq. (1) as the “radiation-reaction force”, and the contribution of Planck is seldom acknowledged. This note attempts to review the history of thoughts on the “radiation reaction”, which seems to be in conflict with the brief discussions in many papers and “textbooks”.3 2 What is “Radiation”? The “radiation reaction” would seem to be a reaction to “radiation”, but the concept of “radiation” is remarkably poorly defined in the literature. -
Lecture 10: Impulse and Momentum
ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Kinetics of a particle: Impulse and Momentum Chapter 15 Chapter objectives • Develop the principle of linear impulse and momentum for a particle • Study the conservation of linear momentum for particles • Analyze the mechanics of impact • Introduce the concept of angular impulse and momentum • Solve problems involving steady fluid streams and propulsion with variable mass W. Wang Lecture 10 • Kinetics of a particle: Impulse and Momentum (Chapter 15) - 15.1-15.3 W. Wang Material covered • Kinetics of a particle: Impulse and Momentum - Principle of linear impulse and momentum - Principle of linear impulse and momentum for a system of particles - Conservation of linear momentum for a system of particles …Next lecture…Impact W. Wang Today’s Objectives Students should be able to: • Calculate the linear momentum of a particle and linear impulse of a force • Apply the principle of linear impulse and momentum • Apply the principle of linear impulse and momentum to a system of particles • Understand the conditions for conservation of momentum W. Wang Applications 1 A dent in an automotive fender can be removed using an impulse tool, which delivers a force over a very short time interval. How can we determine the magnitude of the linear impulse applied to the fender? Could you analyze a carpenter’s hammer striking a nail in the same fashion? W. Wang Applications 2 Sure! When a stake is struck by a sledgehammer, a large impulsive force is delivered to the stake and drives it into the ground. -
Classical Mechanics
Classical Mechanics Hyoungsoon Choi Spring, 2014 Contents 1 Introduction4 1.1 Kinematics and Kinetics . .5 1.2 Kinematics: Watching Wallace and Gromit ............6 1.3 Inertia and Inertial Frame . .8 2 Newton's Laws of Motion 10 2.1 The First Law: The Law of Inertia . 10 2.2 The Second Law: The Equation of Motion . 11 2.3 The Third Law: The Law of Action and Reaction . 12 3 Laws of Conservation 14 3.1 Conservation of Momentum . 14 3.2 Conservation of Angular Momentum . 15 3.3 Conservation of Energy . 17 3.3.1 Kinetic energy . 17 3.3.2 Potential energy . 18 3.3.3 Mechanical energy conservation . 19 4 Solving Equation of Motions 20 4.1 Force-Free Motion . 21 4.2 Constant Force Motion . 22 4.2.1 Constant force motion in one dimension . 22 4.2.2 Constant force motion in two dimensions . 23 4.3 Varying Force Motion . 25 4.3.1 Drag force . 25 4.3.2 Harmonic oscillator . 29 5 Lagrangian Mechanics 30 5.1 Configuration Space . 30 5.2 Lagrangian Equations of Motion . 32 5.3 Generalized Coordinates . 34 5.4 Lagrangian Mechanics . 36 5.5 D'Alembert's Principle . 37 5.6 Conjugate Variables . 39 1 CONTENTS 2 6 Hamiltonian Mechanics 40 6.1 Legendre Transformation: From Lagrangian to Hamiltonian . 40 6.2 Hamilton's Equations . 41 6.3 Configuration Space and Phase Space . 43 6.4 Hamiltonian and Energy . 45 7 Central Force Motion 47 7.1 Conservation Laws in Central Force Field . 47 7.2 The Path Equation . -
Impulse and Momentum
Impulse and Momentum All particles with mass experience the effects of impulse and momentum. Momentum and inertia are similar concepts that describe an objects motion, however inertia describes an objects resistance to change in its velocity, and momentum refers to the magnitude and direction of it's motion. Momentum is an important parameter to consider in many situations such as braking in a car or playing a game of billiards. An object can experience both linear momentum and angular momentum. The nature of linear momentum will be explored in this module. This section will discuss momentum and impulse and the interconnection between them. We will explore how energy lost in an impact is accounted for and the relationship of momentum to collisions between two bodies. This section aims to provide a better understanding of the fundamental concept of momentum. Understanding Momentum Any body that is in motion has momentum. A force acting on a body will change its momentum. The momentum of a particle is defined as the product of the mass multiplied by the velocity of the motion. Let the variable represent momentum. ... Eq. (1) The Principle of Momentum Recall Newton's second law of motion. ... Eq. (2) This can be rewritten with accelleration as the derivate of velocity with respect to time. ... Eq. (3) If this is integrated from time to ... Eq. (4) Moving the initial momentum to the other side of the equation yields ... Eq. (5) Here, the integral in the equation is the impulse of the system; it is the force acting on the mass over a period of time to . -
Power Sources Challenge
POWER SOURCES CHALLENGE FUSION PHYSICS! A CLEAN ENERGY Summary: What if we could harness the power of the Sun for energy here on Fusion reactions occur when two nuclei come together to form one Earth? What would it take to accomplish this feat? Is it possible? atom. The reaction that happens in the sun fuses two Hydrogen atoms together to produce Helium. It looks like this in a very simplified way: Many researchers including our Department of Energy scientists and H + H He + ENERGY. This energy can be calculated by the famous engineers are taking on this challenge! In fact, there is one DOE Laboratory Einstein equation, E = mc2. devoted to fusion physics and is committed to being at the forefront of the science of magnetic fusion energy. Each of the colliding hydrogen atoms is a different isotope of In order to understand a little more about fusion energy, you will learn about hydrogen, one deuterium and one the atom and how reactions at the atomic level produce energy. tritium. The difference in these isotopes is simply one neutron. Background: It all starts with plasma! If you need to learn more about plasma Deuterium has one proton and one physics, visit the Power Sources Challenge plasma activities. neutron, tritium has one proton and two neutrons. Look at the The Fusion Reaction that happens in the SUN looks like this: illustration—do you see how the mass of the products is less than the mass of the reactants? That is called a mass deficit and that difference in mass is converted into energy. -
Optimum Design of Impulse Ventilation System in Underground
ering & ine M g a n n , E a Umamaheswararao Ind Eng Manage 2017, 6:4 l g a i e r m t s DOI: 10.4172/2169-0316.1000238 e u n d t n I Industrial Engineering & Management ISSN: 2169-0316 Research Article Open Access Optimum Design of Impulse Ventilation System in Underground Car Parking Basement by Using CFD Simulation Lakamana Umamaheswararao* Design and Development Engineer, Saudi Fan Industries, KSA Abstract The most significant development in car park ventilation design has been the introduction of Impulse Ventilation. It is an innovative alternative to traditional systems and provides a number of significant benefits. The ventilation of car parks is essential for removing vehicle exhausts Fumes and smoke in case of fire containing harmful pollutants. So design of impulse systems is usually proven by use of CFD (Computational Fluid Dynamic) analysis. In this study considered one of the car parking basement which is in Riyadh, Saudi Arabia and study was conducted by using ANSYS-Fluent. The field study was carried to collect the actual data of boundary conditions for CFD simulation. In this study, two Cases of jet fan smoke ventilation systems were considered, one has 8 jet fans according to the customer and another one has 11 jet fans which positions were changed accordingly. Base on the comparison of simulation data, ventilation system with 11 jet fans can help to improve the evacuation of fumes in the car parking area and it is also observed that the concentration of CO minimized within 15 minutes. Keywords: Impulse ventilation; CFD; AMC hospital; Jet fans The CFD model accounted for columns, beams, internal walls and other construction elements which could form an obstruction to the Introduction air flow as shown in Figure 1 and total car parking area is 3500 2m . -
Physics 101 Today Chapter 5: Newton's Third
Physics 101 Today Chapter 5: Newton’s Third Law First, let’s clarify notion of a force : Previously defined force as a push or pull. Better to think of force as an interaction between two objects. You can’t push anything without it pushing back on you ! Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Newton’s 3 rd Law - often called “action-reaction ” Eg. Leaning against a wall. You push against the wall. The wall is also pushing on you, equally hard – normal/support force. Now place a piece of paper between the wall and hand. Push on it – it doesn’t accelerate must be zero net force. The wall is pushing equally as hard (normal force) on the paper in the opposite direction to your hand, resulting in zero Fnet . This is more evident when hold a balloon against the wall – it is squashed on both sides. Eg. You pull on a cart. It accelerates. The cart pulls back on you (you feel the rope get tighter). Can call your pull the “ action ” and cart’s pull the “ reaction ”. Or, the other way around. • Newton’s 3 rd law means that forces always come in action -reaction pairs . It doesn’t matter which is called the action and which is called the reaction. • Note: Action-reaction pairs never act on the same object Examples of action-reaction force pairs In fact it is the road’s push that makes the car go forward. Same when we walk – push back on floor, floor pushes us forward. -
HW 6, Question 1: Forces in a Rotating Frame
HW 6, Question 1: Forces in a Rotating Frame Consider a solid platform, like a \merry-go round", that rotates with respect to an inertial frame of reference. It is oriented in the xy plane such that the axis of rotation is in the z-direction, i.e. ! = !z^, which we can take to point out of the page. Now, let us also consider a person walking on the rotating platform, such that this person is walking radially outward on the platform with respect to their (non-inertial) reference frame with velocity v = vr^. In what follows for Question 1, directions in the non-inertial reference frame (i.e. the frame of the walking person) are defined in the following manner: the x0-direction points directly outward from the center of the merry-go round; the y0 points in the tangential direction of rotation in the plane of the platform; and the z0-direction points out of the page, and in the same direction as the z-direction for the inertial reference frame. (a) Identify all forces. Since the person's reference frame is non-inertial, we need to account for the various fictitious forces given the description above, as well as any other external/reaction forces. The angular rate of rotation is constant, and so the Euler force Feul = m(!_ × r) = ~0. The significant forces acting on the person are: 0 • the force due to gravity, Fg = mg = mg(−z^ ), 2 0 • the (fictitious) centrifugal force, Fcen = m! × (! × r) = m! rx^ , 0 • the (fictitious) Coriolis force, Fcor = 2mv × ! = 2m!v(−y^ ), • the normal force the person experiences from the rotating platform N = Nz^0, and • a friction force acting on the person, f, in the x0y0 plane. -
Impulse Response of Civil Structures from Ambient Noise Analysis by German A
Bulletin of the Seismological Society of America, Vol. 100, No. 5A, pp. 2322–2328, October 2010, doi: 10.1785/0120090285 Ⓔ Short Note Impulse Response of Civil Structures from Ambient Noise Analysis by German A. Prieto, Jesse F. Lawrence, Angela I. Chung, and Monica D. Kohler Abstract Increased monitoring of civil structures for response to earthquake motions is fundamental to reducing seismic risk. Seismic monitoring is difficult because typically only a few useful, intermediate to large earthquakes occur per decade near instrumented structures. Here, we demonstrate that the impulse response function (IRF) of a multistory building can be generated from ambient noise. Estimated shear- wave velocity, attenuation values, and resonance frequencies from the IRF agree with previous estimates for the instrumented University of California, Los Angeles, Factor building. The accuracy of the approach is demonstrated by predicting the Factor build- ing’s response to an M 4.2 earthquake. The methodology described here allows for rapid, noninvasive determination of structural parameters from the IRFs within days and could be used for state-of-health monitoring of civil structures (buildings, bridges, etc.) before and/or after major earthquakes. Online Material: Movies of IRF and earthquake shaking. Introduction Determining a building’s response to earthquake an elastic medium from one point to another; traditionally, it motions for risk assessment is a primary goal of seismolo- is the response recorded at a receiver when a unit impulse is gists and structural engineers alike (e.g., Cader, 1936a,b; applied at a source location at time 0. Çelebi et al., 1993; Clinton et al., 2006; Snieder and Safak, In many studies using ambient vibrations from engineer- 2006; Chopra, 2007; Kohler et al., 2007). -
A Short History of Physics (Pdf)
A Short History of Physics Bernd A. Berg Florida State University PHY 1090 FSU August 28, 2012. References: Most of the following is copied from Wikepedia. Bernd Berg () History Physics FSU August 28, 2012. 1 / 25 Introduction Philosophy and Religion aim at Fundamental Truths. It is my believe that the secured part of this is in Physics. This happend by Trial and Error over more than 2,500 years and became systematic Theory and Observation only in the last 500 years. This talk collects important events of this time period and attaches them to the names of some people. I can only give an inadequate presentation of the complex process of scientific progress. The hope is that the flavor get over. Bernd Berg () History Physics FSU August 28, 2012. 2 / 25 Physics From Acient Greek: \Nature". Broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves. The universe is commonly defined as the totality of everything that exists or is known to exist. In many ways, physics stems from acient greek philosophy and was known as \natural philosophy" until the late 18th century. Bernd Berg () History Physics FSU August 28, 2012. 3 / 25 Ancient Physics: Remarkable people and ideas. Pythagoras (ca. 570{490 BC): a2 + b2 = c2 for rectangular triangle: Leucippus (early 5th century BC) opposed the idea of direct devine intervention in the universe. He and his student Democritus were the first to develop a theory of atomism. Plato (424/424{348/347) is said that to have disliked Democritus so much, that he wished his books burned. -
Actions for Flood Resilient Homes: Pumping Guidance
Actions for Flood Resilient Homes: Pumping Guidance If dry floodproofing methods fail during a large storm or you’ve chosen wet floodproofing, you may end up with a significant amount of water in your basement. Though your impulse may be to remove the water as soon as possible, it’s important to remember that moving too quickly may cause structural damage to your home. Even though flood waters may have receded, there is still water in the ground that may be exerting force against your basement walls. If that force is greater than the force of water inside your basement, the foundation, basement walls, or floors may rupture or crack. Before flood action During flood action After flood action Pumping procedure—when and how much to pump If you need to pump water out of your basement or house, the Federal Emergency Management Agency (FEMA) recommends taking the following steps to avoid serious damage to your home. 1. Begin pumping only when floodwaters are no longer covering the ground outside. 2. Pump out 1 foot of water, mark the water level, and wait overnight. 3. Check the water level the next day. If the level rose to the previous mark, it is still too early to drain the basement. 4. Wait 24 hours, pump the water down 1 foot, and mark the water level. Check the level the next day. 5. When the water level stops returning to your mark, pump out 2 to 3 feet and wait overnight. Repeat this process daily until all of the water is out of the basement. -
High Temperatures Predicted in the Granitic Basement of Northwest Alberta - an Assessment of the Egs Energy Potential
PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 24-26, 2014 SGP-TR-202 HIGH TEMPERATURES PREDICTED IN THE GRANITIC BASEMENT OF NORTHWEST ALBERTA - AN ASSESSMENT OF THE EGS ENERGY POTENTIAL Jacek Majorowicz1*, Greg Nieuwenhuis1, Martyn Unsworth1, Jordan Phillips1 and Rebecca Verveda1 1University of Alberta Department of Physics, Canada *email: [email protected] Keywords: Heat flow, EGS, Alberta, Canada ABSTRACT Northwest Alberta is characterized by high subsurface temperatures that may represent a significant geothermal resource. In this paper we present new data that allows us to make predictions of the temperatures that might be found within the crystalline basement rocks. In this region the Western Canada Sedimentary Basin (WCSB) is composed of up to 3 km of Phanerozoic sedimentary rocks with low thermal conductivity, which act as a thermal blanket. Commercial well-logging data was cleaned of erroneous data and corrected for paleoclimatic effects to give an average geothermal gradient of 35 K per km, and maximum geothermal gradients reaching 50K per km. These gradients, along with a thermal conductivity model of sedimentary rocks, were then used to estimate heat flow across the unconformity at the base of the WCSB. The calculations assumed a heat generation of 0.5 µW/m3 within the sedimentary rocks. Estimation of temperatures within the crystalline basement rocks requires knowledge of the thermal conductivity (TC) and heat generation (HG) of these rocks. These are mainly granitic Precambrian rocks. Thermal conductivity (TC) and heat generation (HG) of the basement rocks were measured on samples recovered from hundreds of wells that sampled the Pre-Cambrian basement rocks.