# Why Bother Teaching Mechanical Energy Conservation?

Note: It is assumed that the reader has read part I and part II of the series.In view of what has already been said, there seem to be three options for proceeding with the teaching of mechanical energy conservation in introductory physics courses.Make no changes.Keep teaching mechanical energy conservation but fix it first.Abandon mechanical energy conservation and replace it with the law of energy conservation.Option 1 is the default “do nothing” option; it is what we have now and we know exactly what it looks like. Option 3 has been presented in some detail in part II. Because option 2...…Note: It is assumed that the reader has read part I and part II of the series.In view of what has already been said, there seem to be three options for proceeding with the teaching of mechanical energy conservation in introductory physics courses.Make no changes.Keep teaching mechanical energy conservation but fix it first.Abandon mechanical energy conservation and replace it with the law of energy conservation.Option 1 is the default “do nothing” option; it is what we have now and we know exactly what it looks like. Option 3 has been presented in some detail in part II. Because option 2...WW…

# Centrifugal Force Reversal in Kerr Spacetime

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# Physically Reasonable Waves on a String

(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> Physics teachers who are either writing physics questions that deal with waves on a string, or setting up equipment for a class lab or demo of standing waves on a string, might find the following analysis useful. When writing questions for physics tests or homework, it is preferable to use physically plausible values for any quantities (Ref. 1). With that in mind, let us explore what physically limits quantities such as wave speed or string tension in a typical...…(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> Physics teachers who are either writing physics questions that deal with waves on a string, or setting up equipment for a class lab or demo of standing waves on a string, might find the following analysis useful. When writing questions for physics tests or homework, it is preferable to use physically plausible values for any quantities (Ref. 1). With that in mind, let us explore what physically limits quantities such as wave speed or string tension in a typical...WW…

# The Twin Paradox for Freely-falling Observers

(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> The “twin paradox” is often discussed in the introductory treatment of special relativity. Under “twin paradox” we understand the fact that if two twins start from the same place with synchronized clocks, travelling in an arbitrary way and then meet again at the same spacetime point, where they compare their clocks, in general they find different times. According to the clock hypothesis the time of a proper clock is independent of acceleration and given by the proper times...…(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> The “twin paradox” is often discussed in the introductory treatment of special relativity. Under “twin paradox” we understand the fact that if two twins start from the same place with synchronized clocks, travelling in an arbitrary way and then meet again at the same spacetime point, where they compare their clocks, in general they find different times. According to the clock hypothesis the time of a proper clock is independent of acceleration and given by the proper times...WW…

# A Principle Explanation of the "Mysteries" of Modern Physics

(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> All undergraduate physics majors are shown how the counterintuitive aspects (“mysteries”) of time dilation and length contraction in special relativity (SR) follow from the light postulate, i.e., that everyone measures the same value for the speed of light c, regardless of their motion relative to the source (see this , for example). And, we can understand the light postulate to follow from the principle of relativity, sometimes referred to as “no preferred reference...…(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> All undergraduate physics majors are shown how the counterintuitive aspects (“mysteries”) of time dilation and length contraction in special relativity (SR) follow from the light postulate, i.e., that everyone measures the same value for the speed of light c, regardless of their motion relative to the source (see this , for example). And, we can understand the light postulate to follow from the principle of relativity, sometimes referred to as “no preferred reference...WW…

# Anatomy of Compton Scattering

(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> In this article we take as our starting point the original equations which Compton drew up and solved in his ground-breaking 1925 article: From the above equations Compton solved for two variables namely ##\beta## the ratio of electron speed to velocity of light and for ##\nu_{\theta}##, the frequency of the scattered photon. He re-wrote the solution for the second in wavelength form as it is commonly presented (albeit requiring us to replace ##2\sin^2 \frac{\theta}{2}##...…(adsbygoogle=window.adsbygoogle||[]).push({google_ad_client:"ca-pub-6580726045122001",enable_page_level_ads:true}); --> In this article we take as our starting point the original equations which Compton drew up and solved in his ground-breaking 1925 article: From the above equations Compton solved for two variables namely ##\beta## the ratio of electron speed to velocity of light and for ##\nu_{\theta}##, the frequency of the scattered photon. He re-wrote the solution for the second in wavelength form as it is commonly presented (albeit requiring us to replace ##2\sin^2 \frac{\theta}{2}##...WW…

# Is Pressure A Source Of Gravity?

In a previous , I posed the question “Does Gravity Gravitate?” and explained how, depending on how you interpreted the terms “gravity” and “gravitate”, one could answer the question either way, yes or no. This article will treat its title question in a similar fashion. :-)To be sure, this case is a bit simpler than the previous one, because there is only one term that can be given more than one meaning. The term “pressure” is clear: it means the spatial diagonal components of the stress-energy tensor. (More precisely, it means those components in the rest frame of a fluid, but we won’t...…In a previous , I posed the question “Does Gravity Gravitate?” and explained how, depending on how you interpreted the terms “gravity” and “gravitate”, one could answer the question either way, yes or no. This article will treat its title question in a similar fashion. :-)To be sure, this case is a bit simpler than the previous one, because there is only one term that can be given more than one meaning. The term “pressure” is clear: it means the spatial diagonal components of the stress-energy tensor. (More precisely, it means those components in the rest frame of a fluid, but we won’t...WW…

# Massive Meets Massless: Compton Scattering Revisited

In a previous article entitled “” we analysed collisions between a moving and stationary object by defining the co-ordinate axes as being respectively parallel and perpendicular to the post collision direction of motion of the stationary object. In this article we will be adopting the same approach to analyse the well known physical phenomenon known as Compton scattering in which a photon collides with a stationary electron, imparts momentum to the latter and hence loses momentum and energy which manifests in a change of direction (‘scattering’ angle) and wavelength (of the photon).The...…In a previous article entitled “” we analysed collisions between a moving and stationary object by defining the co-ordinate axes as being respectively parallel and perpendicular to the post collision direction of motion of the stationary object. In this article we will be adopting the same approach to analyse the well known physical phenomenon known as Compton scattering in which a photon collides with a stationary electron, imparts momentum to the latter and hence loses momentum and energy which manifests in a change of direction (‘scattering’ angle) and wavelength (of the photon).The...WW…

# Dark Energy Part 1: Einstein-deSitter Cosmology

In this 3-part series, I want to motivate the (re)introduction of the cosmological constant ##\Lambda## into Einstein’s equations of general relativity (GR) per the Supernova Cosmology Project (SCP) Union2.1 type Ia supernova data. As you probably know, this discovery won Perlmutter, Schmitt, and Riess the “for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.” ##\Lambda## is referred to as “dark energy” and as we will see in Part 2 it leads to the accelerating expansion of the universe. In this Insight (Part 1 of the series), I will...…In this 3-part series, I want to motivate the (re)introduction of the cosmological constant ##\Lambda## into Einstein’s equations of general relativity (GR) per the Supernova Cosmology Project (SCP) Union2.1 type Ia supernova data. As you probably know, this discovery won Perlmutter, Schmitt, and Riess the “for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.” ##\Lambda## is referred to as “dark energy” and as we will see in Part 2 it leads to the accelerating expansion of the universe. In this Insight (Part 1 of the series), I will...WW…

# A Beginner's Guide to Baryons | Physics Forums Insights

At the beginning of the 20th century it was thought that all matter consisted of only three particles: the electron, the neutron and the proton. The major outstanding question was how the neutrons held the positively changed protons together within the atomic nucleus.In the search to answer that question, however, it was found that the proton and neutron were not elementary particles at all, but each was composed of three elementary quarks. Furthermore, a menagerie of additional elementary and composite particles was discovered. The centerpiece is the set of eighteen baryons: particles,...…At the beginning of the 20th century it was thought that all matter consisted of only three particles: the electron, the neutron and the proton. The major outstanding question was how the neutrons held the positively changed protons together within the atomic nucleus.In the search to answer that question, however, it was found that the proton and neutron were not elementary particles at all, but each was composed of three elementary quarks. Furthermore, a menagerie of additional elementary and composite particles was discovered. The centerpiece is the set of eighteen baryons: particles,...WW…

# Is Mechanical Energy Conservation Free of Ambiguity?

“Close to any question that is in the textbook, there is another question that has never been answered that is interesting.”[Stephen Wolfram, remarks to The University of Vermont physics students, September 30, 2005]Mechanical energy conservation is the assertion that the sum of kinetic and potential energies of a system (the mechanical energy) does not change as a mass moves from point A to point B. Conventionally we may write$$K_A+U_A=K_B+U_B~~~~~(\rm{I.1a})$$which can be rewritten in a form that does not require specifying the “zero of energy”, $$\Delta K+\Delta...…“Close to any question that is in the textbook, there is another question that has never been answered that is interesting.”[Stephen Wolfram, remarks to The University of Vermont physics students, September 30, 2005]Mechanical energy conservation is the assertion that the sum of kinetic and potential energies of a system (the mechanical energy) does not change as a mass moves from point A to point B. Conventionally we may write$$K_A+U_A=K_B+U_B~~~~~(\rm{I.1a})$$which can be rewritten in a form that does not require specifying the “zero of energy”, $$\Delta K+\Delta...WW…

# An Alternate Approach to Solving 2 Dimensional Elastic Collisions

This article follows on from the previous on an . In that article we determined the equal and opposite collision impulse to have magnitude ##\mu \Delta v## for perfectly inelastic collisions, ##\mu(1+e) \Delta v## for semi-elastic collisions and ##2\mu \Delta v## for elastic collisions which will be the focus here. Reduced mass ##\mu=\frac{m_1m_2}{m_1+m_2}## – where ##m_1## and ##m_2## are the colliding masses – and ##\Delta v## is their relative velocity along the line of collision. e is the coefficient of restitution.Since the previous article focused on 1 dimensional collisions, the aim...…This article follows on from the previous on an . In that article we determined the equal and opposite collision impulse to have magnitude ##\mu \Delta v## for perfectly inelastic collisions, ##\mu(1+e) \Delta v## for semi-elastic collisions and ##2\mu \Delta v## for elastic collisions which will be the focus here. Reduced mass ##\mu=\frac{m_1m_2}{m_1+m_2}## – where ##m_1## and ##m_2## are the colliding masses – and ##\Delta v## is their relative velocity along the line of collision. e is the coefficient of restitution.Since the previous article focused on 1 dimensional collisions, the aim...WW…

# Black Holes Are Not Empty Voids. A Black Hole at the Heart!

(BH’s) are curious because of their mysterious nature and unknown properties. BH’s are not empty voids. They are astronomical objects with a gravitational pull so strong that nothing, not even light, can escape it. The “surface” of a black hole, called the event horizon (EH), defines the boundary where the escape velocity (for any particle) exceeds the speed of light, which is the speed limit of the cosmos. Thus, matter and radiation can fall into the event horizon, but they cannot escape.BH’s can be divided into two main classes. Stellar mass black holes, that form when a star with more...… (BH’s) are curious because of their mysterious nature and unknown properties. BH’s are not empty voids. They are astronomical objects with a gravitational pull so strong that nothing, not even light, can escape it. The “surface” of a black hole, called the event horizon (EH), defines the boundary where the escape velocity (for any particle) exceeds the speed of light, which is the speed limit of the cosmos. Thus, matter and radiation can fall into the event horizon, but they cannot escape.BH’s can be divided into two main classes. Stellar mass black holes, that form when a star with more...WW…

# Can We Do Better Than Mechanical Energy Conservation?

Note: It is assumed that the reader has read of the series.The ambiguity and flaws discussed in part I can be resolved using the law of conservation of energy. In the words of Richard Feynman,There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a...…Note: It is assumed that the reader has read of the series.The ambiguity and flaws discussed in part I can be resolved using the law of conservation of energy. In the words of Richard Feynman,There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a...WW…

# The Evolution of the Universe, Cosmic Web and Connections

The universe was not perfectly uniform when it started, some areas had higher density than others. During the evolution of the universe, these areas of high density contained most of the matter and started forming galaxies where there was the highest concentration of matter. This large scale structure (‘cosmic web’) connects the observed clusters of galaxies via a series of filaments. Figure 1 is a model of what this looks like.Figure 1: Skeleton of a cosmic web traced out by an algorithm run on a sample of observed galaxies. Far right shows the complete web, the left images show close up...…The universe was not perfectly uniform when it started, some areas had higher density than others. During the evolution of the universe, these areas of high density contained most of the matter and started forming galaxies where there was the highest concentration of matter. This large scale structure (‘cosmic web’) connects the observed clusters of galaxies via a series of filaments. Figure 1 is a model of what this looks like.Figure 1: Skeleton of a cosmic web traced out by an algorithm run on a sample of observed galaxies. Far right shows the complete web, the left images show close up...WW…

# Gaia and the Race to Detect More Gravitational Waves

(GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most relativistic objects produce large enough GW’s to be detectable. The Laser Interferometer Gravitational Wave Observatory () and Virgo detectors are using laser interferometry to detect tiny ripples in the fabric of spacetime. They have detected dozens of GW’s from binaries of black holes and neutron stars. Additional method of detecting GW’s is creating a pulsar timing array (), where dozens of millisecond pulsars are monitored to look for the signatures of...…(GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most relativistic objects produce large enough GW’s to be detectable. The Laser Interferometer Gravitational Wave Observatory () and Virgo detectors are using laser interferometry to detect tiny ripples in the fabric of spacetime. They have detected dozens of GW’s from binaries of black holes and neutron stars. Additional method of detecting GW’s is creating a pulsar timing array (), where dozens of millisecond pulsars are monitored to look for the signatures of...WW…

# Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

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