Simple Experiments and Modeling of Incandescent Lamp Spectra

The purpose of this work is to provide physics students and teachers with a simple experiment in modern physics, which utilizes modern spectroscopic methods and provides computational modeling of incandescent lamp spectra. Captured spectra are modeled with Planck’s radiation distribution, so that a temperature can be extracted. Voltage across and current through the lamp are recorded at the time of spectra capture, and the power and temperature data are fit with the Stefan-Boltzmann law. This experiment is further expanded by investigating the lamp’s resistance as a function of temperature. It is seen that typical incandescent lamps obtained at local retail stores are great examples of blackbody radiators, while the common energy efficient fluorescent lamps are not

Erratum: A NON-LINEAR APPROXIMATE SOLUTION TO THE DAMPED PENDULUM DERIVED USING THE METHOD OF SUCCESSIVE APPROXIMATIONS [Georgia Journal of Science, Vol. 76, No. 2, Article 9]

In an earlier publication [Hill and Hasbun, 2018] considered an approximate solution to the damped pendulum, named the improved modified method of successive approximations (IMMSA), and compared it to an approximation from the work of [Johannessen, 2014]. Here, a correction is made to that comparison due to an error made in calculating Johannessen\u27s approximation

The Millikan Oil Drop Experiment: A Simulation Suitable For Classroom Use

Due to advancements in computing techniques it has become possible to extend the accessibility of physics experiments across the physics curriculum by means of computational simulations. The widespread availability of computers in modern classrooms provides virtual access to hands-on physics, chemistry, and biology experiments, among others. Here, specifically, we consider Robert Millikan’s famous oil drop experiment. This experiment requires equipment that can be dangerous and expensive. A more practical approach is achieved via a computer simulation, a useful and a universally available alternative. The goal is to encourage scientific thinking, literacy, and innovation while promoting a free network of academic tools. Here we present a simulation that allows the user to carry out Millikan’s ingenious experiment by measuring the velocities of oil drops as they are influenced by an electric field. This is repeated until enough data is produced to deduce the charge of the electron. The simulation provides a clean and simple user interface, allowing for realistic interactions within a computational environment. For best results, a basic understanding of the theory and experimental procedure is valuable. We use Easy Java Simulations as the programming environment to carry out the simulation presented here

APPLICATION OF A DIATOMIC MOLECULE MODEL POTENTIAL TO A SERIES OF HOMO- AND HETERODIATOMIC MOLECULES

We apply a one-dimensional classical model of a diatomic molecule model potential with modifications to H2, HF, LiF, N2, and CO. We obtain the unknown parameters of this model by digitizing plots of the potential curves for the molecules from a published, Hartree-Fock based theoretical electron correlation calculation (Piris 2017). We then apply the method of successive approximations to the model in order to calculate the wavenumber for each molecule in the series. The wavenumber depends on a parameter which in turn depends on the initial conditions. The value of this parameter for each individual molecule gives zero percent error for the corresponding molecule’s wavenumber, but an average is used in the final calculation of all molecules’ wavenumbers. The resulting wavenumbers are all within seven percent of the experimental values

The Nucleon-Core Interaction: a Nuclear Physics Simulation Suitable for Classroom Use

The orbits of a nucleon and its respective parent nucleus about their common center of mass are simulated in an effort to provide a pedagogical approach to the understanding of the structure of atomic nuclei. The nuclear exercise is treated by solving the problem with an effective force on the system’s reduced mass. The potential governing the mean field is modeled by the Woods-Saxon form-factor with parameters that enable it to describe experimental findings. The Woods-Saxon potential is preferred over the infinite well and harmonic oscillator methods because both require infinite separation energies of the nucleons. The simulation is created using Easy Java Simulations (EJS) which is part of the Open Source Physics project and a MATLAB version (compatible with Octave) is included in the Appendix

Demonstration of a Distributed Bragg Reflector for Polyvinylcarbazole and Cadmium Sulfide Layers: Modeling and Comparison to Experimental Results

Light wave propagation in a periodically stratified medium has many applications in physics, mathematics, and engineering. The subject is of interest to students, teachers, and researchers, as it presents a great opportunity to focus on principles of optics and to understand the basics of mathematical modeling. A complete theory of wave propagation can be derived using Born’s optics theory. We employed that theory to determine the reflectivity of a one-dimensional distributed Bragg reflector (DBR) and do simulations using MATLAB. A DBR is a photonic crystal consisting of alternating layers of materials with different refractive indices. In this study, we modeled theoretical reflectivity of four-period DBR and compared with experimental results previously constructed on a glass substrate and reported by DeSilva et al. (2018). Each period consists of a layer of polyvinyl carbazole and a layer of cadmium sulfide. We used the Cauchy equation for the simulation of the wavelength dependency of the cadmium sulfide refractive index in a wavelength range between 400 and 1000 nm. The theory obtained a center wavelength and a reflectivity for each of the DBR periods in good agreement with the experimental results. Finally, in the appendix, we include a simple MATLAB script that demonstrates the application of the theory to a DBR

Model for the Electrolysis of Water and its use for Optimization

The goal of this research was to study the optimization of the electrolysis of water both theoretically and experimentally. For accuracy, 3 hr experiments were made with measurements recorded every 15 min. The results show that a better model than the classical one is needed for water electrolysis. A new model that fits experimental data better is proposed. The results of this new model not only predict hydrogen production in electrolysis of water better, but show a way to predict gas production of any liquid as well as what voltage to use to optimize it

Modeling the Temperature Behavior of an RLC Circuit

A problem that occurs in the use of electrical appliances is overheating. Electrical device components require reasonable working temperatures to prevent damage and increase efficiency. To gain an understanding of overheating we worked with an RLC circuit (a circuit consisting of a resistor, an inductor, and a capacitor) to represent a simplified model of an electrical component. The behavior of this circuit is similar to that of many electrical appliance components because as current flows through the resistor there is a rise in temperature due to the resistance to the electric current. Therefore, by using the RLC circuit, we can possibly get a better understanding of an electrical component’s temperature behavior. We first investigated the circuit’s differential equation to find the solution for the current. The derived current can be used in the power loss of the resistor, which is equal to the heat dissipated from the circuit resistance. To model the cooling of the system we added radiation, conduction, and convection terms to the differential equation. With each added cooling term the temperature in our system was seen to decrease significantly

A Nonlinear Approximate Solution to the Damped Pendulum Derived Using the Method of Successive Approximations

An approximate analytic solution to the damped pendulum is derived using the method of successive approximations to obtain a nonlinear approximation for the system. We take the approximate solution to the undamped pendulum using the method of successive approximations and compare it to the damped pendulum solution when a linear approximation is used. By looking at these two solutions, we can make an educated guess about the form of the general, approximate solution to the nonlinear damped pendulum. By adjusting the initial guesses and the initial conditions, we derive approximate solutions in three ways. Using MATLAB, the approximate solutions are compared to the full numerical solution through the Euler-Cromer method. To determine how accurate the approximations are, the errors of the approximations are calculated relative to the full numerical Euler-Cromer solution. Each new approximation came with a significant decrease in error, with the final error being 0.0099. This resulted in an improvement to the method of successive approximations. Finally, our best approximation is compared to an available and previously published work