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Reprint: Determination of the Temperature Dependence of Young's Modulus for Stainless Steel Using a Tuning Fork
Tuning forks have been used as high quality frequency standards for decades. Musicians are well aware of the effect that temperature has on the tuning of their instruments. Those effects are generally attributed to either a change in the speed of sound in air (for wind instruments) or thermal expansion for string and percussion instruments. We show that in the case of a tuning fork, thermal expansion is a minor consideration. The primary source of the temperature dependence of the tuning fork is cause by a temperature dependence in the Young’s modulus of the material out of which it is made. The stiffness of the fork changes slightly with temperature, causing a change in the resonant frequency of the tuning fork. We use this effect to determine an empirical formula for the temperature dependence of stainless steel.
Reprint: Design of a Low Cost Gamma Ray Spectrometer to Investigate Special Relativity
We designed a low cost NaI(Tl) scintillation detector and single channel analyzer to be used to measure the rest energy of the electron. We used the instrument to deduce the behavior of electrons following Compton scattering collisions in the crystal. We found a value of the rest energy of the electron to be (0.51±0.02) MeV and experimentally verified Einstein’s energy-momentum relationship.
Reprint: Exploration in Ten Pin: A Simplified Model of a Bowling System
Jocelyn Christensen, Carleton College, Northfield, MN
The complicated physical system of bowling is simplified to a two-dimensional model, where the pins and ball are represented by hard disks, friction is neglected and straight line motion and elastic collisions are assumed. We show that, while not entirely realistic, the model reflects some of the behavior we see occurring in a real, three-dimensional bowling system. This simplified model reveals tremendous sensitivity to the initial parameters of the system and provides insight into the nature and dependence of the elusive strike zone.
Reprint: Laboratory Measurements of Velocity Profiles in Simulated Tornado-Like Vortices
Axial vertical velocity measurements of simulated super-critical tornado-like vortices were made in the Miami University Tornado Vortex Chamber (TVC). Improvements to the Miami TVC tornado generation mechanisms and data acquisition methods aided in the attainment of data with spatial resolution never before achieved in the study of simulated vortices. Axial vertical velocity measurements are presented as a function of super-critical vortex height for varying swirl ratio, and are referred to as velocity profiles. The data suggest a strong correlation between supercritical inner core region diameter and swirl ratio, as well as an apparent breakdown of supercritical structure well below vortex breakdown (vortex bubbling).
Reprint: Energy States of a Gaussian Wavepacket in an Infinite Square Well
An explicit expression is derived for the probability of an arbitrary energy state of a Gaussian wavepacket confined to an infinite square well potential. Approximations are made to determine the normalization factor and the probability. An upper bound on the errors due to the approximations is determine.
Reprint: Body Vibrational Spectra of Metal Flute Models
Reprint: Relativistic Pendula
We solve for the angular motion of the relativistic simple pendulum driven by uniform driving forces of two distinct types: gravity and a uniform electric field. In both cases, we calculate and plot the angular motion of the pendulum in time. We also find the period of the pendulum as a function of its amplitude. While these two relativistic pendula do not differ greatly in their motion, the motion of each type of relativistic pendulum differs significantly from the classical large amplitude pendulum. The classical and relativistic pendula differ greatly in the period vs amplitude characteristics. We also calculated the period of each type of pendulum in the non-inertial frame of the pendulum itself. For a given amplitude, the period in the non-inertial frame is less than that determined in the stationary frame.
Reprint: Modeling Pion Flow in a 139La + 139La Collision
This study focused on the flow behavior of pions created in a 139La + 139La nuclear collision. The system was simulated and studied at beam energies of 400 MeV/A and 1200 MeV/A using the Boltzmann-Uehling-Uhlenbeck (BUU) transport model for nuclear collisions. The dependence of flow on centrality, the size of the impact parameter, was examined for both beam energies. The dependence of flow on the nuclear equation of state, as well as on Coulomb interactions, was studied. At 400 MeV/A, both positive and negative pions were found to exhibit flow for central (small) impact parameters and anti-flow for peripheral (large, on the size of the nuclear radius) impact parameters. Similar results were obtained at 1200 MeV/A, agreeing with previous experimental data. The predicted flow was insensitive to the choice of equation of state and the Coulomb interactions did not have any profound change on the pion behavior.