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Reliable determination of contact angle from the height and volume of sessile drops
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| Pengarang | : | F. Behroozi |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 1) |
| Halaman | : | 28-32 |
| Abstrak | : | Contact angle is an important parameter in characterizing the wetting properties of fluids. For this reason, accurate measurement of the contact angle at liquid-solid interfaces is of great importance in industrial and scientific applications. The most common method for measuring the contact angle is to obtain it directly from the profile of a sessile drop. Though convenient, this method suffers from certain inherent drawbacks. Here, we describe an alternative method that uses the height and volume of a sessile drop as constraints to construct its profile by numerical integration of two parametric differential equations. The integration yields, self consistently, the average value of the contact angle along the entire contact line as well as the footprint radius of the drop and its crown radius of curvature. As a test case, the new method is used to obtain the contact angle of pure water on two different substrates, Teflon and Lucite. For each substrate, four drops ranging in volume from 10. to 40 μl are used. The computed contact angles are consistent across the four different drop sizes for each substrate and are in good agreement with the literature values. |
Laboratory demonstration of acoustic source localization in two dimensions
| Pengarang | : | Frank Lamelas |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 1) |
| Halaman | : | 24-27 |
| Abstrak | : | A high-resolution table-top experiment in source localization is carried out using four USB microphones. We show that the acoustic source location can be determined with an accuracy of 1 cm if timing measurements are carried out as follows. First, the sound source is a noise pulse played through a cell-phone speaker, ensuring the presence of high-frequency components and an easily identified abrupt onset of the sound signal. Second, we normalize the clock rates of the four computers used with the microphones. The position of the source is calculated using an analytical expression which depends on the microphone layout and the arrival times of the sound signal at the four microphones. The experiment can be carried out in an undergraduate laboratory. |
Flying in formation: The orbital dynamics of LISA's three spacecraft
| Pengarang | : | Joseph C. Amato |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 1) |
| Halaman | : | 10-17 |
| Abstrak | : | LISA is a space-based gravitational wave observatory that is anticipated to launch in 2034. Its constellation of three spacecraft will be located at the vertices of an equilateral triangle that will follow the Earth about the Sun. The spacecraft will be deployed in three heliocentric elliptical orbits that, to first order in their eccentricity, maintain the observatory's size and configuration. How LISA accomplishes this is an ideal illustration of basic orbital dynamics. The physics underlying the choice of orbits is explained at a level suitable for introductory undergraduate physics students. |
Analytical solution of gravity tunnels through an inhomogeneous Earth
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 1) |
| Halaman | : | 10-17 |
| Abstrak | : | A piecewise linear approximation of the Preliminary reference Earth model (PREM) is used for the Earth's velocity profile. The analytical solution derived for the motion on the shortest path and the path of fastest descent corresponds to the direct numerical integration of the PREM. This explains why traversal times can be approximated by the assumption of constant gravity, while the gravity of the Earth is certainly not constant. |
Comoving frames and the Lorentz–Fitzgerald contraction
| Pengarang | : | |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 1) |
| Halaman | : | 5–9 |
| Abstrak | : | In special relativity, accelerated objects are described through instantaneous comoving frames, to which the usual transformations are then applied. This is not always possible, however. I analyze a simple example of a rod thrown from a train onto a stationary platform. The lack of absolute simultaneity implies that the rod stretches, and its points move with respect to each other. Its length, therefore, changes. Typically, the rod as a whole has no instantaneous rest length and thus no definable proper length. A fortiori, it has no instantaneous rest frame, and the (instantaneous) Lorentz contraction formula is inapplicable. |
Isaac Newton and Natural Philosophy
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 687-688 |
| Abstrak | : | In the preface of his magnum opus The Mathematical Principles of Natural Philosophy, or Principia for short, Newton gave a succinct statement of his philosophy: Applying his philosophical principle, Newton discovered that the mathematical form of the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In the third book of the Principia, he showed that this relation is in good agreement with astronomical observations. But Newton's gravitational force implied the existence of an action at a distance contrary to the prevalent view of philosophers and mathematicians at the time, who believed that only contact forces could exist. On the European Continent most of them regarded Newton's gravitation as an occult force which should not have any place in philosophy. He was also criticized for not describing the cause of gravitation. |
The hardwall method of solving the radial Schrödinger equation and unmasking hidden symmetries
| Pengarang | : | Siu A. Chin |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 682-686 |
| Abstrak | : | Solving for the bound state eigenvalues of the Schrödinger equation is a tedious iterative process using the conventional shooting or matching method. In this paper, we bypass a eigenvalue's dependence on the eigenfunction by trying all eigenvalues to a desired accuracy. When the eigenvalue is known, the integration for the eigenfunction is then trivial. By outputting the radial distance at which the wave function crosses zero (the hardwall radius) for a given energy, the hardwall method automatically determines the entire spectrum of eigenvalues of the radial Schrödinger equation without iterative adjustments. Moreover, such a spherically symmetric hardwall can unmask the accidental degeneracy of eigenvalues due to hidden symmetries. We illustrate the method for the Coulomb, harmonic, Coulomb plus harmonic, and the Woods-Saxon potentials. |
Entropy and unavailable energy
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 680-681 |
| Abstrak | : | We improve and clarify an explanation of how the entropy increase during a process is related to the energy that becomes unavailable to be transformed into work. |
Comment on “Peculiarities in the gravitational field of a filamentary ring” [Am. J. Phys. 87, 384–394 (2019)]
| Pengarang | : | J. West |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 679 |
| Abstrak | : | In a recent article, the dynamics of a particle in the gravitational field of a uniform ring in the plane of the ring was examined. Parts of this work duplicate the results of previous work by West et al. in a paper published in this journal in 1998, and additional work extending those results in a paper by Tobin and West in 2006. |
Alternative statements of the Rayleigh monotonicity law for linear time-invariant resistor networks driven by only voltages or only currents
| Pengarang | : | Seppo J. Karrila |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 675-678 |
| Abstrak | : | Networks of linear time-invariant (LTI) resistors are a classical topic with many applications, used to model a variety of flow phenomena. In this short communication, we provide conceptually simple proofs of the following intuitively appealing bounds, which also imply the classical Rayleigh monotonicity law (RML): (i) For an LTI resistor network, driven by some node voltages, when a set of resistors is removed the total power dissipation is reduced by at least an amount that was consumed in the removed resistors. (ii) The complementary or dual result for such a network, but when current driven, is that shorting some resistors decreases the total power dissipation by at least as much as used to occur in these resistors before shorting. In fact, ideal diodes can be allowed as network branches and the same results hold. The short derivations assume that Dirichlet's and Thomson's minimum principles are known. With the expanding applications of a linear network theory, we hope that these variants of the monotonicity theorem will prove pedagogically useful. |