Free Fall Motion Research Articles

Smartphones in the teaching of Physics Laws: Projectile motion| El teléfono inteligente en la enseñanza de las Leyes de la Física: movimiento de proyectiles.|

New technologies are called upon to play an important role as beneficial tools for meaningful learning in the classroom. In particular, smartphones can be regarded as pocket computers that, in addition to a remarkable memory and computing capacity, incorporate sensors such as accelerometers, gyroscopes, magnetometers, light sensors, etc., which turn them into easily available measurement instruments for practical classes in an educational environment. In this study, the suitability of these devices for demonstrating Classical Mechanics, minimizing the use of resources and class time, has been assessed in two real classrooms (with 16 to 19 year-old students) by conducting experiments related to projectile motion (vertical free fall and parabolic motion). A simple methodology that only involves a mobile phone, a free burst camera application and open-source tools (GIMP and OpenOffice Calc) for data processing is presented. The results obtained in non-perfected conditions led to an estimate of the acceleration of gravity with an error lower than 2%. Further analyses and alternative procedures are also suggested in the discussion section. No major difficulties were encountered with the high school students or with the first year university ones, and a high degree of satisfaction was found.

Novedad empírica y creación de conceptos

Due to the historical origin and development of reason, an inventory of its main concepts at a particular moment is less interesting to us than the study of their formation and fixation. This process is studied here in the light of examples from the history of physics. The first one concerns the subsumption of the well-known phenomena of free fall and planetary motion to a new concept of gravity in the 17th century; the remaining examples, drawn from 19th century electrodynamics and 20th century microphysics and cosmology, display the interplay of such concepts with empirical novelties that prompt them in some case and realize them in others.

THE EFFECTS OF ACCRETION FLOW DYNAMICS ON THE BLACK HOLE SHADOW OF SAGITTARIUS A*

ABSTRACT A radiatively inefficient accretion flow (RIAF), which is commonly characterized by its sub-Keplerian nature, is a favored accretion model for the supermassive black hole at the Galactic center, Sagittarius A*. To investigate the observable features of an RIAF, we compare the modeled shadow images, visibilities, and spectra of three flow models with dynamics characterized by (i) a Keplerian shell that is rigidly rotating outside the innermost stable circular orbit (ISCO) and infalling with a constant angular momentum inside ISCO, (ii) a sub-Keplerian motion, and (iii) a free-falling motion with zero angular momentum at infinity. At near-millimeter wavelengths, the emission is dominated by the flow within several Schwarzschild radii. The energy shift due to these flow dynamics becomes important and distinguishable, suggesting that the flow dynamics are an important model parameter for interpreting the millimeter/sub-millimeter very long baseline interferometric observations with the forthcoming, fully assembled Event Horizon Telescope (EHT). As an example, we demonstrate that structural variations of Sagittarius A* on event horizon-scales detected in previous EHT observations can be explained by the non-stationary dynamics of an RIAF.

Avaliação do módulo da aceleração da gravidade com Arduino

http://dx.doi.org/10.5007/2175-7941.2016v33n2p619 Nesse trabalho, utilizamos a plataforma de hardware livre Arduino para automatizar o processo de coleta de dados no movimento de queda de um objeto, em experimento capaz de fornecer o módulo da aceleração da gravidade local com boa precisão. A partir de sensores posicionados em alturas conhecidas, coletamos os intervalos de tempo gastos por uma esfera para percorrer diferentes distâncias verticais, sendo sua aceleração determinada através da análise de ajuste linear da curva de variação de altura por intervalo de tempo versus intervalo de tempo, onde o dobro da inclinação da reta média corresponde ao módulo local g da aceleração da gravidade. Em virtude das condições de lançamento, os efeitos da resistência do ar não foram considerados na obtenção de g, de modo que consideramos ser esse um movimento de queda livre como boa aproximação. O instrumento desenvolvido nos permitiu obter o valor médio de g diferindo em apenas 1% do valor encontrado na literatura, mostrando que o Arduino é uma ferramenta interessante para aquisição de dados e automatização de experimentos de Física. Reforçamos nesse trabalho a importância da utilização das novas tecnologias no ensino de Ciências, em especial de Física.

Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial

Obviously, in Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass [Formula: see text] of the falling body is omitted (because it is a test mass; put otherwise, the center of mass of the system coincides with the center of the main, and fixed, mass [Formula: see text]; or else, we consider only a homogeneous gravitational field). Conversely, an additional (in the opposite or same direction) acceleration proportional to [Formula: see text] would rise either for an observer at the center of mass of the system, or for an observer at a fixed distance from the center of mass of [Formula: see text]. These elementary, but overlooked, considerations fully respect the equivalence principle (EP) and the (local) identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and gauge dependency in general relativity. Because of its importance in teaching and in the history of physics, coupled to the introductory role to Einstein’s EP, the approximate nature of Galilei’s law of free fall is explored herein. When stepping into general relativity, we report how the geodesic free fall into a black hole was the subject of an intense debate again centered on coordinate choice. Later, we describe how the infalling mass and the emitted gravitational radiation affect the free fall motion of a body. The general relativistic self-force might be dealt with to perfectly fit into a geodesic conception of motion. Then, embracing quantum mechanics, real black holes are not classical static objects any longer. Free fall has to handle the Hawking radiation, and leads us to new perspectives on the varying mass of the evaporating black hole and on the varying energy of the falling mass. Along the paper, we also estimate our findings for ordinary masses being dropped from a Galilean or Einsteinian Pisa-like tower with respect to the current state of the art drawn from precise measurements in ground and space laboratories, and to the constraints posed by quantum measurements. Appendix A describes how education physics and high impact factor journals discuss the free fall. Finally, case studies conducted on undergraduate students and teachers are reviewed.

Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle.

The differential electrostatic space accelerometer is an equivalence principle (EP) experiment instrument proposed to operate onboard China’s space station in the 2020s. It is designed to compare the spin-spin interaction between two rotating extended bodies and the Earth to a precision of 10−12, which is five orders of magnitude better than terrestrial experiment results to date. To achieve the targeted test accuracy, the sensitive space accelerometer will use the very soft space environment provided by a quasi-drag-free floating capsule and long-time observation of the free-fall mass motion for integration of the measurements over 20 orbits. In this work, we describe the design and capability of the differential accelerometer to test weak space acceleration. Modeling and simulation results of the electrostatic suspension and electrostatic motor are presented based on attainable space microgravity condition. Noise evaluation shows that the electrostatic actuation and residual non-gravitational acceleration are two major noise sources. The evaluated differential acceleration noise is 1.01 × 10−9 m/s2/Hz1/2 at the NEP signal frequency of 0.182 mHz, by neglecting small acceleration disturbances. The preliminary work on development of the first instrument prototype is introduced for on-ground technological assessments. This development has already confirmed several crucial fabrication processes and measurement techniques and it will open the way to the construction of the final differential space accelerometer.

An investigation into the effectiveness of smartphone experiments on students’ conceptual knowledge about acceleration

This study is a first attempt to investigate effectiveness of smartphone-based activities on students’ conceptual understanding of acceleration. 143 secondary school students (15–16 years old) were involved in two types of activities: smartphone- and non-smartphone activities. The latter consisted in data logging and ‘cookbook’ activities. For the sake of comparison, all activities featured the same phenomena, i.e., the motion on an inclined plane and pendulum oscillations. A pre-post design was adopted, using open questionnaires as probes. Results show only weak statistical differences between the smartphone and non-smartphone groups. Students who followed smartphone activities were more able to design an experiment to measure acceleration and to correctly describe acceleration in a free fall motion. However, students of both groups had many difficulties in drawing acceleration vector along the trajectory of the studied motion. Results suggest that smartphone-based activities may be effective substitutes of traditional experimental settings and represent a valuable aid for teachers who want to implement laboratory activities at secondary school level. However, to achieve a deeper conceptual understanding of acceleration, some issues need to be addressed: what is the reference system of the built-in smartphone sensor; relationships between smartphone acceleration graphs and experimental setup; vector representation of the measured acceleration.

Going nuts: Measuring free-fall acceleration by analyzing the sound of falling metal pieces

Galilei presented the kinematics of a one-dimensional accelerated motion with ease and in terms of elegant geometry. Moreover, he believed, “Philosophy [i.e. physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it.” In classroom practice, however, it can be difficult to reveal this mathematical heart of nature; free fall and other accelerated motions often get obscured by friction or other sources of errors. In this paper, we introduce a method of analyzing free-fall motion indirectly by evaluating the noise of freely falling metal pieces. The method connects a deeper understanding of the mathematical structure of accelerated motion with the possibility to derive a numerical value for the free-fall acceleration g.

抜重に伴う身体重心の動きを利用する即応的な移動動作の構築支援に関する基礎的研究

抜重に伴う身体重心の動きを利用する即応的な移動動作の構築支援に関する基礎的研究

On the effect of distortion and dispersion in fringe signal of the FG5 absolute gravimeters

The knowledge of absolute gravity acceleration at the level of 1 × 10−9 is needed in geosciences (e.g. for monitoring crustal deformations and mass transports) and in metrology for watt balance experiments related to the new SI definition of the unit of kilogram. The gravity reference, which results from the international comparisons held with the participation of numerous absolute gravimeters, is significantly affected by qualities of instruments prevailing in the comparisons (i.e. at present, FG5 gravimeters). Therefore, it is necessary to thoroughly investigate all instrumental (particularly systematic) errors. This paper deals with systematic errors of the FG5#215 coming from the distorted fringe signal and from the electronic dispersion at several electronic components including cables. In order to investigate these effects, we developed a new experimental system for acquiring and analysing the data parallel to the FG5 built-in system. The new system based on the analogue-to-digital converter with digital waveform processing using the FFT swept band pass filter is developed and tested on the FG5#215 gravimeter equipped with a new fast analogue output. The system is characterized by a low timing jitter, digital handling of the distorted swept signal with determination of zero-crossings for the fundamental frequency sweep and also for its harmonics and can be used for any gravimeter based on the laser interferometry. Comparison of the original FG5 system and the experimental systems is provided on g-values, residuals and additional measurements/models. Moreover, advanced approach for the solution of the free-fall motion is presented, which allows to take into account a non-linear gravity change with height.

Super free fall of an inviscid liquid through interconnected vertical pipes

In this work the super free fall motion of the interface of a liquid column flowing downwards, suddenly from the rest in a system of vertical concentrically interconnected tubes, is studied theoretically, using a one-dimensional model in the inviscid regime. The ratio of the surface area of the upper tube to that of the lower one, , is assumed to be smaller than unity. Experiments show a good agreement with the main results of the developed theory.

Alternative classical force of gravitation: A study of the free fall motion

The purpose of this work is to clarify the mathematical form of an alternative classical force of gravitation, which has been described in a previous paper. The purpose of this investigation is to find a solution to the problem of the velocity curve of spiral galaxies, without dark matter hypothesis. In the first part, we study the free fall motion, in the case of our force, and we determine a possible mathematical expression for it. In the second part, we discuss the validity of our assumptions.

Using Tracker to understand ‘toss up’ and free fall motion: a case study

This paper reports the use of Tracker as a computer-based learning tool to support effective learning and teaching of ‘toss up’ and free fall motion for beginning secondary three (15 year-old) students. The case study involved (N = 123) students from express pure physics classes at a mainstream school in Singapore. We used eight multiple-choice questions pre- and post-test to gauge the impact on learning. The experimental group showed learning gains of d = 0.79 ± 0.23 (large effect) for Cohen’s d effect size analysis, and gains with a gradient of <g> total = 0.42 ± 0.08 (medium gain) above the traditional baseline value of <g> non interactive = 0.23 for Hake’s normalized gain regression analysis. This applied to all of the teachers and students who participated in this study. Our initial research findings suggest that allowing learners to relate abstract physics concepts to real life through coupling traditional video analysis with video modelling might be an innovative and effective method for teaching and learning about free fall motion.

Enhancement of bone quality and longitudinal growth due to free-fall motion in growing rats

Objectives This study is to investigate the synchronous phenomena between bone quality and longitudinal length in a same subject affected by landing exercise. Physical exercise on the ground induces external loading to human body due to resistance from ground which can activate bone generation or remodeling. Especially, when the impact stimulation is applied to bone, it may improve bone quality and lengthening.

Numerical Simulation of Water Entry of Wedges Based on the CIP Method

The hydrodynamic problems for water entry of wedges are studied by a constrained interpolation profile (CIP) based on Cartesian grid method. The CIP scheme was applied to the Cartesian grid based on flow solver, which was first described. The tangent of hyperbola for interface capturing (THINC) scheme was applied to capture the free surface. The CIP method was extended to capture the dynamics in the water entry approach. The simulations were performed in three aspects. First, pressure distributions for the wedges entering into water with constant speed were predicted, and the results were compared with the similarity solutions by the boundary element method (BEM). Then simulations were conducted for the free-falling wedges entering into water with one degree of freedom. The results were compared with the published experimental data. Finally, the impact of a wedge on the water surface in a free fall motion with an initial heel angle was studied. The motion of the wedge was subjected to three degrees of freedom, and the results were also compared with those of experiments.

Simulation of General Physics laboratory exercise

Laboratory exercises are an important part of general Physics teaching, both during the last years of high school and the first year of college education. Due to the need to acquire enough laboratory equipment for all the students, and the widespread access to computers rooms in teaching, we propose the development of computer simulated laboratory exercises. A representative exercise in general Physics is the calculation of the gravity acceleration value, through the free fall motion of a metal ball. Using a model of the real exercise, we have developed an interactive system which allows students to alter the starting height of the ball to obtain different fall times. The simulation was programmed in ActionScript 3, so that it can be freely executed in any operative system; to ensure the accuracy of the calculations, all the input parameters of the simulations were modelled using digital measurement units, and to allow a statistical management of the resulting data, measurement errors are simulated through limited randomization.

Design of New Double-Wing Product Drop Test Machine

In order to simulate the free-fall motion of package, a new double-wing product drop test machine was designed. The lifting motion of the test bed was realized by the cooperation between rolling screw and stepping motor, while the opening and closing of double wing was realized by the coordinating transmission of guide rail and lead screw pair. Compared to similar products sold in the market, the new double-wing product drop test machine is low in cost, simple in structure, convenient in processing, stable in performance and beautiful in appearance. It can satisfy the demands of packing companies and academic institution, with practical application and promotion value.

Fully nonlinear simulation for fluid/structure impact: A review

This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method (BEM). Fully nonlinear boundary conditions are imposed on the unknown free surface and the wetted surface of the moving body. The review includes (1) vertical and oblique water entry of a body at constant or a prescribed varying speed, as well as free fall motion, (2) liquid droplets or column impact as well as wave impact on a body, (3) similarity solution of an expanding body. It covers two dimensional (2D), axisymmetric and three dimensional (3D) cases. Key techniques used in the numerical simulation are outlined, including mesh generation on the multivalued free surface, the stretched coordinate system for expanding domain, the auxiliary function method for decoupling the mutual dependence of the pressure and the body motion, and treatment for the jet or the thin liquid film developed during impact.

A sensor fusion method for tracking vertical velocity and height based on inertial and barometric altimeter measurements.

A sensor fusion method was developed for vertical channel stabilization by fusing inertial measurements from an Inertial Measurement Unit (IMU) and pressure altitude measurements from a barometric altimeter integrated in the same device (baro-IMU). An Extended Kalman Filter (EKF) estimated the quaternion from the sensor frame to the navigation frame; the sensed specific force was rotated into the navigation frame and compensated for gravity, yielding the vertical linear acceleration; finally, a complementary filter driven by the vertical linear acceleration and the measured pressure altitude produced estimates of height and vertical velocity. A method was also developed to condition the measured pressure altitude using a whitening filter, which helped to remove the short-term correlation due to environment-dependent pressure changes from raw pressure altitude. The sensor fusion method was implemented to work on-line using data from a wireless baro-IMU and tested for the capability of tracking low-frequency small-amplitude vertical human-like motions that can be critical for stand-alone inertial sensor measurements. Validation tests were performed in different experimental conditions, namely no motion, free-fall motion, forced circular motion and squatting. Accurate on-line tracking of height and vertical velocity was achieved, giving confidence to the use of the sensor fusion method for tracking typical vertical human motions: velocity Root Mean Square Error (RMSE) was in the range 0.04–0.24 m/s; height RMSE was in the range 5–68 cm, with statistically significant performance gains when the whitening filter was used by the sensor fusion method to track relatively high-frequency vertical motions.

Numerical simulation of the water entry of a structure in free fall motion

To solve the problems concerning water entry of a structure, the RANS equations and volume of fluid (VOF) method are used. Combining the user-defined function (UDF) procedure with dynamic grids, the water impact on a structure in free fall is simulated, and the velocity, displacement and the pressure distribution on the structure are investigated. The results of the numerical simulation were compared with the experimental data, and solidly consistent results have been achieved, which validates the numerical model. Therefore, this method can be used to study the water impact problems of a structure.