Gravitational Acceleration Research Articles

RESEARCH OF THE PROPERTIES OF A MECHANICAL ROBOT USING THE EXAMPLE OF A PHYSICAL PENDULUM

The article examines the properties of a mechanical robot and provides recommendations for changes in its design. The relevance of the use of robots in the world is beyond doubt, such robots are used in places that pose a danger to humans or are inaccessible to humans. In each case, the accuracy of positioning and the accuracy of the robot's actions directly affect the efficiency of the tasks assigned to the robot. Practicing robot movements traditionally takes place at robotics competitions, which are widely held around the world. In recent robotics competitions, one of the exercises in the competition was an exercise where the robot had to hang from a beam using its mechanical levers. The researched robot oscillates in the air while hanging on a crossbar on mechanical levers. In the studies, the task was to overcome these negative phenomena - mechanical oscillations, by studying the problem and conducting physical research. In order to conduct physical research and study the issue, a decision was made to replace the real object – the robot – with an appropriate replacement structure. For such a replacement design, a physical pendulum (classical and reversible) is adopted. In physical pendulums, the main parameter is the moment of inertia I, which is determined from the formula: , where m is the mass of the pendulum, g is the acceleration of free fall, d is the distance from the axis of the suspension to the center of mass of the pendulum, T is the oscillation period of the pendulum. The accepted hypothesis is that an increase in the moment of inertia of a real object will lead to the need to increase the force that forces this object to swing. Experimental installations were formed during laboratory research; measured variables – I, independent variables – g, T, dependent variables – m, d were analyzed; experiments were carried out to assess the impact on the moment of inertia I of the distance from the suspension axis to the center of mass of the pendulum d and the influence on the moment of inertia I of the mass of the pendulum m. The obtained results of physical research allow us to provide recommendations on changing the design of a real object - a robot. The recommendations make it possible to eliminate the negative phenomenon – rocking the robot on the crossbar, which will allow to perform the corresponding task better. These recommendations include the following: 1. Load the structure as much as possible by increasing the mass m. 2. Extend the robot levers as much as possible by increasing the distance d. 3. Lower the center of gravity of the robot as much as possible. After making constructive changes in the structure of the robot, it is planned to build its mathematical model for further research.

Simple experiment and simulation of a rotating liquid's free surface

This work explains an easy and cost-effective method to investigate the behavior of the free surface of a liquid in a rotating container. By means of two standing cameras, we recorded the movement of the container from top and the changing profile of the liquid surface from lateral view. In the resulting videos, we noticed the usual parabolic shape of the free surface, characteristic to rotating liquids. The videos were then analyzed by employing the Tracker software and we found the rotation period of the container and the displacement of the parabola apex with respect to the initial standstill position. From the acquired data we were able to calculate the gravitational acceleration with excellent precision. For the second part of the work, we created a Python script for simulating the same experiment. The user can interactively change the involved main physical parameters, observing the implicit modification of the parabola’s shape. Our work proposes a didactic alternative approach for studying and simulation of a rotating liquid free surface, while the attained results are comparable with the ones obtained by traditional methods.

History of height reference systems in the territory of the Republic of Serbia

The Republic of Serbia inherited two unique reference height systems. The first, the Precise levelling of the Austro-Hungarian Monarchy (APL), was a significant undertaking by the Military Geographical Institute from Vienna between 1874 and 1905. The reference surface of the APL, the mean sea level, was determined in Trieste based on a year of tide gauge measurements in 1875. This system, which remained used in Serbia and later in Yugoslavia until 1999, was replaced by the Second High Precision Levelling Network of Yugoslavia, carried out by domestic geodetic service between 1970 and 1973, and the mean sea level was determined based on five tide gauges, epoch 1971,5. Notably, during the execution of levelling measurements no measurements of gravitational acceleration were taken along the levelling lines. As a result, the heights were and continue to be expressed in the normal orthometric (spheroidal) height system, a practice that has endured to this day. This paper meticulously chronicles the most significant stages and characteristics in establishing reference height systems in Serbia's territory.

A pair of entrapping or coalescing bubbles affected by convection during downward solidification

In this study, the development of solute concentration and velocity fields of a pair of entrapping or coalescing bubbles during downward solidification is provided. The gas-induced pores in the metal not only deteriorates the properties of the processed workpiece by causing stress concentration and defects within the material, but pore formation in sea ice also plays an important role in global warming. Using COMSOL Multiphysics version 5.2, the unsteady, two-dimensional transport equations of mass, momentum, energy, and concentration are solved. The results show that bubble coalescence is facilitated by decreasing solid thermal conductivity and interpore spacing. Unlike the symmetric distribution of concentration observed with a low Henry's law constant and liquid solute diffusivity, an asymmetric distribution occurs, with high and low concentration gradients near the leading and rear edges of each bubble, respectively, due to the liquid velocity from the upstream direction. An outward flow in the opposite direction occurs near the triple-phase line, resulting in an inflection region in the iso-concentration field. The thickness of the concentration boundary layer surrounding the pores also decreases with decreasing Henry's law constant and liquid solute diffusivity, as well as with increasing ambient pressure, gravitational acceleration, solid thermal conductivity, and surface tension. The predicted contact angle during solidification aligns well with Abel's equation. Solute segregation associated with the formation of multiple pores can be controlled.

Model for Determining Earth's Gravitational Acceleration on a Mathematical Pendulum

Gravity is an accelerating property of the earth that causes objects to fall freely. The acceleration of gravity is not the same at every place on the Earth's surface. To measure the Earth's gravity (small g), scientists can use various techniques, such as dropping a mass from a certain height and measuring the time it takes to fall to the ground or using a mathematical pendulum to measure the period of oscillation and use it to calculate the acceleration due to gravity. In this paper, a study of the mathematical pendulum in the measurement of the Earth's gravitational acceleration is conducted, and the measurement experiment is illustrated. Method To measure the length of the pendulum, you must have a ruler, meter stick, or tape measure. At the top end of the string, start the measurement at the point where the string rotates out of place. Then, measure up to the center of the pendulum, which is the object hanging on the string. From the results of this study, it can be concluded that the value of the period of a pendulum is affected by several factors, including the length of the rope used and the angle of initial deviation, while the factors that do not affect the period are the mass and diameter of the pendulum.

Measurement of Acceleration Due to Gravity Using Arduino

The undertaken research paper is an easy experiment based on Arduino was constructed in order to investigate the acceleration of the object while it was falling freely and to estimate the value of "g" (the acceleration that is generated by gravity). The reseach aimed to achieve three objectives through this research: first, to comprehend the manner in which airborne gravity gradiometers synthesise gravity fields using residual terrain modelling and the equivalent source layer method; second, to evaluate the durability of systems based on Arduino in various environments; and third, to contrast the accuracy, efficiency, and user-friendliness of these systems with those that are more conventional. The investigation of the acceleration due to gravity measurement using Arduino was conducted using secondary sources, which include books, websites, academic papers, newspapers, and magazines. These sources are not directly comparable. The evaluation and severity determination of a diverse array of research topics are facilitated by this explanatory research approach to the analysis of the conceptual components. The result of the study implies that in order to obtain distance time curves, readings realted to gravity is made at a variety of intervals throughout the course of application of the traditional kinematic equations made it possible to compute the acceleration that happened during the free fall. There has been found to be a good agreement between “the shape of the distance-time graphs” that were gathered from the secondary setup and the graphs that were expected, and the values of g that were calculated were within the range that was anticipated. It has been further discovered that the magnitude of gravitational acceleration is 9.805 metres per second squared after a series of research study were carried out.

Advanced Numerical Simulation of Pendulum Dynamics: A Comprehensive Analysis of Environmental Influences and Non-Linear Behavior

This study explores the intricate dynamics of pendulum motion by numerically simulating the influence of environmental factors, including temperature, pressure, and humidity. Employing a high-precision Euler method with a time step of 0.0001 seconds, a 1-meter-long pendulum was modeled under varying conditions: temperatures ranging from 0°C to 40°C, pressures between 950 hPa and 1050 hPa, and humidity levels from 20% to 80%. The simulation incorporated key factors such as thermal expansion, air resistance, and non-linear oscillatory behavior for initial displacements up to 30°. Results reveal that a 40°C rise in temperature induces a 0.0007-second change in period and a 0.001 m/s² variation in calculated gravitational acceleration, predominantly due to rod expansion. Conversely, the effects of pressure and humidity were found to be negligible. Non-linear analysis at a 30° initial displacement indicated a 0.5% increase in period compared to 5°, underscoring the impact of the initial angle on pendulum dynamics. The model demonstrated remarkable accuracy for small-angle oscillations, aligning within 0.01% of theoretical predictions and 0.1% of experimental data. These findings offer valuable insights into pendulum behavior under diverse environmental conditions, providing a robust foundation for advancing the design and calibration of precision instruments and timekeeping mechanisms.

Evaluation of volumetric threshold shear strain of gravel-sand mixtures in centrifuge model tests

A series of dynamic centrifuge modeling tests were conducted to evaluate the volumetric threshold shear strain of loose gravel-sand mixtures composed of various ratios of gravel and sand by weight. The maximum and minimum void ratios of the mixtures were evaluated, and the optimum packing condition was determined when the mixture contained approximately 60–70 % gravel by weight. A total of six centrifuge modeling tests were performed at 50-g centrifuge gravitational acceleration. Each centrifuge model was subjected to six shaking events consisting of uniform sinusoidal motions with various amplitudes and numbers of cycles. During the entire duration of the test, the development of excess pore water pressure and settlement was monitored. Empirical relationships of pore water pressure ratio and shear strains were developed for these mixtures. The development of excess pore water pressure in the mixtures with greater than 60 % gravel exhibits transient behavior, while residual excess pore water pressure was observed in the mixtures with less than 60 % gravel. Based on the results, the volumetric threshold strain evaluated from the generation of pore water pressure and volume change during shaking is similar. The values were found to be in a range of 0.03–0.10 % and are influenced by soil composition. The threshold strain increases as the amount of gravel in the soil mixture increases.

On the boundary-layer asymmetry in two-dimensional annular Rayleigh–Bénard convection subject to radial gravity

Radial unstable stratification is a potential source of turbulence in the cold regions of accretion disks. To investigate this thermal effect, here we focus on two-dimensional Rayleigh–Bénard convection in an annulus subject to radially dependent gravitational acceleration $g \propto 1/r$ . Next to the Rayleigh number $Ra$ and Prandtl number $Pr$ , the radius ratio $\eta$ , defined as the ratio of inner and outer cylinder radii, is a crucial parameter governing the flow dynamics. Using direct numerical simulations for $Pr=1$ and $Ra$ in the range from $10^7$ to $10^{10}$ , we explore how variations in $\eta$ influence the asymmetry in the flow field, particularly in the boundary layers. Our results show that in the studied parameter range, the flow is dominated by convective rolls and that the thermal boundary-layer (TBL) thickness ratio between the inner and outer boundaries varies as $\eta ^{1/2}$ . This scaling is attributed to the equality of velocity scales in the inner ( $u_i$ ) and outer ( $u_o$ ) regions. We further derive that the temperature drops in the inner and outer TBLs scale as $1/(1+\eta ^{1/2})$ and $\eta ^{1/2}/(1+\eta ^{1/2})$ , respectively. The scalings and the temperature drops are in perfect agreement with the numerical data.

Linear instability in thermally stratified quasi-Keplerian flows

Quasi-Keplerian flow, a special regime of Taylor–Couette co-rotating flow, is of great astrophysical interest for studying angular momentum transport in accretion disks. The well-known magnetorotational instability (MRI) successfully explains the flow instability and generation of turbulence in certain accretion disks, but fails to account for these phenomena in protoplanetary disks where magnetic effects are negligible. Given the intrinsic decrease of the temperature in these disks, we examine the effect of radial thermal stratification on three-dimensional global disturbances in linearised quasi-Keplerian flows under radial gravitational acceleration mimicking stellar gravity. Our results show a thermo-hydrodynamic linear instability for both axisymmetric and non-axisymmetric modes across a broad parameter space of the thermally stratified quasi-Keplerian flow. Generally, a decreasing Richardson or Prandtl number stabilises the flow, while a reduced radius ratio destabilises it. This work also provides a quantitative characterisation of the instability. At low Prandtl numbers $Pr$ , we observe a scaling relation of the linear critical Taylor number $Ta_c\propto Pr^{-6/5}$ . Extrapolating the observed scaling to high $Ta$ and low $Pr$ may suggest the relevance of the instability to accretion disks. Moreover, even slight thermal stratification, characterised by a low Richardson number, can trigger the flow instability with a small axial wavelength. These findings are qualitatively consistent with the results from a traditional local stability analysis based on short wave approximations. Our study refines the thermally induced linearly unstable transition route in protoplanetary disks to explain angular momentum transport in dead zones where MRI is ineffective.

Modeling of Photodynamic Self-Oscillation Based on a Suspended Liquid Crystal Elastomer Ball System.

Self-oscillation enables continuous motion by transforming constant external stimuli into mechanical work, eliminating the necessity for supplementary control systems. This holds considerable promise in domains like actuators, wearable devices and biomedicine. In the current study, a novel suspended liquid crystal elastomer (LCEs) ball system consisting of a light-responsive hollow LCE ball and an air blower is constructed. Stable illumination allows for its continuous periodic oscillation. Drawing from the theoretical model in conjunction with the dynamic LCE model, the control equations for the system are established, and its dynamic motion characteristics are explored from theoretical viewpoint. The numerical calculations suggest that two motion patterns are present, i.e., hovering and self-oscillatory patterns. The critical conditions required to initiate the transition between two motion patterns are quantified for different system parameters. As evidenced by the outcomes, manipulating the light intensity, damping coefficient, contraction coefficient, air density, gravitational acceleration, bottom illumination zone height, characteristic coefficient and vertical wind speed at the blower outlet facilitates precise control over the motion patterns as well as the amplitude and frequency. With its simple structure, customizable dimensions, remote activation and active manipulation, this system may potentially change the design approach for energy harvesting, microsensors and aerial vehicles.

Self-sustained chaotic movement of electrothermal responsive liquid crystal elastomer pendulum

Self-sustained movement has the ability to absorb energy from the external environment to maintain its own movement. In the present work, a self-sustained chaotic simple pendulum system featuring an electrothermal responsive liquid crystal elastomers fiber and a mass ball is proposed and examined. The power-on state is achieved in the system through the infusion of liquid metal into this fiber. Which enables the fiber to shrink, feeding energy into the system to compensate for the energy dissipation resulting from damping, thus allowing the system to maintain its self-sustained movement. On the basis of the existing dynamic liquid crystal elastomer model, the dynamic governing equations are established, and the movement behavior of the system under electrothermal stimulation is theoretically explored. Numerical findings suggest that the simple pendulum system presents three different movement patterns, namely stationary pattern, self-sustained oscillatory pattern, and self-sustained chaotic pattern. Moreover, five system parameters of elastic coefficient, viscosity coefficient, gravitational acceleration, shrinkage coefficient and electrothermal strength are examined. The present work can contribute to a better understanding of self-sustained chaotic systems driven by electrothermal responsive materials and offer guidance for further exploration of applications such as chaos machine, and mind-brain chaos analysis.

Modulation of spin–orbit coupled Bose–Einstein condensates: analytical characterization of acceleration-induced transitions between energy bands

Abstract The effects of modulating spin-orbit coupled Bose–Einstein condensates are analytically studied. A sinusoidal driving of the coupling amplitude is shown to induce significant changes in the energy bands and in the associated spin-momentum locking. Moreover, in agreement with recent experimental results, gravitational acceleration of the modulated system is found to generate transitions between the modified energy bands. The applicability of the Landau–Zener (LZ) model to the understanding of the experimental findings is rigorously traced. Through a sequence of unitary transformations and the reduction to the spin space, the modulated Hamiltonian, with the gravitational potential incorporated, is shown to correspond to an extended version of the LZ scenario. The generalization of the basic LZ model takes place along two lines. First, the dimensionality is enlarged to combine the description of the external dynamics with the internal-state characterization. Second, the model is extended to incorporate two avoided crossings emerging from the changes induced in the energy bands by the modulation. Our approach allows a first-principle derivation of the effective model-system parameters. The obtained analytical results provide elements to control the transitions.

Effects of particle elongation on dense granular flows down a rough inclined plane.

Granular materials in nature are nearly always nonspherical, but particle shape effects in granular flow remain largely elusive. This study uses discrete element method simulations to investigate how elongated particle shapes affect the mobility of dense granular flows down a rough incline. For a range of systematically varied particle length-to-diameter aspect ratios (AR), we run simulations with various flow thicknesses h and slope angles θ to extract the well-known h_{stop}(θ) curves (below which the flow ceases) and the Fr-h/h_{stop} relations following Pouliquen's approach, where Fr=u/sqrt[gh] is the Froude number, u is the mean flow velocity, and g is the gravitational acceleration. The slope β of the Fr-h/h_{stop} relations shows an intriguing S-shaped dependence on AR, with two plateaus at small and large AR, respectively, transitioning with a sharp increase. We understand this S-shaped dependence by examining statistics of particle orientation, alignment, and hindered rotation. We find that the rotation ability of weakly elongated particles (AR≲1.3) remains similar to spheres, leading to the first plateau in the β-AR relation, whereas the effects of particle orientation saturate beyond AR≈2.0, explaining the second plateau. An empirical sigmoidal function is proposed to capture this nonlinear dependence. The findings are expected to enhance our understanding of how particle shape affects the flow of granular materials from both the flow- and particle-scale perspectives.

EXPLORING AI WITH SENSE THROUGH APPLYING THE GRAVITY IN MIND MECHANISM

The study of the laws of motion has been advancing, with significant contributions from key figures like Galileo and Newton. Analogous to the gravitational forces observed in the natural world, individuals occasionally find themselves irresistibly drawn to specific entities. The gravity in mind, the basis of free-fall motion in one’s mind, acts as a sensor to make an individual sense subtle judgments about things like common sense, as if it were whispering to our minds. Since it has been said for more than half a century that judging common sense is the most difficult task for AI, this paper explores whether AI can possess true intelligence by applying this mechanism. Empirical data from many different types of games show that Game Refinement (GR) zone is located in 0.07-0.08, which respectively corresponds to the lower limit (fairness) and upper limit (engagement). In other words, there is a border between objectivity and subjectivity in a thing, and this is the minimal objectivity, or the resignation in game context. Based upon this, in unconventional circumstances, when a greater gravitational acceleration operates within the mind, a sense of “playfulness” is generated, disrupting the harmony of comfort and discomfort sustained by the gravity in mind. The study concludes that applying the “gravity in mind” mechanism to AI could significantly blur the line between human and artificial intelligence, enhancing AI decision-making capabilities.

Quantum geometric approach: Nature and characteristics of emerged quantum-conditioned spacetime curvatures on three-sphere

General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein’s GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR’s spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed.

Numerical study of flow boiling on microcavity surface under the action of an electric field using lattice Boltzmann method

The microcavity setting promotes bubble nucleation, and the presence of an electric field enables bubble detachment. In this study, the synergistic effect of electric field and microcavity in improved flow boiling heat transfer was analyzed based on the pseudopotential lattice Boltzmann method. The investigation was focused on the influence of wall superheat, Reynolds (Re) number, electric field intensity, liquid subcooling, and gravitational acceleration on the flow boiling performance under two forms of electric field distributions for uniform conducting microcavity surface (MC–UCS) and conducting–insulating microcavity surface (MC–CIS). Compared with the MC–UCS, the MC–CIS maintained a stable wetting state in the microcavity through inhibition of sliding and merging of bubbles. The increase in electric field intensity and Re number improved convective heat transfer in the microcavity but at the expense of a larger frictional pressure drop. The boiling phenomenon on the microcavity surface weakened with the increase in liquid subcooling, which caused difficulty for the electric field to improve the heat transfer performance by improving bubble behavior. Electrical force can replace buoyancy force to perturb the vapor–liquid interface under low gravitational acceleration. This condition allows the fluid shear force to drive bubbles away from the microcavity surface quickly. The results can provide theoretical and technical guidance for the realization of the enhanced synergistic heat transfer between electric fields and microstructures.

Modeling Gravity Gradients from Surface Gravity Anomaly Data

Gravity gradients are useful to characterize near mass anomalies since they are much more sensitive to short wavelength anomalies than gravitational accelerations. Estimating gravity gradients from surface gravity data is based on numerical implementations of solutions to geodetic boundary value problem for determination of disturbing potential. One of methods to solve this problem is least-squares collocation which is basically based on data and a defined covariance function. This study deals with estimating gravity gradient tensor components from along track surface gravity anomaly data. The Least-Squares Collocation solution is based on a stationary local covariance function defined for the disturbing potential which allows upward continuation of the observations to a desired altitude. The modeling method is evaluated in using Earth Gravitational Model 2008(EGM2008) and real airborne gravity gradiometry data collected over Southern Texas, Oklahoma region. The results show that modeled gravity gradients estimated in both on the ground and at a certain altitude have basically good agreement with EGM08 gradients. Modeled gradients including horizontal components in the east-west direction exhibit some discrepancies in comparison to the airborne gradiometry data, which may be attributed to some measurement errors in the gradient data.

Reevaluation of Plate-Fin Heatsink Natural Convection Correlations for Sideways and Three-Dimensional Inclinations

The common orientations of the plate-fin heat sink for natural convection cooling of electronics are vertical and upward-facing horizontal. However, depending on various use scenarios, the heat sink may be inclined, intentionally or otherwise. In our previous papers concerning this subject, the author proposed a set of correlations for plate-fin heat sinks covering all inclination angles backward and forward (pitch rotation) from the vertical position of the heat sink. The set was based on a series of computational simulations with a validated model. At the time, tilting the heat sink sideways (roll rotation) was not considered. In the present study, though, the sideways inclination of the plate-fin heat sinks is simulated using our previous model only by adjusting the direction of the gravitational acceleration vector, thus requiring no additional validation. It is determined that the previously proposed correlation is valid up to 80° sideways inclinations of the heat sink. Interesting flow structures are observed when the heat sink is tilted 90° sideways. Furthermore, it is demonstrated that the correlation surprisingly remains valid if the heat sink is simultaneously rotated in both axes (pitch and roll).

Design of Experimental Series on the Free Fall of Object

An experimental set for measuring the gravitational acceleration to compare free falling motion was developed in this research. It used DIY relay by a simple relay control to o’clock automatically measure to free falling time of the object. The measured falling time was displayed on a general clock which the user could read it. Recorded falling time at different falling height was analyzed to get the gravitational acceleration. The results showed that the value of measured gravitational acceleration was very close to the standard value. The magnitude of the gravitational pull measured from the developed machine is equal to And can be measured from a company machine Compare with the gravitational field value of the standard measured by the National Institutes of Health, Bangkok, Thailand, which is equal to . It’s percentage of deviation from standard value was 0.918% and, it’s percentage of deviation from Ready-made gantry fall testing machine value was 0.481%. This experimental set demonstrates that it can be used to measure the gravitational acceleration effectively.