Newtonian Force Research Articles

Gravitational fields of the magnetic-type

Local conformal symmetry introduces the conformal curvature (Weyl tensor) that gets split into its (gravito-) electric and magnetic (tensor) parts. Newtonian tidal forces are expected from the gravitoelectric field, whereas general-relativistic frame-dragging effects emerge from the gravitomagnetic field. The symmetric, traceless gravitoelectric and gravitomagnetic tensor fields can be visualized by their eigenvectors and eigenvalues. In this paper, we depict the gravitoelectric and gravitomagnetic fields around a slowly rotating black hole. This suggests that the phenomenon of ultra-fast outflows observed at the centers of active galaxies may give evidence for the gravitomagnetic fields of spinning supermassive black holes. We also question whether the current issues in our contemporary observations might be resolved by the inclusion of gravitomagnetism on large scales in a perturbed FLRW model.

Cosmological Density Perturbations from Matter Domination to Recombination in Newtonian and MONDian Gravity Scenarios

Cosmological density perturbations governed by Newtonian and MONDian force laws scenarios for the period from matter domination to recombination have been investigated. Particularly, we find solutions for the density contrast equations obtained for both cases with respect to a homogeneous spatially flat Friedman-Lemaitre-Robertson-Walker (FLRW) background using the Lie symmetry approach. Numerical solutions of the density contrast equations for both cases also have been provided in order to study the evolution of the density contrast. For the Newtonian case we find a limiting mass that dictates whether the growth of the density contrast is possible or not. Interestingly, in the Newtonian case, physical growth of the density contrast is not possible since the horizon mass is smaller than the limiting mass. On the other hand, growth of the density contrast is possible depending on the initial condition and the fluctuation mass of the MOND-dominated region despite the radiation pressure that leads to future structure formation.

Finding the Planck length multiplied by the speed of light without any knowledge of G, c, or ℏ, using a Newton force spring

In this paper, we show how one can find the Planck length multiplied by the speed of light, lpc, from a Newton force spring with no knowledge of the Newton gravitational constant G, the speed of light c, or the Planck constant h. This is remarkable, as for more than a hundred years, modern physics has assumed that one needs to know G, c, and the Planck constant in order to find any of the Planck units. We also show how to find other Planck units using the same method. To find the Planck time and the Planck length, one also needs to know the speed of light. To find the Planck mass and the Planck energy in their normal units, we need to know the Planck constant, something we will discuss in this paper. For these measurements, we do not need any knowledge of the Newton gravitational constant. It can be shown that the Planck length times the speed of light requires less information than any other Planck unit; in fact, it needs no knowledge of any fundamental constant to be measured. This is a revolutionary concept and strengthens the case for recent discoveries in quantum gravity theory completed by (Haug 2020 Phys. Essays 33 46–78).

The asymptotic solutions of the governing system of a charged symmetric body under the influence of external torques

This paper investigates the motion of a dynamically symmetric rigid body about one of its fixed points in which it is incurred to Newtonian force field, electromagnetic field and external torques. These torques acted in the direction of the principal axes of the body and are represented by perturbing and gyrostatic torques. The body rotates initially about the symmetry dynamic axis with high angular velocity. Therefore, a small parameter can be introduced. The averaging method is applied to convert the governing system of motion into another convenient averaging one in terms of a small parameter. The asymptotic analytical solutions of the latter system are obtained for some distinct applications depending upon the perturbing torques and the restoring one. The good effect of the body parameters on the motion is clarified in the graphical representations of the obtained solutions of the considered applications. The significance of this work is due to its great implementation of practical life like submarines, devices that maintain the stability and measure the orientations of airplanes and for several physics and engineering applications.

A novel compliant mechanism based system to calibrate spring constant of AFM cantilevers

Calibrating spring constant of atomic force microscope (AFM) cantilevers is necessary for the measurement of micro/nano newton forces, which are commonly-used in the characterization of micro/nano functional surfaces and materials, cell manipulation, and many more applications. This paper presents a novel compliant mechanism based system to calibrate the spring constant of AFM cantilevers. The calibration system is mainly composed of a compliant suspension mechanism and an electromagnetic force actuator, where two kinds of compliant structures of “L” shape flexures and “Archimedes” planar flexures are assembled in parallel to achieve compact devices, respectively. The characteristics of the suspension mechanism are investigated by analytical model and finite element analysis (FEA). Furthermore, a prototype of the calibration system is established and experimental tests are carried out to verify the performance. An electromagnetic force actuator is employed to provide calibration force. Meanwhile, a capacitance sensor is utilized to monitor the displacement of the suspension mechanism. The calibration results of AFM cantilevers reveal that the compliant mechanism based calibration system has a good performance and it can calibrate the spring constant of AFM cantilevers accurately and effectively.

The phenomenology of the quantum-corrected gravitational force

The Newtonian gravitational force can be derived from the Heisenberg uncertainty principle. In the realm of high-energy physics, it is necessary to replace the standard uncertainty principle by the generalized uncertainty principle (GUP). The generalized uncertainty principle can provide some corrections into the gravitational force. In this paper, we have applied the GUP to modify the gravitational force. The modified gravitational force has been applied to find the GUP corrections into Binet's equation. The modified Binet's equation has been used to study the advance of the perihelion of Mercury. It is shown that the GUP may provide the precession of Mercury's perihelion in the context of Newtonian physics. The modified gravitational force can also be applied to find the modified Friedmann equation in which the correction terms may play the role of dark energy to provide an accelerating universe.

Physical model test study on shear strength characteristics of slope sliding surface in Nanfen open-pit mine

A physical model for the footwall slope of Nanfen open-pit mine, China was established using a self-developed deep geological engineering disaster model test system. A thermosensitive similar material, paraffin, was selected to simulate a weak structural plane in the slope to reproduce the landslide process. From an experimental perspective, the variation trend of shear strength parameters of weak structural plane and the mechanical support characteristics of NPR (negative Poisson’s ratio) anchor cable under the condition of a large landslide deformation and failure were examined. The results of this model test showed that slope failure has four distinct stages: (1) soil compaction stage, (2) crack generation stage, (3) crack propagation stage, and (4) sliding plane transfixion stage. According to the test results, the rock mechanics parameters of weak surface in the footwall slope of Nanfen open-pit mine were calculated. The cohesion is approximately 1.35 × 105 Pa, and the internal friction angle is approximately 6.33°. During slope failure, the NPR anchor cable experiences a large deformation but no damage occurs, indicating that the NPR anchor cable can be continuously monitored and reinforced during the deformation and failure of landslide. The stress characteristics of NPR anchor cables during the test are consistent with the monitoring results of Newtonian force at the landslide site, proving that NPR anchor cables are effective and reasonable in landslide monitoring and early warning.

Analysis of Copenhagen problem with a repulsive quasi‐homogeneous Manev‐type potential within the frame of variable mass

AbstractThe present problem is devoted to the special case of restricted problem of three bodies, always referred as the Copenhagen problem when we consider the primaries of equal masses. In this manuscript, we have considered the third body of infinitesimal mass as variable and moreover, instead of taking only Newtonian potential and forces, a quasi‐homogeneous potential produced by the main primaries has also been taken into account. This implies that, in order to approximate the phenomena such as the radiation pressure or the primaries' nonsphericity, we insert an inverse cube corrective term to the gravitational law of inverse square. In this model, the impact of the parameters, arise as a result of variable mass on the number and locations of the in‐plane and out‐of‐plane equilibrium points, is discussed. Moreover, their stability is also analyzed and the impact of these parameters on the regions, where motion of the third particle is possible, is unveiled. The basins of convergence associated with these equilibrium points are also illustrated by the Newton–Raphson iterative scheme of two or more variables.

A potential role of Zfra in mitigating traumatic brain injury transition to Alzheimer’s disease‐like symptom in mice

Most recently, tumor suppressor WWOX is defined as a risk factor for Alzheimer’s disease(AD). Previously, we determined that accumulation of pS14‐WWOX in the brain hippocampus and cortex correlates with the occurrence of AD and probably other neurodegeneration. Zinc finger‐like protein that regulates apoptosis (Zfra) suppresses pS14‐WWOX accumulation and restores memory loss in triple transgenic mice (3xTg) for AD. During the acute phase traumatic brain injury (TBI), overly expressed WWOX becomes phosphorylated at Tyr33 and is accumulated in the nuclei to cause neuronal death in the impacted areas. We determined that in the novel object recognition tests, mice surviving from TBI (2.8 to 3.3 Newtonian force) significantly spent less exploring time on new objects in both long‐term and short‐term memory tests post TBI for 18 weeks, indicating the occurrence of damage in long‐ and short‐term memory. Further, control and TBI mice were subjected to Morris water maze tests post TBI for 10 weeks to determine the hippocampus‐dependent, spatial memory. Both groups showed a time‐dependent decrease in escape latency, indicating that mild TBI didn’t affect the learning capabilities. BALB/c mice received Zfra4‐10 peptide via tail vein injections prior to TBI (1.7 Newtonian force). Two weeks later, these treated mice significantly spent more time on probing the new object in the short‐term memory task compared to control mice, suggesting that Zfra peptide prevents TBI‐induced memory loss. Interestingly, by immunohistochemistry, significant upregulation of tau phosphorylation at T181 and amyloid beta aggregates was shown rapidly in death‐inducing impact in BALB/c mice (3.5 Newton), and that Zfra significantly prevented the upregulation (~20 to 33%). Together, our observations suggest the transition of TBI to AD‐like symptom in mice are likely to occur, and that Zfra4‐10 peptide prevents the transition.Support or Funding InformationMinistry of Science & Technology, Taiwan, National Health Research Institute, Taiwan, Department of Defense, USA

Possible existence of a third fundamental long-range force

Abstract It is inferred that, in addition to the Coulomb and Newtonian forces, there should exist a third fundamental long-range force, which acts between intrinsic angular momenta. This inference is based on the quantum Einstein gravity, that is, the manifestly-covariant, BRS-invariant, canonically quantized theory of general relativity. The form of the potential of the third fundamental long-range force is determined by calculating the non-relativistic limit of the Bethe–Salpeter kernel in the lowest-order perturbation theory. The observability of this force is also discussed.

INVESTIGATION OF THE EVOLUTION EQUATIONS OF THE AXISYMMETRIC BODY WITH

In this article we consider mutually gravitating non-stationary two bodies: first body is «central», it is a sphere with a spherical density distribution, the second body is «satellite», which has an axisymmetric dynamic structure and form. Newtonian force interaction is characterized by an approximate expression of the force function, which takes into account the second harmonic. The differential equation of translational-rotational motion of the axisymmetric body is derived with variable mass and variable size in a relative coordinate system. The axes of the own coordinate system for nonstationary two bodies coincides with the main axes of inertia and this position remains unchanged during evolution. The mass of bodies are varied isotropically in the different rates. The problem is investigated by methods perturbation theory. The equations of secular perturbations of translational-rotational motion of satellite are deduced in the analogues osculating elements Delaunay-Andoyer. The solutions of the differential equations of the perturbed motion are obtained by the numerical method and the graphs are constructed using the Wolfram Mathematica package.

Investigation into position deviation effect on micro newton force sensor

The position deviation effect on force sensor with a resolution of micro newton scale was investigated by theory model analysis and numerical simulation method. The finite element method and theoretical model were used to analyse the influence of the electrostatic micro force sensors when the electrode position of the cylindrical capacitor changed. Relationship between the sensor output micro force and the position deviation of the internal electrode in the cylindrical capacitance was obtained. It was found that different position deviation form had different degrees of influence on the sensor’s output result and the regions with little effect by position deviation were existed. For translation along Z-axis, the region was [-4 mm, 14 mm]. For translation along r-axis, the region was [-0.2 mm, 0.2 mm]. And for rotation around r-axis, the region was [-1°, 1°]. The corresponding maximum errors of the micro force output were 1.49%, 2.09% and 2.20%, respectively.

Relation between solutions of the Schrödinger equation with transitioning resonance solutions of the gravitational three-body problem

It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schrödinger equation for a wide range of masses that transition between energy states. In the macroscopic scale, the resonance solutions are shown to transition from one resonance type to another through weak capture at one of the bodies, while in the Schrödinger equation, one obtains quantized wave solutions transitioning between different energies. The resonance transition dynamics provides a classical model of a particle moving between different energy states in the Schrödinger equation. This methodology provides a connection between celestial and quantum mechanics.

An Approach to Quantum Gravitodynamics and Some Important Results

We present in this article a new approach to the theory of gravitation. Here, the gravitational field of a gravitating body is assumed to be four fold. The gravitating body of mass M possesses gravitoelectric mass M, gravitomagnetic mass -2M. The test particle possess electric and magnetic masses that are algebraically of the same sign of that of the source body, i.e., m and -2m. Based on the electrostatic force formula, we find four forces acting on the test particle. The sum of these forces gives exactly the Newtonian gravitation force and gravitational potential energy. The classical theory of this approach yields four sets of Maxwellian equations and thus, four spin 1 bosons convey the complete force of gravity. The quantum version of this approach to gravity is illustrated here by presenting the fundamental Feynman diagrams that issue from the new theory. We work out scattering cross-section of interaction of an electron with a fixed gravitating mass partially. Of the four Feynman diagrams, we work out cross-section of scattering for only the simplest diagram. The non-relativistic limit of the cross-section is found and compared with that of electric Rutherford scattering. It is found that the electromagnetic cross-section is 1017 times larger than the gravitational cross-section for the one process we considered. The work is fundamental and sheds new light onto quantum gravitodynamics.

Determination of Excess Removability of Self-Adhesive Resin Cements

Objective: This study aimed to determine the force required to remove a defined amount of self-adhesive resin cements excess from a (pretreated) dentin surface after tack curing. Methods: Bovine teeth (n=5) were ground flat to expose dentin, polished (grit 320 sandpaper), distilled water rinsed, and gently air-dried. With the aid of a drilling template fixed with superglue (Sekundenkleber, Renfert GmbH), 1 to 3 cylindrical cavities (4.5±0.1mm diameter x 2.0±0.1mm depth) were drilled. Superglue was mechanically removed after drilling. Resin cement weighing 30mg was placed in the cavity and pushed through with a stainless-steel rod (4.0±0.05mm diameter x 2.0±0.1mm height), so that all of the excess cement was pushed out onto one side of the cavity to form a half moon. Excess cement was cured for a defined time of 5 seconds, from a defined distance (2mm spacer) from the tooth surface using an EliparTM S10 light curing device (3M ESPE). Excess cement was sheared off using a jig (Zwick Z010, n=5; speed= 0.75mm/min). Maximum force (N) to shear off the excess cement was recorded. Results: Experimental Cement and Calibra® Universal were statistically lower in mean newton force than the other selfadhesive resin cements. TheraCem® Ca and RelyX™ Unicem 2 were not statically different from each other. Maxcem EliteTM Chroma and G-CEM LinkAce® were statistically lower than TheraCem® Ca and RelyX™ Unicem 2. Conclusion: A method was developed to quantify force needed to remove cement excess. Under standardized conditions, different levels of removal force were identified. PANAVIA™ SA Cement Plus, Calibra® Universal and Experimental Cement require a significantly lower force for excess removal. SpeedCEM® Plus and Maxcem EliteTM Chroma require an intermediate force. RelyX™ Unicem 2 and TheraCem® Ca require a significantly higher force to achieve excess removal. Excess removal force can be lowered by reducing irradiation time as shown with RelyX™ Unicem 2 (one second cure) and RelyX™ Unicem 2 (two second cure).

Particle Pair Production in Cosmological General Relativity—Redux

We model the universe on the interaction of two cosmic particles based on the Cosmological General Relativity (CGR) of Carmeli and obtain a theoretical value for the Hubble constant h at zero distance and no gravity. CGR is a 5-dimensional theory of time t, space x, y, z and velocity v. A minimum cosmic acceleration a0=dv/dt=c/τ results from a linearized version of CGR, where c is the vacuum speed of light and τ is the Hubble-Carmeli time constant. The force due to the Carmeli acceleration a0 counteracts the Newtonian gravitational force between the two particles. Each particle is unstable and disintegrates into baryons, leptons and radiation. By the uniform expansion of the black body radiation field, we obtain the expression , where A is a constant, T0 is the temperature of the cosmic microwave background black body, Ωbphys is the physical baryon density parameter and pc ≈3.086×1018cm·pc-1. Using standard values for T0 and Ωbphys we obtain a value τ=(4.15121±0.00206) ×1017s, which gives a value for the Hubble constant at zero distance and no gravity of h=1/τ=(74.33982±0.03694)km·s-1·Mpc-1. From the value for τ, we get the age of the universe of (13.15467 ± 0.00653) × 109 years.

Multidimensional item response theory and the force and motion conceptual evaluation

Many studies have examined the structure and properties of the Force Concept Inventory (FCI); however, far less research has investigated the Force and Motion Conceptual Evaluation (FMCE). This study applied Multidimensional Item Response Theory (MIRT) to a sample of N=4528 FMCE post-test responses. Exploratory factor analysis showed that 5, 9, and 10-factor models optimized some fit statistics. The FMCE uses extensive blocking of items into groups with a common stem; these blocks factored together in most models. A confirmatory analysis, which constrained the MIRT models to a theoretical model constructed from expert solutions, produced a model requiring only 8 principles, fundamental reasoning steps. This was substantially fewer than the 19 principles identified in the FCI by a previous study. Correlation analysis also demonstrated that the two instruments were very dissimilar. The reduced number of principles and the repetition of items using a single principle allowed the extraction of eight single-principle subscales, seven with Cronbach’s alpha greater than the 0.7 required for acceptable internal consistency. The differences between the FCI and the FMCE suggest that the two instruments could provide complementary, but different, information about student understanding of Newton’s laws with the FCI measuring an integrated Newtonian force concept and the FMCE measuring details of that force concept.Received 6 June 2019DOI:https://doi.org/10.1103/PhysRevPhysEducRes.15.020141Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAssessmentConcepts & principlesInstructional materials developmentResearch methodologyPhysics Education Research

Wrist Rehabilitation System Using Augmented Reality for Hemiplegic Stroke Patient Rehabilitation: A Feasibility Study

Objective: Our objective was to investigate the effect of the rehabilitation system using augmented reality (AR) on upper extremity motor performance of patients with stroke. Methods: The system using AR applying mirror therapy mechanism provides the intervention protocol for the patient with hemiplegia after stroke. The system consists of a patient positioning tool (a chair), a white surface table, an image acquisition unit, an image processing unit, an image displaying unit, an arm holder, a Velcro-strap, and two blue circle stickers. To assess the feasibility of our system in motor function recovery, a stroke patient was recruited to receive the AR intervention. The treatment was performed two times a day for ten minutes over two weeks (ten days of treating weeks), except for the time of installation, calibration, and three minute breaks. Jebsen Taylor hand function test and Arm Motor Fugl-Meyer assessment were used as primary and secondary outcome measures, respectively, to evaluate the effect of motor function recovery. Additionally, stroke impact scale, Korean version-Modified Barthel Index (K-MBI), active range of motion of wrist joint (ROM), and the grasp force in Newtons were measured. Participants’ feedback and adverse effects were recorded as well. Results: Motor function improvements were exhibited in wrist and hand subtest of Arm Motor Fugl-Meyer (baseline: 19; post-intervention: 23), proximal arm subtest of Fugl-Meyer (baseline: 31; post-intervention: 34), ROM (extending ROM: 10° and 3° for flexion and extension, repeatedly), stroke impact scale (baseline: 46; post-intervention: 54), K-MBI (baseline: 92; post-intervention: 95), nine-hole pegboard (baseline: 30 s; post-intervention: 25 s), and grasp force in Newtons (baseline: 12.7; post-intervention: 17.7). However, the adverse effects were reported after the intervention. Conclusion: The system using AR applying mirror therapy mechanism demonstrated the feasibility in motor function recovery for the stroke patient.

Whiskered Parabolic Tori in the Planar $$(n+1)$$-Body Problem

The planar \((n+1)\)-body problem models the motion of \(n+1\) bodies in the plane under their mutual Newtonian gravitational attraction forces. When \(n\ge 3\), the question about final motions, that is, what are the possible limit motions in the planar \((n+1)\)-body problem when \(t\rightarrow \infty \), ceases to be completely meaningful due to the existence of non-collision singularities. In this paper we prove the existence of solutions of the planar \((n+1)\)-body problem which are defined for all forward time and tend to a parabolic motion, that is, that one of the bodies reaches infinity with zero velocity while the rest perform a bounded motion. These solutions are related to whiskered parabolic tori at infinity, that is, parabolic tori with stable and unstable invariant manifolds which lie at infinity. These parabolic tori appear in cylinders which can be considered “normally parabolic”. The existence of these whiskered parabolic tori is a consequence of a general theorem on parabolic tori developed in this paper. Another application of our theorem is a conjugation result for a class of skew product maps with a parabolic torus with its normal form generalizing results of Takens (Ann Inst Fourier 23(2):163–195, 1973), and Voronin (Funktsional Anal i Prilozhen 15(1):1–17, 96, 1981).

Neo-Cartesian unified fluid and field theory: from Klein-Gordon equation to de Broglie’s Lorentz invariant mechanics

A unified fluid and field theory containing all forces as special cases postulates that primordial fluid is formed by discrete, 3D-extended energy-like sagions obeying usual energy-momentum conservation laws. Contrary to Newtonian mechanics, mass and force are not primitive notions (hence, “Cartesian”), but the theory is atomistic (hence “neo”). Collective fluid behaviour obeys the homogeneous Klein-Gordon equation, or homogeneous 3D-wave equation, which besides usual harmonic periodic solutions has three families of quantized, Galilean-Lorentz isomorph, nonperiodic solutions discovered around 1995. Here, quantum mechanics is relativistic ab initio thus ensuring consistency with Einstein’s general theory of relativity, which is extended to include effects upon gravity of chemical and nuclear composition, as indeed observed by Eötvös (1890s), and Majorana (1919). Planck constant is identified with the bit of minimum angular momentum in sagion-sagion interactions, thus introducing quantum features at the root of classical mechanics. Acceleration produced by successive pushes of a small projectile (say, a sagion, disagion, trisagion, 4-sagion) leads to a curve resembling Einstein’s mass increase. This reinterprets one aspect of the restricted theory of relativity: rather than mass increase, Bertozzi experiment demonstrates inefficient transfer of linear momentum. The lower branch in our background universal acceleration curve is associated to static friction.