Modified gravity and the origin of inertia

Modified gravity theory is known to violate Birkhoff's theorem. We explore a key consequence of this violation, the effect of distant matter in the Universe on the motion of test particles. We find that when a particle is accelerated, a force is experienced that is proportional to the particle's mass and acceleration and acts in the direction opposite to that of the acceleration. We identify this force with inertia. At very low accelerations, our inertial law deviates slightly from that of Newton, yielding a testable prediction that may be verified with relatively simple experiments. Our conclusions apply to all gravity theories that reduce to a Yukawa-like force in the weak field approximation.Comment: 4 pages, 3 figures; published version with updated reference

Incorporación de lignosulfonato de calcio y cemento para mejorar las propiedades de la subrasante en la carretera Paruro – Cusco – 2022

Existen factores que afectan la inestabilidad de la vía afectando las propiedades físico mecánicas, es por todo ello que en el proceso constructivo surge el interés de buscar temas de investigación relacionadas a dar una solución para mejorar las propiedades físico mecánicas del suelo para la subrasante y que al mismo tempo representen ser económicas .Es por ello el siguiente tema de investigación tiene por objetivo demostrar que la incorporación de lignosulfonato de calcio y cemento influye en las propiedades de la subrasante en la carretera, el cual se usó la metodología aplicada , de diseño experimental –cuasi experimental teniendo como población la subrasante del lugar de tema de investigación y como parte de las muestras se considerara las calicatas. Lo cual se realizó los ensayos con la incorporación del lignosulfunato de calcio y cemento en % de 0, 2, 4, 6 y 8% donde se obtuvo el mejor resultado con el 6% para el CBR con el lignosulfonato de calcio obteniendo 19.31% con referencia a la muestra patrón 14.65%; llegando a la conclusión que al adicionar el lignosulfunato de calcio y cemento mejora las propiedades de la subrasante y resulta económico el empleo del lignosulfunato de calcio

On Virtual Displacement and Virtual Work in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for holonomic (velocity independent), non-holonomic (velocity dependent), scleronomous (time independent) and rheonomous (time dependent) constraints. It is observed that for holonomic, scleronomous constraints, the virtual displacements are the displacements allowed by the constraints. However, this is not so for a general class of constraints. For simple physical systems, it is shown that, the work done by the constraint forces on virtual displacements is zero. This motivates Lagrange's extension of d'Alembert's principle to system of particles in constrained motion. However a similar zero work principle does not hold for the allowed displacements. It is also demonstrated that d'Alembert's principle of zero virtual work is necessary for the solvability of a constrained mechanical problem. We identify this special class of constraints, physically realized and solvable, as {\it the ideal constraints}. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.Comment: 12 pages, 10 figures. This article is based on an earlier article physics/0410123. It includes new figures, equations and logical conten

Encyclopédie, ou Dictionnaire Raisonné des Sciences, des Arts et des Metiers

Tomos 1º e 2º AB-AZ, BA-C