Simple variable mass systems: Newton’s second law

Abstract The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i.e. a principle (axiom) of completeness intended to generalize Newton’s second law of motion for the case of a non-stationary variable-mass point (system) that varies with time. This generalization leads to hyperdynamic dependencies describing such motion from new accurate qualitative standpoints.

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Newton’s Second Law of a particle with variable mass

Revista Brasileira de Ensino de Física ◽

10.1590/1806-9126-rbef-2021-0090 ◽

2021 ◽

Vol 43 ◽

Author(s):

M.T. Thomaz

Keyword(s):

Center Of Mass ◽

Variable Mass ◽

Variable Number ◽

Second Law ◽

Constant Mass ◽

First Case ◽

Inertial Frames ◽

Newton's Second Law ◽

Over Time ◽

Number Of Particles

We approach the question of the movement of a particle with variable mass observed from an inertial frame. We consider two different situations: (i) a particle whose intrinsic mass value varies over time; (ii) the center of mass (CM) of a set of particles with constant mass but with a variable number of particles belonging to it. We show that Newton’s Second Law distinguishes the case in which the intrinsic mass of the particle varies over time from systems composed of particles, with constant mass, whose total mass varies over time. In the first case, we study the consequences of the equation of motion of a particle with variable mass is not covariant in inertial references under Galilean transformations. We also show that the equation that drives the dynamics of the CM of a system with variable number of particles preserves the equivalence of all inertial frames under the Galilean transformations. We verify the non-conservation of the linear momentum vector of the CM of a set of free particles during the time that one particle leaves or comes into the system.

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Numerical and experimental investigations of the dynamics of a variable mass pendulum

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215590454 ◽

2015 ◽

Vol 230 (12) ◽

pp. 2124-2132

Author(s):

Tomasz Bartkowiak ◽

Jakub Krzysztof Grabski ◽

Jan Adam Kołodziej

Keyword(s):

Mathematical Model ◽

Variable Mass ◽

Experimental Investigations ◽

Second Law ◽

Reactive Force ◽

Test Rig ◽

Simple Experiment ◽

Air Resistance ◽

Variable Mass Systems ◽

Loss Of Mass

In this paper, the numerical and experimental results for the dynamics of pendulum with variable mass were described. Mathematical model was developed taking into account the loss of mass, reactive force, air resistance, and friction. A corresponding test rig was designed and built in order to validate the numerical results. The purpose of the paper is to show that in case of the variable mass systems the second Newton’s law cannot be directly applied in the traditional form. The simple experiment was designed to support the thesis that the modification of Newton’s second law is necessary.

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Feeling Newton’s Second Law

The Physics Teacher ◽

10.1119/1.5088467 ◽

2019 ◽

Vol 57 (2) ◽

pp. 88-90 ◽

Cited By ~ 2

Author(s):

Vincent P. Coletta ◽

Josh Bernardin ◽

Daniel Pascoe ◽

Anatol Hoemke

Keyword(s):

Second Law ◽

Newton's Second Law

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Scootin' with Newton: Teaching Newton's Second Law Using Motion

Strategies ◽

10.1080/08924562.2002.10590996 ◽

2002 ◽

Vol 16 (2) ◽

pp. 7-11

Author(s):

Deborah A. Stevens-Smith ◽

Shelley W. Fones

Keyword(s):

Second Law ◽

Newton's Second Law

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A dynamic method to measure the shear strength of snow

Journal of Glaciology ◽

10.3189/002214310791968502 ◽

2010 ◽

Vol 56 (196) ◽

pp. 333-338 ◽

Cited By ~ 16

Author(s):

Tsutomu Nakamura ◽

Osamu Abe ◽

Ryuhei Hashimoto ◽

Takeshi Ohta

Keyword(s):

Shear Strength ◽

Strain Rate ◽

Reasonable Agreement ◽

Dynamic Method ◽

Second Law ◽

Snow Density ◽

Newton's Second Law

AbstractA new vibration apparatus for measuring the shear strength of snow has been designed and fabricated. The force applied to a snow block is calculated using Newton’s second law. Results from this apparatus concerning the dependence of the shear strength on snow density, overburden load and strain rate are in reasonable agreement with those obtained from the work of previous researchers. Snow densities ranged from 160 to 320 kg m−3. The overburden load and strain rate ranged from 1.95 × 10−1to 7.79 × 10−1kPa and 2.9 × 10−4to 9.1 × 10−3s−1respectively.

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