Newton’s Second Law: Problem Solving and Situation Analysis

Author(s):  
Robert A. Morse
Author(s):  
Ricardo Lopes Coelho

Resumo Aprendemos no liceu e na universidade que a segunda lei de Newton é F=ma. Porém, Newton nunca escreveu a equação. Além disso, não há acordo entre os historiadores da ciência em relação à equação que expressa a segunda lei de Newton. Físicos do séc. XVIII, que citaram e explicaram as leis de Newton, não usaram F=ma. Portanto, se a tese dos manuais contemporâneos fosse correta, teríamos de admitir que todos aqueles físicos interpretaram mal a segunda lei de Newton. Por outro lado, Euler defendeu ter descoberto um novo princípio de mecânica, que é F = ma. Comparando a segunda lei de Newton e o princípio de Euler compreendemos que elas diferem significativamente. Este resultado da pesquisa histórica tem implicações nos problemas conceptuais da mecânica e na resolução de problemas, como iremos ver.Palavras-chave: A segunda lei de Newton; o princípio de Euler; manuais. Abstract We learned at high school and university that Newton’s second law is F=ma. However, Newton never wrote this equation. Furthermore, there is no agreement among historians of science as to the equation that expresses Newton’s second law. 18th century physicists, who quoted and explained Newton’s laws of motion, did not use F=ma. Therefore, if contemporary textbook writers’ claim were correct, we would have to admit that all those physicists misunderstood Newton’s second law. They did not grasp that his law was F=ma. Furthermore, Euler claimed to have discovered a principle of mechanics, which is F=ma. This paper of Euler provides us with the means of clarifying the issue. We can compare Newton’s second law and Euler’s principle with each other and verify whether there are significant differences between both laws. The result is that Newton’s second law is not Euler's principle. This result of historical research has implications for the conceptual problems of mechanics and problem solving, as we shall see. Keywords: Newton’s second law; Euler’s principle; textbooks.


2019 ◽  
Vol 57 (2) ◽  
pp. 88-90 ◽  
Author(s):  
Vincent P. Coletta ◽  
Josh Bernardin ◽  
Daniel Pascoe ◽  
Anatol Hoemke

Strategies ◽  
2002 ◽  
Vol 16 (2) ◽  
pp. 7-11
Author(s):  
Deborah A. Stevens-Smith ◽  
Shelley W. Fones

2010 ◽  
Vol 56 (196) ◽  
pp. 333-338 ◽  
Author(s):  
Tsutomu Nakamura ◽  
Osamu Abe ◽  
Ryuhei Hashimoto ◽  
Takeshi Ohta

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.


Author(s):  
N. Duke Perreira

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.


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