Let nature speak: the case of the Atwood machine
Ricardo Coelho (University of Lisbon)
Paper short abstract:
There are several solving strategies of the Atwood machine problem. These use different theoretical elements to reach the solution of the problem. An approach directly based on the characteristics of the machine enables us to achieve the same goal in a simpler and clearer way.
Paper long abstract:
The Atwood machine, invented by George Atwood in 1784, is nowadays a basic physics laboratory device (two bodies connected by a string passing over a pulley) and a typical problem in introductory physics textbooks. In the last decades, some authors (Crawford 1987, Gonzalez 1997, Newburgh et al. 2004, Coelho 2013) have proposed solving strategies for the compound Atwood machine problem, which use more intuitive ideas than the standard strategies. The present paper will give an overview of both alternative and standard solving strategies. It turns out from the analysis of all these strategies that these use different theoretical elements (Newton’s second law, equivalence principle, Lagrange equations, among others) to obtain the solution of the problem. There are, however, two characteristics of the phenomenon, which can be easily demonstrated (the inextensibility of the string and the weights of the hanging bodies), on which a solving strategy can be based. Thus, instead of applying the Newtonian, Lagrangean or other theories to the machine, we can let the machine speak. This latter approach provides us with an understanding of the phenomenon, which in turn constitutes the guiding idea in the problem solving. Moreover, the typical conceptual problem of classical mechanics – force is the cause of acceleration – is overcome by means of the approach that is closer to nature. The present case study leads us to the idea that this motto ‘Let Nature and Material Things Speak’ could play an important role in physics education.
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