Introducing advanced concepts for young students

Abstract

The compound Atwood's machine (Atm) problem is revisited in order to introduce young students on advanced concepts in Physics. Atm is an old-fashioned device. However, it allows us to speak about relativity of motion, principle of equivalence, inertial and non-inertial frames of reference, general covariance and invariance under coordinate transformations. Besides, it also provides experimental support for our theoretical models. We have started with coordinate transformations and inertial and non inertial reference frames followed by the principle of equivalence. The composed Atm was worked out in the following. We calculate the acceleration in the machine applying Newton's Laws to describe its dynamics in an inertial frame on the fixed pulley center and in a non-inertial one on the moving pulley center. Coordinate transformations mapping inertial frame solutions in non-inertial ones and vice-versa allow students catch on relativity concepts and the role played by general covariance. A comparison between these solutions showed the importance of the principle of equivalence in the evaluation of the intensity of gravity locally. In addition, according to this coordinate transformation the non-inertial reference frame equations of motion are equivalent to one single Atm plus one falling mass. Our results have also shown, in agreement with experimental outcomes, that after movement starts single Atm becomes lighter than $m_{3}$ mass, consequently $m_{3}$ mass is falling. It is a non-intuitive experimental result first observed for the 1854 Poggendorff's fall machine. A measure of single Atm's mass reduction was reported in 2016's last issue of Physics Education.