In this paper, we show the potential of webcams as precision measuring instruments in a physics laboratory. Various sources of error appearing in 2D coordinate measurements using low-cost commercial webcams are discussed, quantifying their impact on accuracy and precision, and simple procedures to control these sources of error are presented. Finally, an experiment with controlled movement is performed to experimentally measure the errors described above and to assess the effectiveness of the proposed corrective measures. It will be shown that when these aspects are considered, it is possible to obtain errors lower than 0.1%. This level of accuracy demonstrates that webcams should be considered as very precise and accurate measuring instruments at a remarkably low cost.
In this paper, we present a simple experiment to introduce the nonlinear behaviour of oscillating systems in the undergraduate physics laboratory. The transverse oscillations of a spring allow reproduction of three totally different scenarios: linear oscillations, nonlinear oscillations reducible to linear for small displacements, and intrinsically nonlinear oscillations. The chosen approach consists of measuring the displacements using video photogrammetry and computing the velocities and the accelerations by means of a numerical differentiation algorithm. In this way, one can directly check the differential equation of the motion without having to integrate it, or perform an experimental study of the potential energy in each of the analysed scenarios. This experiment allows first year students to reflect on the consequences and the limits of the linearity assumption for small displacements that is so often made in technical studies.
This paper presents an experimental study of the dynamics of a chain sliding off of a table, using video analysis to test a theoretical model. The model consists of two variable-mass subsystems, with friction between the chain and the table and assumes that all links move at the same speed. In order to check the model, the chain position x(t) is obtained using video analysis. The smoothed function x(t) and its derivatives v(t) and a(t) are numerically computed using a local regression algorithm. In this way, the differential equation governing the motion can be directly tested, instead of comparing the position with the solution of the differential equation. Our procedure is very sensitive to deviations between the model and reality, so we can detect the point at which the chain ceases to be in tension and the model is no longer valid. This experiment shows students the limitations of simplified models and offers an opportunity to assess a model's range of validity.
In this work we propose using phase diagrams to explain the dynamical behaviour of simple mechanical systems. First the motion of the system x t ( ) is experimentally measured, and then the derivatives, v t ( ) and a t ( ), are obtained from it and the motion equation = f x v a ( , , ) 0 is represented graphically. This idea is applied to the study of a system with linear viscous drag, explaining the evolution of the system towards the dynamical equilibrium point corresponding to the limit velocity. The phase diagrams of the viscous drag are compared with those of the Coulomb drag, which is not continuous and does not necessarily lead to a uniformly accelerated motion. The method is illustrated by an experiment in a dynamic track with magnetic damping. The use of phase diagrams allows for the checking the linearity of this damping. Moreover it allows for the identification of the existence of a small Coulomb drag between the track and the cart that appears as a small discontinuity of the function a v ( ) when the direction of the movement changes.
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