Abstract
The experiment investigating in this chapter consists in abandoning a metal ball on the top of a curved launching platform mounted on a metal rod. Upon reaching the base of the platform, the ball is launched horizontally marking the reaching range on a sheet using the carbon paper. This experience serves to illustrate the conservation of mechanical energy, assuming the hypothesis that the ball rolls without slipping, and also the importance of taking into account its rotational kinetic energy. However, in the way that the experiment is traditionally presented there is no description of the motion in real time, so it is not possible to realize that the ball rolls and slides in most of the way, only reaching the condition of pure rolling at the end of the platform. This misconception is the reason of the systematic difference between the predicted energy balance and that one obtained by experimental measurements. In this chapter the proposed theoretical model takes into account the curvature and the width of the track. The video analysis allows to extract experimental data of the full movement that clearly illustrate a transition from rolling with slipping to pure rolling for different initial tilted angles.
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Notes
- 1.
The didactical equipment used here is manufactured by the company CIDEPE (Centro Industrial de Equipamentos de Ensino e Pesquisa—www.cidepe.com.br). The experimental development as well as the data analysis presented here is useful for any similar commercial or homemade equipment.
- 2.
If we ignore the uncertainty of the local acceleration of gravity, which is irrelevant to the final result, because it is much smaller than the remaining uncertainties involved here, an estimate of the uncertainty can be obtained from [7]
\( {\delta v}_0=\sqrt{{\left(\frac{\partial {v}_0}{\partial D}\delta D\right)}^2+{\left(\frac{\partial {v}_0}{\partial H}\delta H\right)}^2} \)
Calculating the partial derivatives, we find
\( {\delta v}_0=\sqrt{{\left(\sqrt{\frac{g}{2 H}}\delta D\right)}^2+{\left(\frac{D}{2 H}\sqrt{\frac{g}{2 H}}\delta H\right)}^2}=\sqrt{{\left(\frac{v_0}{D}\delta D\right)}^2+{\left(\frac{v_0}{2 H}\delta H\right)}^2}=0.009\kern0.5em \mathrm{m}/\mathrm{s} \).
- 3.
de Jesus and Barros [3] discuss uncertainty estimates of the position in video analysis.
References
J.R. Pimentel, M.A. da Silva, Influência do raio efetivo no movimento de projéteis esféricos lançados horizontalmente. Cad. Bras. Ens. Fís. 22(2)), 209–219 (2005)
I. Arriassecq, M. Lester, S. Stipcich, Cuerpo rígido: experiencia de laboratorio con material de bajo costo. Cad. Cat. Ens. Fís. 8(2)), 168–170 (1991)
V.L.B. de Jesus, M.A.J. Barros, As múltiplas faces da dança dos pêndulos. Rev. Bras. Ens. Fis. 36(4), 4309 (2014)
A. Goya, C.A. Laburú, P.S. Camargo Filho, Estudo comparativo de rolamento e a determinaÓÐo do inÚcio de deslizamento de uma esfera num plano inclinado. Rev. Bras. Ens. Fis. 36, 2502 (2014)
V.L.B. de Jesus, D.G.G. Sasaki, Vídeo-análise de um experimento de baixo custo sobre atrito cinético e atrito de rolamento. Rev. Bras. Ens. Fis 36(3), 3503 (2014)
A.V. Andrade-Neto, J.A. Cruz, M.S.R. Miltão, E.S. Ferreira, Rolamento e atrito de rolamento ou por que um corpo que rola pára. Rev. Bras. Ens. Fis. 35(3), 3704 (2013)
J.R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd edn. (University Science Books, Sausalito, 1996)
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de Jesus, V.L.B. (2017). Horizontal Launch and Mechanical Energy by Video Analysis. In: Experiments and Video Analysis in Classical Mechanics . Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-52407-8_11
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