This work focuses on investigating the time of sinking of a Saxon bowl proposed by ‘International Young Physicists’ Tournament in 2020. A quasi-static model is built to simulate the motion path of the bowl and predict the sinking time subsequently. The model assumes an open axisymmetric bowl with a hole in its base. The hole is modelled as a pipe for which the flow profile is governed by a modified Bernoulli’s equation which has a Coefficient of Discharge (C_d) added to account for energy losses. The motion of the entire bowl is assumed to be in quasi-static equilibrium for an infinitesimal time interval to calculate the volumetric flow rate through the hole. The model is used to predict the sinking times of various bowls against independent variables - hole radius, bowl dimensions, mass of bowl, mass distribution of bowl, and Coefficient of Discharge - and predict the motion path of bowls of different, axisymmetric geometries. Characterisation of C_d was done by draining a bowl filled with water and measuring the time taken to do so. Experimental verification was completed through measuring sinking times of 3D printed hemispherical bowls of the different variables in water. Motion tracking of bowls with different geometries was done using computational pixel tracking software to verify the model’s predictive power. Data from experiments for sinking time against the variables corroborate with the model to a great degree. The motion path tracked, matched the modelled motion path to a high degree for bowls of different shapes, namely a hemisphere, cylinder, frustum, and a free-form axisymmetric shape. The work is poised for an undergraduate level of readership.
This work focuses on exploring the phenomenon of Wilberforce pendulum, a research problem for the International Young Physicists’ Tournament in 2021. A Wilberforce pendulum is a system which has a mass hanging vertically from the bottom of a long helical string. The mass is allowed to undergo both rotational motion about and translational motion along its vertical axis with the spring. Under appropriate initial conditions, the pendulum can exhibit coupled oscillations, where the mass switches between vertical oscillations (where it bobs up and down) and azimuthal oscillations (periodic rotations about the vertical axis). This paper aims to explore this phenomenon in three stages: firstly, an analysis on the mechanics of helical springs for an intuitive explanation for the onset of coupled oscillations; secondly, a comprehensive Lagrangian formulation which models the ‘beating’ motion path of the pendulum and its lightly damped oscillations; thirdly, an experimental verification of our model and the conditions required for clear coupling between the two modes of oscillations. The findings presented in this paper reveal some interesting features of the Wilberforce pendulum and help us gain some understanding of its physical properties. This phenomenon can also be regarded as an extremely insightful problem for introductory college physics courses focussed on the subject of oscillations and resonance, as its construction is easy and inexpensive, and it is a clear demonstration of coupled oscillatory motion.
Rural building models were tested to research the action of flood on buildings, three different water heights with 0.6, 0.9 and 1.2 meters were applied to this experiment to simulate small-scale, medium-scale and large-scale flood respectively. The model was placed at 3, 6 and 9 meters far from the floodgate. In this paper, the effect of the water height and the distance between model and floodgate on the values and distributions of the flow pressure are studied. Some conclusions can be drawn: the flow pressures, force and bending moments of the flow surface increase with the increasing water height and the relationship are approximately linear; the values and distributions of the flow pressure are independent of the floodgate distance and the force and bending moment of the flow surface increase with the distance from 3 meter to 6 meter but decrease with the distance from 6 meter to 9 meter.
Recently, frequent torrential floods cause tremendous casualties and economic losses to the national people in China. In this paper, six 1:6 scale rural building models made of PMMA are tested to research the flow pressure of flood, which will provide the basic data for the flood-resistant design of rural buildings. The experiment of flood on buildings is carried on the large wave-current tank. The height of water is 0.6, 0.9 and 1.2 meters and the distances between the building and floodgate are 3, 6 and 9 meters respectively. The flow pressure is obtained by the sensor transducer. Based on the experimental results, the distribution of the flow pressure and some effect factors are investigated. Results show that the variation of flow pressure distributions decreases gradually with the vertical distance from bottom to top in the vertical direction. The flow pressure in the horizontal direction is different because of the boundary and holes effect.
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