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In this work, we developed the equations regarding the movement of a smooth sphere in the presence of drag forces, in the high-speed regime, where the resistive force is proportional to the square of its velocity. This regime is commonly found in various everyday situations in which objects of all kinds are thrown into the air. The equations studied in basic undergraduate courses disregard the drag of the air and, therefore, are idealized equations, not consistent with the actual nature of the observed movement. Here, we intend to assist the reader in traveling a bit closer to reality and contemplating the complexity of some equations when we try to model the world as it truly is. This subject is of extreme importance for undergraduate students in the field of aeronautical engineering and mechanics, as it is essential to understand how drag forces affect the behavior of objects in motion. [ABSTRACT FROM AUTHOR]

The incorporation of discussions about the nature of scientific knowledge in science teaching activities is a fundamental and quite challenging aspect. This paper aims to present an empirical contrast of theoretical models exploring the particular case of the movement of bodies with variable mass as a way to highlight the role of the scientific modeling process in an experimental situation. We investigate the implications of assuming certain idealizations in the contrasted models, explaining the representative character of scientific knowledge in the development of experimental investigations, incorporating the influence of different resistive forces on these bodies, such as air drag forces and rolling resistance. Thus, we seek to expose an example of a situation with the potential to be explored by teachers in overcoming naive epistemological conceptions by students. Also, the investigation involves the use of open-source computational resources in the construction of numerical solutions of theoretical models and the collection of experimental data, favoring the use of free technologies in physics teaching. Four of the six empirically contrasted theoretical models also had their analytical solutions deduced and compared with their respective numerical solutions. The results show that the choice of the best theoretical model that represents the collected data involves more than the analysis of the quality of the adjustment of the models because it demands an evaluation of the hypotheses assumed in the theoretical models and the decisions made by the researcher. [ABSTRACT FROM AUTHOR]

In this work we present a low-cost activity that aims to investigate the drag force, which acts on the geometry of a disc, through the damped oscillations of a mass-spring system. Using cardboard disks of different radii and controlling the mass of the oscillatory system, keeping it fixed, we studied the influence of the exclusive variation of the magnitude of the drag force on the dynamics of this system, by varying the radius of the disk, keeping all the others fixed system accessible parameters. The video analysis technique is used to track the movement of the system, leading the student to investigate and draw conclusions about the functional dependence of the viscous frictional force with the radius of the disk, as well as to obtain the spring elastic constant and an estimate for the thickness of the disks. [ABSTRACT FROM AUTHOR]

This work describes the differential equations of motion and the respective solutions for speed v(t) and altitude y(t) as a function of time, relative to a rocket that follows a vertical trajectory in an upward motion were described. Four models are considered: in the first, the drag force of the air is neglected; in the second it is considered a linear drag force with speed; in the third and fourth models it is considered that the drag force is proportional to the square of the speed. The third model is distinguished by considering the total mass of a rocket constant. In the fourth model, a complete solution is presented, considering that the mass decreases linearly with time. To test these models, the experimental flight of the Epsilon-8 model rocket from the UFPR Carl Sagan Rocket Group was used. Experimental parameters related to the thrust curve as a function of the Epsilon-8 time (static test) were used, in which from the model rocket mass variation rate it was possible to obtain the rate of exhaust of the gases expelled in the engine. The third and fourth models, since they are more realistic, were used to adjust the experimental curve for v(t) and y(t). The third model, although it has an approximate solution, proves to be reasonable in the prediction of the peak, with an error of 8.6%. The fourth model, being the most complete, predicts the peak with an error of only 1.5% precisely in the time of the experimental peak. [ABSTRACT FROM AUTHOR]

The incorporation of discussions about the nature of scientific knowledge in science teaching activities is a fundamental and quite challenging aspect. This paper aims to present an empirical contrast of theoretical models exploring the particular case of the movement of bodies with variable mass as a way to highlight the role of the scientific modeling process in an experimental situation. We investigate the implications of assuming certain idealizations in the contrasted models, explaining the representative character of scientific knowledge in the development of experimental investigations, incorporating the influence of different resistive forces on these bodies, such as air drag forces and rolling resistance. Thus, we seek to expose an example of a situation with the potential to be explored by teachers in overcoming naive epistemological conceptions by students. Also, the investigation involves the use of open-source computational resources in the construction of numerical solutions of theoretical models and the collection of experimental data, favoring the use of free technologies in physics teaching. Four of the six empirically contrasted theoretical models also had their analytical solutions deduced and compared with their respective numerical solutions. The results show that the choice of the best theoretical model that represents the collected data involves more than the analysis of the quality of the adjustment of the models because it demands an evaluation of the hypotheses assumed in the theoretical models and the decisions made by the researcher. [ABSTRACT FROM AUTHOR]

In the present work a biphasic flow study of the RH degasser was carried out in physical models. The mathematical modeling was made using the Eulerian approach. The influence of different non-drag forces was studied, such as: turbulent dispersion force, wall lubrication force and lift force. In the study, the mathematical modeling was used to determine the circulation rate in the physical model of the RH degasser of USIMINAS in the 1:5 scale. For the validation of the mathematical model, tests were made in the physical model using techniques to obtain homogenization time of salt solutions. The flow monitoring was done by using ordinary camera and high-speed camera. It was determined that the non-drag forces have influence on the two-phase flow (air/water) and the combined forces of turbulent dispersion, wall lubrication force and lift force lead to best results, when compared with the experimental results. Non-drag forces were determined to influence the air / water two-phase flow, the combination of turbulent dispersion, wall lubrication and lifting forces having the best results compared to the experimental results. [ABSTRACT FROM AUTHOR]

The article "Critical commentary on the article Analysis of projectile motion in the presence of dissipative forces for high-speed regime" discusses mistakes found in a study about the motion of projectiles with dissipative forces. The authors of the study found analytical solutions that are not valid for high-speed regime. The commentator points out errors in the differential equations presented by the authors and concludes that all the results of the study are not valid for the motion of projectiles with drag forces proportional to the square of the velocity. The commentator also indicates other articles that address this problem. [Extracted from the article]

Flow of viscous fluids are not usually discussed in detail in general and basic courses of physics. This is due in part to the fact that the Navier-Stokes equation has analytical solution only for a few restricted cases, while more sophisticated problems can only be solved by numerical methods. In this text, we present a computer simulation of wind tunnel, i.e., we present a set of programs to solve the Navier-Stokes equation for an arbitrary object inserted in a wind tunnel. The tunnel enables us to visualize the formation of vortices behind object, the so-called von Kármán vortices, and calculate the drag force on the object. We believe that this numerical wind tunnel can support the teacher and allow a more elaborate discussion of viscous flow. The potential of the tunnel is exemplified by the study of the drag on a simplified model of wing whose angle of attack can be controlled. A link to download the programs that make up the tunnel appears at the end. [ABSTRACT FROM AUTHOR]