The exact expressions for the drain time and the height, velocity and acceleration of the free surface are found for the draining reservoir problem of the incompressible and non-viscous liquid. Contrary to the conventional approximate results, they correctly describe the initial time dependence of the liquid velocity and acceleration. Torricelli's…

This paper was first motivated by the following question: "A pair of twins, R and S, each gives the "same" hard push on a block. R's block is on a rougher floor than S's. Who does more work?" It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the…

Considering our atmosphere as a steady viscous gaseous envelope that co-rotates with the Earth, we obtain a solution for the form in which this induced rotational effect decreases as a function of the distances to the centre of the Earth and to the rotation axis. (Contains 1 figure.)

Problems in projectile motion are a time-honored staple of high school and even first-year university physics. They can become confusing for some students, yet boring for the stronger students. Herein we present two alternative approaches to such questions, one we call "breaking down gravity," which makes these questions easier to solve, and the…

When thinking of models for sinusoidal waves, examples such as tides of the ocean, daily temperatures for one year in your town, light and sound waves, and certain types of motion are used. Many textbooks [1, p. 222] also present a "Ferris wheel description problem" for students to work. This activity takes the Ferris wheel problem out of the…

During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

In preparing to teach the advanced physics course at my high school, I found it useful to work through the end of chapter problems in the book used by the advanced class. A problem on motion in one dimension involved a stunt woman in free fall from a tree limb onto a horse running beneath her. The problem presents a connected learning opportunity…

The focus of the current study is to understand which unique features of an immersive virtual reality environment have the potential to improve learning relative motion concepts. Thirty-seven undergraduate students learned relative motion concepts using computer simulation either in immersive virtual environment (IVE) or non-immersive desktop…

In this paper, canonical transformations generated by constants of motion in the case of the Kepler problem are discussed. It is shown that canonical transformations generated by angular momentum are rotations of the trajectory. Particular attention is paid to canonical transformations generated by the Runge-Lenz vector. It is shown that these…

This paper outlines the solution that the Team of Austria found to problem number 7, "skateboarder", presented in the finals of the 22nd International Young Physicists' Tournament (IYPT) in Tianjin, China. We investigated how a skateboarder can accelerate from rest on a horizontal surface without touching an external support. The focus was laid on…

We conducted a series of experiments to investigate the extent to which prompting the construction of a force diagram affects student solutions to simple mechanics problems. A total of 891 university introductory physics students were given typical force and motion problems under one of the two conditions: when a force diagram was or was not…

Physics is the study of forces and motion--the science of matter and energy and the interaction between the two. The big idea the children explore, as well as the question they ask as they engage in physical knowledge activities related to physics, is "How does it move?" Many teachers translate naturally as they come to know the children they…

In this article, I will extend the falling ball method to measure the viscosity of liquids regardless of the degree of their viscosity. For this, I will show that one can obtain a measurement of the terminal velocity of a falling spherical ball in a viscous liquid by solving numerically the equation of motion which describes the dynamics of the…