The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation…

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

The purpose of this publication is to bring attention to some physics problems whose answers seem to be paradoxical and, at first glance, do not agree with a limiting case check. Solving a problem on the motion of a system consisting of two masses and a spring, it is natural to examine the answer by considering a case when a spring constant is…

In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed. This is due to the impossibility of expressing, in terms of simple elementary functions, the solutions of the nonlinear differential equation (NLDE) that models the pendulum, which is why the authors usually choose the linearized…

Pole vaulting, the aim of which is to jump over a crossbar with the help of a long flexible pole, is considered to be one of the most complicated and technically demanding motions in track and field athletics. Pole vault performance is basically influenced by the energy exchange between the vaulter and pole. It depends on the sprinting, jumping…

Many introductory physics courses begin with the teaching of motion and kinematics. This naturally leads to the use of constant acceleration equations to solve various problems involving common motions (free fall being a notable example). Students can sometimes get the impression that these equations are the only thing they need to remember in…

Force probes are versatile tools in the physics lab, but their internal workings can introduce artifacts when measuring rapidly changing forces. The Dual-Range Force Sensor by Vernier uses strain gage technology to measure force, based on the bending of a beam. Strain gages along the length of the beam change resistance as the beam bends. The…

Students are well aware of the effect of the deflection of sports balls when they have been given a spin. A volleyball, tennis, or table tennis ball served with topspin results in an additional downward force that makes the ball difficult to catch and return. In soccer, the effect of sidespin causes the ball to curve unexpectedly sideways,…

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical…

We describe a simple experiment about sliding friction of an object moving with non-constant speed along an inclined plane. This experiment can be used to study the entire dynamical process of force and motion in various ways, depending on the mathematical level of the students. We discuss how video measurement and analysis, and mathematical…

In this paper, the feasibility of a Genetic Algorithm Optimization (GAO) education software based Fuzzy Logic Controller (GAO-FLC) for simulating the flight motion control of Unmanned Aerial Vehicles (UAVs) is designed. The generated flight trajectories integrate the optimized Scaling Factors (SF) fuzzy controller gains by using GAO algorithm. The…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

The familiar system involving a uniform ladder sliding against a vertical wall and a horizontal floor is considered again. The floor is taken to be smooth and the wall to be possibly rough--a situation where no matter how large the static friction coefficient between the ladder and the wall, the ladder cannot lean at rest and must slide down.…

The use of collaborative problem solving within mathematics education is imperative in this day and age of integrative science. The formation of interdisciplinary teams of mathematicians and scientists to investigate crucial problems is on the rise, as greater insight can be gained from an interdisciplinary perspective. Mathematical modelling, in…