Related papers: Long Jump
The rise of the top is studied by considering slipping friction. For this case, equations of motion are obtained by using Euler equations for a heavy symmetric top with a hemispherical peg. Different situations are considered to see how the…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
We study vertical jumping in a simple robot comprising an actuated mass-spring arrangement. The actuator frequency and phase are systematically varied to find optimal performance. Optimal jumps occur above and below (but not at) the robot's…
This note illustrates how a simple random walk with possibly long jumps is related to fractional powers of the Laplace operator. The exposition is elementary and self-contained.
The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the…
The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. Here, we consider the dynamics of the chain…
Ball and hoop system is a well-known model for the education of linear control systems. In this paper, we have a look at this system from another perspective and show that it is also suitable for demonstration of more advanced control…
When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact provided a critical flow rate is exceeded. We here examine a phenomenon that arises below this jump threshold, a…
A pressure chamber is designed to study the crumpling process under an ambient force. The compression force and its resulting radius for the ball obey a power law with an exponent that is independent of the thickness and initial size of the…
Many university texts on Mechanics deal with the problem of the effect of the air drag force, using as example the slowing down of a parachute. Hardly no one discuss what happens when the drag force is proportional to both $u$ and $u^2$. In…
Although it is commonly expected that a metal disk placed on the surface of water will sink, our investigation has revealed a surprising phenomenon: a vertical jet directed onto the disk from above can allow it to remain afloat. This result…
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights versus ranks. For the US stock market, it is linear on a…
A small drop that splashes into a deep liquid sometimes reappears as a small rising jet, for example when a water drop splashes into a pool or when coffee drips into a cup. Here we describe that the growing and rising jet continuously…
Track and field world records have risen and fallen throughout the history of the sport. A recent rash of record-breaking performances has prompted the question: "How good can we get?". This article offers a review of several attempts to…
Paper strips, e.g. confetti, descending to the floor begin to rotate around the horizontal axis after a short time. This slows down the vertical velocity compared to free fall and adds a horizontal velocity component. The frequency of…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
The slinky, released from rest hanging under its own weight, falls in a peculiar manner. The bottom stays at rest until a wave hits it from above. Two cases -- one unphysical one where the slinky is able to pass through itself, and the…
Streaks of success have always fascinated people and a lot of research has been conducted to identify whether the "hot hand" effect is real. While sports have provided an appropriate platform for studying this phenomenon, the majority of…
Special relativity includes a concealed mechanism for reducing time-dilation effects in two mutually-receding objects. Forwarding their signals via one or more intermediate physical relay stages (a "probe chain") allows enhanced…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…