Related papers: Solving the paradox of the folded falling chain by…
The one-dimensional fall of a folded chain with one end suspended from a rigid support and a chain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicit time dependence, the falling chains are…
In the present paper we revisit, theoretical and experimentally, the fall of a folded U-chain and of a pile-chain. The model calculation implies the division of the whole system into two subsystems of variable mass, allowing to explore the…
When a falling ball chain strikes a surface, a tension is created that pulls the chain downward. This causes a downward acceleration that is larger than free-fall, which has been observed by recent experiments. Here a theoretical…
A vertically hanging chain is released from rest and falls due to gravity on a scale pan. We discuss the various experimental and theoretical aspects of this classic problem. Careful time-resolved force measurements allow us to determine…
The freely jointed chain is often applied to model the thermodynamics of single polymer chains, but the traditional formulation of the model lacks internal energy changes due to bond stretching. For this reason, the extensible freely…
When a falling chain strikes a surface, it can accelerate downwards faster than free-fall. This counterintuitive effect occurs when a tension is created in the chain above where it strikes the surface. The size of this tension, and how it…
Simple demonstrations based on the equivalence principle are given of how a folded chain and a horizontal flat chain fall down when one chain end is fixed to a rigid support.
Although the stretching of polymers and biomolecules is important in numerous settings, their response when confined to two-dimensions is relatively poorly-studied. In this paper, we derive closed-form analytical expressions for the…
It is common to study polymer physics through the use of idealized single-chain models, and the most popular of these is the freely jointed chain model. In certain thermodynamic ensembles, statistical mechanical treatment of this model is…
The dynamics of the tip of the falling chain is analyzed. Results of laboratory experiments are presented and compared with results of numerical simulations. Time dependences of the velocity and the acceleration of the chain tip for a…
A freely falling chain from a cup at certain height can jump. The process can be divided into two parts: a stable suspension and an accelerating procedure. Variational principle and force analysis demonstrate that the shape of stable…
We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each crosslink increases until it…
The chain fountain is an entertaining, counter-intuitive phenomenon. When a chain flows up over the edge of a container and then falls to the ground below, it is observed that the top of the chain rises up above the containers edge. Here…
Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized…
A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
It has been known for more than 300 years that the shape of an inelastic hanging cable, chain, or rope of uniform linear mass density is the graph of the hyperbolic cosine, up to scaling and shifting coordinates. But given two points at…
In this work, we examine the whip dynamics in a freely falling chain. We consider an inextensible chain with free ends in the presence of gravity hanging from a fixed pulley. If the configuration is unbalanced, the chain begins to…
The mechanical resistance of a polyethylene strand subject to tension and the way its properties are affected by the presence of a knot is studied using first-principles molecular dynamics calculations. The distribution of strain energy for…
For a 2-dimensional freely jointed chain with 3 particles and a related model, the average and variance of the kinetic energies of each particle in thermal equilibrium are exactly obtained. The same is done for a related model. The excess…