Mass redistribution in variable mass systems

Abstract

We have developed an alternative formulation based on F = M a rather than F = dP/dt for studying variable mass systems. It is shown that F = M a can be particularly useful in this context, as illustrated by various examples involving chains and ropes. The method implies the division of the whole system into two parts, which are considered separately, allowing to explore certain aspects as constraint forces.

The motion of a freely falling chain tip

“…If one assumes that the chain leaves the heap without friction, the problem becomes tractable analytically and, as one can demonstrate, it falls with a constant acceleration. The surprise is that the acceleration is not g, as one would expect, but g/3 1 .…”

Defect Properties of CuInS2 Single Crystals Grown by Horizontal Bridgman Method with Controlling S Vapor Pressure

“…The above qualitative reasoning carried out within the simplified model of the chain dynamics can be turned into a quantitative approximate calculation. In the calculation, the falling chain is treated as a variable mass system [16]. We assume the chain has a length L and that its mass M is distributed uniformly along it.…”

The motion of whips and chains

“…A 10). Now since β j 1, we have ln β j β j − 1, so that (incorporating the assumption (A.1)) ln α k .…”

“…In recent years the problem has been debated in the physics literature, in particular the issue of whether energy is conserved and whether the tip of the chain falls at an acceleration equal to gravity or faster [7,6,8,10,16,17,27,35,39,40,37]. See Wong and Yasui [42] or McMillen [23] for a good survey of the literature.…”