Falling spring and falling catenary as cases of force propagation

TL;DR

This paper investigates how force disturbances propagate through static equilibrium systems using the examples of falling spring and catenary, highlighting finite velocity effects in force transmission.

Contribution

It introduces a conceptual and experimental analysis of force propagation in static systems, connecting it to wave motion concepts and providing minimal theoretical background.

Findings

Force disturbance propagates with finite velocity.

Falling spring and catenary illustrate force transmission delay.

Potential application to understanding wave phenomena.

Abstract

At every points of a static equilibrium system, the net force is zero. If one of the composite forces of this system is disappeared, it is no more in equilibrium and this effect of absence spreads through the system with a finite velocity. So it takes finite time before this absence is manifest at the other points. A frequently asked question may describe this situation well. ``If the Sun disappears abruptly, does this affect us instantly?" In this question centripetal force due to the gravity of the Sun does not disappear simultaneously all over the place, so the Earth sustains its elliptical motion for a while. As this example shows, it is a well known fact that the force does spread with a finite velocity. But for the specific problems it is sometimes not easy to notice this property of the force. To help this, we consider the motion of a falling spring and a falling catenary. We study the conceptual aspects of these motions and apply it to the experimental data. A minimal theoretical background is also treated. For the future, we anticipate that this work would be useful for enhancing the concept of wave motion.