A mass is supported to the ceiling by a light string Hanging

A mass is supported to the ceiling by a light string. Hanging from its bottom is an equivalent light string. If one pulls on the lower string, slowly building the force, the top string breaks and the mass falls to the floor. If instead the lower string is pulled very quickly with a large (impulsive) force, it breaks and the mass remains hanging by the top string. What principle of physics does this illustrate

Solution

As we slowly pull the string downwards, a tension develops in the lower and upper string and eventually it breaks. However, if we pull the string suddenly the lower one breaks while the upper one would suffer small elongation due to the pull it will suffer for a fraction of a second.

Since the force is impulsive, it is applied over a very short period of time (say .01 seconds , for example), and since the mass will accelerate due to the extension of the string (per extension = 1/2at^2), the t is so small that it doesn\'t have much time to extend, thus it\'s extension, and the force in the string, will be very small (just whatever extension the weight of the mass puts on it, not much more extension from the the additional force), and the lower string will break before the extension of the upper string is significant enough to break the upper string (force is proportional to extension, per Hooke\'s law)