Why is this so?

Question

Suspend a heavy weight from a light string and attach a similar string below it. If you pull on the lower string with an steadily increasing force, the upper string will break; if you pull the lower string with a jerk, the lower string will break.

Answer 1

String will break when the tension on it exceeds its break point. The tension on the upper string T = W + F; where W = mg the weight of the weight and F is the force you add by pulling on the lower string. The tension on the lower string is just T = F because the weight is above it.

But when you jerk the bottom string, we have Ft = delp; where t, during a jerk, is very short; so the weight's momentum changes very little (delp is small) and the force added to the weight is therefore small. This means all the jerk force is resident in the lower string and the tension in the upper one remains at about W. A bit higher because there is some momentum change in that short t, but not much.

Answer 2

This requires the string be somewhat elastic. The first case is simple, the force on the top string is the force on the bottom string plus the weight, so you would expect it to break first.

In the second case, the inertia of the heavy mass [weight being a force due to gravity so technically it isn't a heavy weight - pedantic isn't it] prevents the jerk force from immediately being applied to the upper string. The mass is accelerated by the jerk, but if the jerk is quick, there isn't enough time for the mass to gain any speed, the lower string breaks and the acceleration of the mass is resisted by extra tension in the upper string causing it to rebound.

Answer 3

momemtum, or lack of, in the second case