3.4.3—Problems involving forces due to elastic

For an elastic string, the tension is zero when slack and proportional to extension only while taut and within the elastic range. In a force problem, combine this law with resolved force or moment equations.

Find the current length from the geometry before calculating extension. Check whether the calculated tension is positive; a negative tension means the string cannot supply that force and is slack.

Two equal elastic strings supporting a mass may have equal tensions only by symmetry; each tension’s vertical component, not the full tension, balances the weight.

An elastic string can pull but not push. Do not continue Hooke’s law into compression or beyond the stated elastic limit.