Five foot-pounds of work are needed to stretch a certain spring from 1 ft to 3 ft beyond its natural length.?

Question

How far beyond its natural length will a 6-pound weight stretch the spring?

Answer 1

It all depends on whether one is near the point beyond which Hooks law nolonger applies.
Assume the spring is not about to break.
Assume in the original problem the spring was initially stretched 1 foot beyond its length and the average force required to stretch the spring the additional 2 feet is 2.5 pounds. That means that at 2 feet the spring is exerting twice the force that was being applied at one foot. At 3 feet it was applying 3 times the force that was being applied at 1 foot.
The average force happens when the spring has been streched half the distance. there fore at one foot the force is
half 2.5=1.25pounds
Each foot the spring is stretched the force is 1.25 pounds more.
1.25 pounds per foot goes into 6 pounds 4.2 feet.