Answer :
In order to lengthen the spring from its natural length to 0.9 feet beyond it, 4.608 feet-pounds of labor must be done.
Given data;
A force of 6 pounds is required to hold a spring stretched 0.5 feet beyond its natural length.
The force required = force in spring
6 = 0.5 * k
Where k is spring constant.
∴ k = 6/0.5 = 12 pound/feet
Energy stored in the spring = (k * 2) / 2, if the spring is stretched by a distance 'x'
Conserving energy, we get energy stored in the spring = work done in stretching the spring
∴Work done = 0.6 * (12) * (0.9)²
= 4.608 feet-pound
Hence, 4.608 feet-pound work is done in stretching the spring from its natural length to 0.9 feet beyond its natural length.
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