Answer:
The work done in stretching the spring is 8 lb.ft
Step-by-step explanation:
Given;
Applied force, F = 192 lb
extension of the spring, x = 3 ft
Determine the spring constant from the applied force and extension;
[tex]k = \frac{F}{x} \\\\k = \frac{192 \ lb}{3 \ ft} \\\\k = 64 \ lb/ft[/tex]
When the spring is stretched 6 inches beyond its natural length, the work done is calculated as follows;
x = 6 inches = 0.5 ft
[tex]W = \frac{1}{2} kx^2\\\\W = \frac{1}{2} (64 \ lb/ft)(0.5 \ ft)^2\\\\W = 8 \ lb.ft[/tex]
Therefore, the work done in stretching the spring is 8 lb.ft
