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Sagot :
The total length of the spring is approximately 4.92 ft.
To remedy this question we need to apply Hooke's law. In physics, Hooke's regulation is an empirical law which states that the force (F) had to enlarge or compress a spring by using a ways (x) scales linearly with admire to that distance.
Mathematically F = kx, where ok is the spring constant and x is spring stretch/compression.
Length of the spring=3ft
Extended length=6ft
Length extended(x)=(6-3)ft=3ft
Force applied(F)=13 lb
Work done to extend the spring(w)=8ft-lb
Now by using Hooke's Law:
F=kx
or,[tex]13=k\times 3[/tex]
or,[tex]k=\frac{13}{3}[/tex]
Work done by the spring can be defined as
[tex]w=\frac{1}{2} k x^2[/tex]
Substituting the values we get:
[tex]or,8=\frac{1}{2}\times \frac{13}{3} \times x^2\\or,x^2=\frac{48}{13}\\or,x=1.921...[/tex]
Therefore total length of the spring=3+1.92 ft=4.92 ft.
To learn more about equilibrium length of spring:
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