If the stiffness of the cord is no less than 28 pounds per foot, the cord stretch will be approximately 7 feet long
Given the equation that related the stiffness of the cord is expressed as:
[tex]K=\frac{(2W(S+L))}{S^2}[/tex] where:
W is the weight
K = cord stiffness (pounds per foot)
L = free length of cord (feet)
S = stretch (feet)
Given the following parameters
W = 190 pounds
L = 52 feet
k = 28 pounds per foot
Required
Stretch S
Substitute the given expressions into the equation above to have:
[tex]28=\frac{(2(190)(S+52))}{S^2}\\28S^2=380(S+52)\\28S^2 = 380S+19,760\\28S^2 - 380S-19,760=0\\[/tex]
On factorizing the result
The stretch is approximately 7 feet long
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