SOLUTION: Hooke's Law states that the distance, d, a string is stretched varies directly with the force, F, applied to the spring. If a force of 12 pounds stretches a spring 3 inches, how fa

Algebra ->  Algebra  -> Human-and-algebraic-language -> SOLUTION: Hooke's Law states that the distance, d, a string is stretched varies directly with the force, F, applied to the spring. If a force of 12 pounds stretches a spring 3 inches, how fa      Log On

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Question 158168: Hooke's Law states that the distance, d, a string is stretched varies directly with the force, F, applied to the spring. If a force of 12 pounds stretches a spring 3 inches, how far will the spring stretch when a force of 30 pounds is applied?
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
Since the "distance, d, a string is stretched varies directly with the force, F", this means that we have the equation d=kF


d=kF Start with the given equation


3=k%2812%29 Plug in d=3 and F=12


3%2F12=k Divide both sides by 12 to isolate k


1%2F4=k Reduce


So the variation constant is k=1%2F4 (or in decimal form k=0.25)


d=kF Go back to the original equation


d=%281%2F4%29F Plug in k=1%2F4


d=%281%2F4%29%2830%29 Since we want the distance when the "force of 30 pounds is applied", we need to plug in F=30


d=30%2F4 Multiply


d=15%2F2 Reduce


d=7.5 Convert to decimal form


So the distance is 7.5 inches when a force of 30 pounds is applied.