Rational Expressions & Functions: Hooke's Law, 12 lbs force,

[jlaw]

Hi!

Could an Algebra Wizard please check my work :?:

Problem: 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?

It makes sense to me to divide 12 by 3 = 4 lbs per inch
Then divide 30 by 4 = 7.5 inches
but I believe that the problem needs to be represented into
a rational expression or a complex fraction (those might be the same thing, don't know?)
Would this be right ? Is there another way to formulate this into a rational expression?
30
12/3

Thanks so much for all your help and valuable time!
Sincerely,
Julia

 

[royhaas]

Re: Rational Expressions & Functions

Your calculation is correct.

 

[masters]

Re: Rational Expressions & Functions

Hi!

Could an Algebra Wizard please check my work :?:

Problem: Hooke’s Law states that the distance, d, a string is stretched varies directly with the force, F, applied to the spring.

If d varies directly as F, this means \(\displaystyle d=kF\), where k is called the constant of proportionality.

If a force of 12 pounds stretches a spring 3 inches,

\(\displaystyle 3=k(12)\Longrightarrow \boxed{k=\frac{1}{4}}\). The constant of proportionality is \(\displaystyle \frac{1}{4}\)

how far will the spring stretch when a force of 30 pounds is applied?

\(\displaystyle d=\frac{1}{4}(30)\)

\(\displaystyle d=7.5 \ \ inches\)

 

[jlaw]

THANK YOU VERY MUCH Royhaas and Masters (what an appropriately "cool" name)!!