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Hooke's Law and Work; easy problem, I shouldn't have trouble, but I get it wrong

  1. Oct 8, 2012 #1

    B3NR4Y

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    A string of natural length 10 in. stretches 1.5 in. under a weight of 8-lb. Find the work done in stretching the spring from its natural length to a length of 14 in.


    2. Relevant equations
    \begin{equation}
    W= \int_a^b \, f(x)dx
    \end{equation}
    \begin{equation}
    f(x)=kx
    \end{equation}

    3. The attempt at a solution
    \begin{equation}
    8=k(\frac{3}{2})
    \end{equation}
    \begin{equation}
    k=\frac{16}{3}
    \end{equation}
    \begin{equation}
    W=\frac{16}{3} \int_0^4 \, xdx
    \end{equation}
    \begin{equation}
    W= \frac{16}{3} \, (\frac{1}{2} x^{2} |^{4}_{0})
    \end{equation}
    \begin{equation}
    \frac{2048}{9}
    \end{equation}
    Book says the answer is:
    \begin{equation}
    \frac{128}{3} ft-lbs.
    \end{equation}
     
  2. jcsd
  3. Oct 8, 2012 #2

    B3NR4Y

    User Avatar
    Gold Member

    *facepalm* Gotta love arithmetic mistakes.
     
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