B3NR4Y
Gold Member
- 170
- 1
Homework Statement
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.
Homework Equations
\begin{equation}
W= \int_a^b \, f(x)dx
\end{equation}
\begin{equation}
f(x)=kx
\end{equation}
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}