
Spring
A spring has a natural length of 2 ft, and a force of a 15 lb is required to hold it compressed at a length of 18 in. How much work is done in stretching this spring from its natural length to a length of 3 ft?
Working:
$\displaystyle 18 in=\frac{18}{12} ft=1.5 ft$
x=compression=21.5=0.5 ft
F=kx
15=k*0.5
k=30 lb/ft
$\displaystyle W=\frac{1}{2}kx_2^2\frac{1}{2}kx_1^2$
= $\displaystyle \frac{1}{2}k(x_2^2x_1^2)$
= $\displaystyle \frac{30}{2}(1^20^2)$
= 15*1
= 15 lbft
Edit: Never mind; I solved it myself.