Answer
(a) The wings must exert a force of $5.1~N$
(b) The energy stored in the resilin is $0.077~J$
Work Step by Step
(a) $Y = \frac{F/A}{\Delta L/L}$
$Y$ is Young's modulus
$F$ is the force
$A$ is the cross-sectional area
$\Delta L$ is the change in length
$L$ is the original length
We can find the required force:
$F = \frac{Y~A~\Delta L}{L}$
$F = \frac{(1.7\times 10^6~N/m^2)(1.0\times 10^{-6}~m^2)(3.0\times 10^{-2}~m)}{1.0\times 10^{-2}~m}$
$F = 5.1~N$
The wings must exert a force of $5.1~N$
(b) We can find the energy in the system:
$U = \frac{1}{2}~F~\Delta L$
$U = \frac{1}{2}~(5.1~N)(3.0\times 10^{-2}~m)$
$U = 0.077~J$
The energy stored in the resilin is $0.077~J$
