Experiments performed on the wing of a hawkmoth (Manduca sexta) show that it def

Question

Experiments performed on the wing of a hawkmoth (Manduca sexta) show that it deflects by a distance of x = 4.8{ m mm} when a force of magnitude F = 3.4{ m mN} is applied at the tip, as indicated in the figure(Figure 1) .

B)Treating the wing as an ideal spring, find the energy stored in the wing when it is deflected. Express your answer using two significant figures. U=_____J

C)What force must be applied to the tip of the wing to store twice the energy found in part (b)? Express your answer using two significant figures.

Explanation / Answer

A) k = F / x = 3.5*10^-3N / 4.8*10^-3m = 0.729 N/m B) E = 0.5*k*x^2 = 0.5*0.729*(4.8*10^-3)^2 = 8.4*10^-6 J C) E proportional to x^2, so to double E need deflection of x*sqrt(2) = 6.79mm Required force = kx = 0.729*6.79*10^-3 = 4.95 mN

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