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

Question

Experiments performed on the wing of a hawkmoth (Manduca sexta) show that it deflects by a distance of x= 4.8 mm when a force of magnitude F = 3.2 mN is applied at the tip, as indicated in the figure(Figure 1) .

a) Treating the wing as an ideal spring, find the force constant of the wing. (Express answer using two significant figures)

b) Treating the wing as an ideal spring, find the energy stored in the wing when it is deflected. (Express answer using two significant figures)

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

Explanation / Answer

A) k = F / x = 3.5*10-3 / 4.8*10^-3 = 0.729 N/m = 0.73 N/m

B) E = 1/2*k*x2 = 0.5*0.729*(4.8*10-3)2 = 8.39*10-6 J

C) E proportional to x2, so E needs deflection of x*sqrt(2) = 6.79 mm
Required force = kx = 0.729*6.79*10-3 = 4.95 mN

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