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 = 4.7mm when a force of magnitude F = 2.9mN 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 your 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 your 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 your answer using two significant figures.

Explanation / Answer

A. Since it is an ideal spring, F = - kx

2.9 * 10-3 N = - k * - 4.7 * 10-3 m

Hence, spring constant = k = 0.61 N/m

B. Energy stored = 0.5 * k * x2 = 0.5 * 0.61 * 4.7 * 4.7 * 10-6 = 6.815 * 10-6 J

C. Twice the energy = 2 * 6.815 * 10-6 J = 13.63 * 10-6 J

Let the deflection for this energy be 'd'.

So, 13.63 * 10-6 J = 0.5* k * d2

So, d2 = 44.688 * 10-6

Hence, d = 6.68 * 10-3 m

Therefore, force applied = - k * d = 4.077 mN

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