Question

While hovering, a typical flying insect applies an average force equal to twice its weight during each downward stroke. Take the mass of the insect to be 10 g, and assume the wings move an average downward distance of 1.0 cm during each stroke. Assuming 100 downward strokes per second, estimate the average power output of the insect.

Short answer

The average output power of insect is 0.196 W.

Step-by-step solution

Identification of given data

The given data can be listed below,

• The mass of the insect is, m=10 g

• The distance of wings moved is, d = 1cm

Concept/Significance of average velocity.

Power is the amount of energy transformation from one kind to another in unit time or the rate at which work is done in moving from point A to point B in space.

Determination of the average power output of the insect

The work done by the insect is given by,

$\mathrm{W}=\mathrm{Fd}\mathrm{cos\theta }$

Here, F is the force acting on the insect, d is the distance moved by wing, $\theta$is the angle between force and displacement whose value is zero because they are in same direction.

Substitute all the values in the above,

role="math" localid="1664861021749" $\begin{array}{l}w=2mgd\cos 0^0\\ =2(0.01\mathrm{kg})(9.8\mathrm{m}/{\mathrm{s}}^2)\left(0001\mathrm{m}\right)\\ =196\times {10}^{-3}\mathrm{J}\end{array}$

The wind strokes per second is 100, so the time taken for one stroke is given by,

$\begin{array}{l}t=\frac{1}{100}s\\ =001s\end{array}$

The average power output of the insect is given by,

$P=\frac{W}{t}$

Here,Wis the work done by the insect andtis the time taken by the wind strokes.

Substitute all the values in the above,

role="math" localid="1664861156154" $$\begin{gathered} \mathrm{P}=\frac{1.96\times {10}^{-3}\mathrm{J}}{0001\mathrm{s}} \\ =0.196\mathrm{w} \end{gathered}$$

Thus, the power output of insect is 0.196 W.