Chapter 10, Problem 61P

To determine

To Explain: Whether the six-legged insect is remaining on the top of the water.

Answer to Problem 61P

The insect remains on the top, due to having the maximum mass.

Explanation of Solution

Given:

Radius, $r=3.0\times {10}^{-5}\text{m}$

Mass of the insect, $m=0.016\text{g}$

Formula used:

The surface tension formula for the insect is,

  $2\pi r\gamma \cos \theta \approx \frac{1}{6}mg$

Where, $m$ is the mass,

  $r$ is the radius,

  $g$ is the acceleration due to gravity,

and $\gamma$ is the surface tension.

Calculation:

The amount of force acting on a single leg,

  $T=2\pi r$

So, the total force acting on the six legs,

  $F_t=6\left(T.2\pi r\right)$

  $\begin{array}{l}\therefore F_t=6\left(2\times 3.14\times 3\times {10}^{-5}\right)\\ =113.04\times {10}^{-5}\text{N}\end{array}$

In order to remain on the top, the mass of the insect is to be maximum,

The maximum mass,

  $\begin{array}{c}m=\frac{F_t}{g}\\ =\frac{8.14\times {10}^{-5}\text{N}}{9.8}\\ =0.83\times {10}^{-5}\text{kg}\\ =8.3\times {10}^{-6}\text{kg}\end{array}$

Conclusion:

So, the insect remains on the top, due to having the maximum mass.