91Ó°ÊÓ

The mass of a flea is

$\begin{array}{c}{m}_{fl}=210\text{‰Ӽg}\\ =210×\left(1\text{‰Ӽg}×\frac{{10}^{−9}\text{ k²µ}}{1\text{‰Ӽg}}\right)\\ =210×{10}^{−9}\text{ k²µ}\end{array}$

The mass of a froghopper is

$\begin{array}{c}{m}_{fr}=12.3\text{″¾²µ}\\ =12.3×\left(1\text{″¾²µ}×\frac{{10}^{−6}\text{ k²µ}}{1\text{‰Ӽg}}\right)\\ =12.3×{10}^{−6}\text{ k²µ}\end{array}$

The weight of a house cat is

$W_c=45\text{ N}$

The acceleration due to gravity on Earth is

$g=9.8{\text{″¾/²õ}}^{\text{2}}$

The downward gravitational force on a body of mass $m$ is

$F_g=mg$ …(1)

From equation (1), the weight of the flea is

$\begin{array}{c}{W}_{fl}=m_{fl}g\\ =210×{10}^{−9}\text{ k²µ}×9.8{\text{″¾/²õ}}^{\text{2}}\\ =2.06×{10}^{−6}×\left(1{\text{ k²µ.m/s}}^{\text{2}}×\frac{1\text{ N}}{1{\text{ k²µ.m/s}}^{\text{2}}}\right)\\ =2.06×{10}^{−6}\text{ N}\end{array}$

The weight is $2.06×{10}^{−6}\text{ N}$.

From equation (1), the weight of the froghopper is

localid="1662114275316" $\begin{array}{c}{W}_{rl}=m_{fr}g\\ =12.3×{10}^{−6}\text{ k²µ}×9.8{\text{″¾/²õ}}^{\text{2}}\\ =1.2×{10}^{−4}×\left(1{\text{ k²µ.m/s}}^{\text{2}}×\frac{1\text{ N}}{1{\text{ k²µ.m/s}}^{\text{2}}}\right)\\ =1.2×{10}^{−4}\text{ N}\end{array}$

The weight is $1.2×{10}^{−4}\text{ N}$$1.2×{10}^{−4}\text{ N}$.

From equation (1), the mass of the cat is

localid="1662114293691" $\begin{array}{c}{m}_c=\frac{W_c}{g}\\ =\frac{45\text{ N}}{9.8{\text{″¾/²õ}}^2}\\ =4.6â‹\dots \left(\frac{1}{{\text{m/s}}^2}\right)â‹\dots \left(1\text{ N}×\frac{1\text{ k²µ}â‹\dots {\text{m/s}}^2}{1\text{ N}}\right)\\ =4.6\text{ k²µ}\end{array}$

The mass of the cat in pounds is

localid="1662114310998" $\begin{array}{c}{m}_c=4.6\text{ k²µ}\\ =4.6â‹\dots \left(1\text{ k²µ}×\frac{\text{2.20462 p´Ç³Ü²Ô»å²õ}}{1\text{ k²µ}}\right)\\ =10.14\text{ p´Ç³Ü²Ô»å²õ}\end{array}$

Thus, the mass if 10.14 pounds or 4.6 kg.