A typical adult human has a mass of about $\mathbf{70}\mathbf{}\mathbf{Kg}$. (a) What force does a full moon exert on such a human when directly overhead with its centre$\mathbf{378000}\mathbf{km}$ away? (b) Compare this force with the pressure exerted on the human by the earth.

The given data can be listed below as follows,

• The mass of the adult human is about $70\text{\hspace{0.17em}kg}$.
• The distance between the centre of the full moon and the human is$378000\text{km}$ which is$378\times {10}^6\text{m}$ .
• The known value of the acceleration due to gravity is $9.8\text{\hspace{0.17em}m}/{\text{s}}^{\text{2}}$.
• The known mass of the moon is$7.34\times {10}^{22}\text{kg}$ .
• The known value of gravitational constant G is $6.67\times {10}^{-11}{\text{Nkg}}^{\text{-2}}{\text{m}}^{\text{2}}$.

The law states that the force exerted by a particle is inversely proportional to the distance’s square and directly proportional to the masse’s products.

The product of the masses divided by the square of their distances gives the force exerted by the full moon. Moreover, the mass multiplied by power produces the pressure exerted by humans on earth.

a) From Newton's law of gravitation, the relationships between the moon's motion and the motion of the body are expressed as:

$\mathrm{F}=\mathrm{G}\frac{{\mathrm{m}}_1{\mathrm{m}}_2}{{\mathrm{r}}^2}$

Here ${\mathrm{m}}_1$ is the mass of humans and ${\mathrm{m}}_2$the mass of the moon. Furthermore,${\mathrm{r}}^2$ it is the distance between the moon's centre and the human and $\mathrm{G}$is the gravitational constant.

Substituting all the values in the above equation, we get,

$\begin{array}{c}\mathrm{F}=\frac{6.67\times {10}^{-11}{\text{\hspace{0.17em}Nkg}}^{\text{-2}}{\text{m}}^{\text{2}}\times 70\text{\hspace{0.17em}kg}\times 7.34\times {10}^{22}\text{\hspace{0.17em}kg}}{{(378\times {10}^6\text{\hspace{0.17em}m})}^2}\\ =2.4\times {10}^{-3}\text{\hspace{0.17em}N}\end{array}$

Thus, the force exerted by the full moon on the human is $\mathbf{2}\mathbf{.4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{\text{N}}$.

$\mathit{F}\mathbf{=}\mathit{m}\mathit{g}$

Where mis the mass of the human and g is the acceleration due to gravity at earth’s surface.

Substituting all the values in the above equation, we get,

$\begin{array}{c}F=70{\text{\hspace{0.17em}kg×9.8\hspace{0.17em}m/s}}^{\text{2}}\\ =686{\text{\hspace{0.17em}kgm/s}}^{\text{2}}\\ =686{\text{\hspace{0.17em}kgm/s}}^{\text{2}}\times \frac{\text{N}}{{\text{\hspace{0.17em}kgm/s}}^{\text{2}}}\\ =686\text{\hspace{0.17em}N}\end{array}$

Hence, the force exerted by humans on the earth is lower that is $686\mathrm{N}$.

The comparison of this force with the pressure exerted on the human by the earth.

$\begin{array}{c}\frac{{\mathrm{F}}_{\mathrm{moon}}}{{\mathrm{F}}_{\mathrm{earth}}}=\frac{2.4\times {10}^{-3}\text{\hspace{0.17em}N}}{686\text{\hspace{0.17em}N}}\\ =3.5\times {10}^{-6}\end{array}$

Thus, they compare this force with the pressure exerted on the human by the earth is localid="1655712460973" $3.5\times {10}^{-6}$.