Question

A $60$kg person stands on the Earth’s surface.

(a) What is the approximate magnitude of the gravitational force on the person by the Earth?

(b) What is the magnitude of the gravitational force on the Earth by the person?

Short answer

The approximate magnitude of the gravitational force on the person by the earth is $588\backslash mathrm\{~N\}.$

The magnitude of the gravitational force on the earth by the person is $588\mathrm{N}$.

Step-by-step solution

 Identification of given data

The given data can be listed below,

The mass of the earth,$M_E=5.97\times {10}^{24}\mathrm{kg}$

The mass of the person,$m=60\mathrm{kg}$

The gravitational constant,$G=6.673\times {10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2$

The distance between the person and the earth is the radius of the earth,$r=6.37\times {10}^6\mathrm{m}$

Concept/Significance of the gravitational force

An attractive force that creates attraction between objects is called gravitational force. It always tries to pull masses together; it never pushes them apart.

Determination of the magnitude of the gravitational force on the person by the earth.

(a)

The gravitational force on the person is given by,

$F_{\text{earth on}man}=\frac{G{M}_{E}m}{r^2}$

Here, $M_E$is the mass of the earth whose value is $5.97\times {10}^{24}\mathrm{kg},G$is the constant of gravitation whose value is $6.673\times {10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2,m$is the mass of the person, $r$is the distance between the earth and the person.

Substitute values in the above,

$\backslash begin\left\{aligned\right\}F\_\{\backslash text\{earthonman\left\}\right\}\&=\backslash frac\{\backslash left(6.67\backslash times10^\{-11\}\backslash mathrm\left\{Nm\right\}^\left\{2\right\}/\backslash mathrm\left\{kg\right\}^\left\{2\right\}\backslash right)\backslash left(5.97\backslash times10^\left\{24\right\}\backslash mathrm\{~kg\}\backslash right\left)\right(60\backslash mathrm\{~kg\}\left)\right\}\{\backslash left(6.37\backslash times10^\left\{6\right\}\backslash mathrm\{~m\}\backslash right)^\{2\left\}\right\}\backslash \backslash \&=588\backslash mathrm\{~N\}\backslash end\left\{aligned\right\}$

Thus, the approximate magnitude of the gravitational force on the person by the earth is$588\backslash mathrm\{~N\}.$

Determination of the magnitude of the gravitational force on the earth by the person

(b)

The magnitude of gravitational force on the earth by the person is given by,

$F_{\text{man on earth}}=\frac{G{M}_{E}m}{r^2}$

Here, $M_E$is the mass of the earth whose value is $5.97\times {10}^{24}\mathrm{kg},G$is the constant of gravitation whose value is $6.673\times {10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2,m$is the mass of the person, $r$is the distance between the earth and the person.

Substitute all the values in the above,

$\backslash begin\left\{aligned\right\}F\_\{\backslash text\{manonearth\left\}\right\}\&=\backslash frac\{\backslash left(6.67\backslash times10^\{-11\}\backslash mathrm\left\{Nm\right\}^\left\{2\right\}/\backslash mathrm\left\{kg\right\}^\left\{2\right\}\backslash right)\backslash left(5.97\backslash times10^\left\{24\right\}\backslash mathrm\{~kg\}\backslash right\left)\right(60\backslash mathrm\{~kg\}\left)\right\}\{\backslash left(6.37\backslash times10^\left\{6\right\}\backslash mathrm\{~m\}\backslash right)^\{2\left\}\right\}\backslash \backslash \&=588\backslash mathrm\{~N\}\backslash end\left\{aligned\right\}$

Thus, the magnitude of the gravitational force on the earth by the person is $588\mathrm{N}$.