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

(a) The approximate magnitude of the gravitational force on the person by the earth is$588\hspace{0.33em}N$

(b) The magnitude of the gravitational force on the earth by the person is$588\hspace{0.33em}N$ .

Step-by-step solution

Identification of given data

The given data can be listed below,

The mass of the earth,$M_E=5.97\times {10}^{2}4kg$,

The mass of the person,$m=60\hspace{0.33em}kg$

The gravitational constant,$G=6.673\times {10}^{-11}\hspace{0.33em}N\cdot m^2/k{g}^2$

The distance between the person and the earth is the radius of the earth,

$r=6.37\times {10}^6\hspace{0.33em}m$

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 $5.97\times {10}^{2}4\hspace{0.33em}kg$ , G is the constant of gravitation whose value is $6.673\times {10}^{-11}\hspace{0.33em}N\cdot m^2/k{g}^2$,m is the mass of the person, r is the distance between the earth and the person.

Substitute values in the above,

localid="1658071986924" $$\begin{gathered} F_{\text{earh on man}}=\frac{\left(6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2\right)\left(5.97\times {10}^{24}\mathrm{kg}\right)(60\mathrm{kg})}{{\left(6.37\times {10}^6\mathrm{m}\right)}^2} \\ =588N \end{gathered}$$

Thus, the approximate magnitude of the gravitational force on the person by the earth is $588N$

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,

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

Here, $M_E$is the mass of the earth whose value is localid="1658072256414" $5.97\times {10}^{24}\hspace{0.33em}kg$, G is the constant of gravitation whose value is $6.673\times {10}^{-11}\hspace{0.33em}N\cdot m^2/k{g}^2$ ,m is the mass of the person, r is the distance between the earth and the person.

Substitute all the values in the above,

localid="1658072379993" $$\begin{gathered} F_{\text{man on earth}}=\frac{\left(6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2\right)\left(5.97\times {10}^{24}\mathrm{kg}\right)(60\mathrm{kg})}{{\left(6.37\times {10}^6\mathrm{m}\right)}^2} \\ =588N \end{gathered}$$

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