Question

Calculate the approximate gravitational force exerted by the Earth on a human standing on the Earth's surface. Compare with the approximate gravitational force of a human on another human at a distance of 3 m. What approximations or simplifying assumptions must you make?

Short answer

The value of approximate gravitational force is$F=3.11\times {10}^{15}N$

Step-by-step solution

Identification of given data

Distance of human = 3 m

Gravitational force

Gravitational force is the attraction of all the masses in the universe.

Calculation of the gravitational force

According to the Newton’s low of gravitation

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

Where

G – Gravitational constant $6.67\times {10}^{-11}{m}^3\overline{)kg.s}$

role="math" localid="1653973046667" $m_1-$ - Mass of 1 object

$m_2-$Mass of 2 objects

role="math" localid="1653973083756" $r-$ Distance between two object = 3m

Let us assume that mass of object one is $m_1=70kg$

And second mass is as mass of earth $m_2=6\times {10}^{24}kg$

So after putting the values we get

$$\begin{gathered} F=\frac{G{m}_1{m}_2}{r^2} \\ F=\frac{6.67\times {10}^{-11}{m}^3\overline{)kg.s^2\times 70kg\times 6\times {10}^{24}kg}}{3^2} \\ F=3.11\times {10}^{15}N \end{gathered}$$

Thus the value of gravitational force is $F=3.11\times {10}^{15}N$