Ian: New page: Use the theory of gravitation equation $F=\frac{Gm_{1}m_{2}}{{d}^{\ 2}}$ where, $G=6\textrm{.}67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-...$

Ian — Fri, 12 Mar 2010 17:22:51 GMT

New page: Use the theory of gravitation equation <math>F=\frac{Gm_{1}m_{2}}{{d}^{\ 2}}</math> where, <math>G=6\textrm{.}67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-...

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Use the theory of gravitation equation

<math>F=\frac{Gm_{1}m_{2}}{{d}^{\ 2}}</math>

where,

<math>G=6\textrm{.}67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-2}}</math>

In this case

<math>{{m}_{1}}</math>
is the mass of the earth and
<math>{{m}_{2}}</math>
is the mass of the man.

<math>d</math>
is the distance of the man from the centre of the earth and thus is the sum of the radius of the earth and his height above sea level.

Thus

<math>{{m}_{1}}=</math>
<math>\text{5}\textrm{.}\text{98}\times \text{1}0^{\text{24}}\text{ }\text{kg}</math>

<math>{{m}_{2}}=80\ \text{kg}</math>

The radius of the earth is

<math>\text{6}\textrm{.}\text{37}\times \text{1}0^{\text{6}}\text{ m }</math>

and the height of the man above sea level is <math>5000\ \text{m}</math>

which gives

<math>d=</math><math>\text{13}\textrm{.}\text{37}\times \text{1}0^{\text{6}}\text{ m }</math>

Inserting all these quantities in the gravitation equation

<math>\begin{align}
& F=\frac{\left( 6\textrm{.}67\times {{10}^{-11}} \right)\times \left( 5\textrm{.}98\times {{10}^{24}} \right)\times 80}{{{\left( 6\textrm{.}375\times {{10}^{6}} \right)}^{2}}} \\
& =\frac{319\textrm{.}10\times {{10}^{14}}}{40\textrm{.}64\times {{10}^{12}}}=7\textrm{.}85\times {{10}^{2}}\ =785\ \text{N} \\
\end{align}</math>

Solution 2.9a - Revision history

Ian: New page: Use the theory of gravitation equation F=\frac{Gm_{1}m_{2}}{{d}^{\ 2}} where, G=6\textrm{.}67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-...

Ian: New page: Use the theory of gravitation equation $F=\frac{Gm_{1}m_{2}}{{d}^{\ 2}}$ where, $G=6\textrm{.}67\times 10^{-11}\text{ kg}^{\text{-1}}\text{m}^{\text{3}}\text{s}^{\text{-...$