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Solution 2.10

From Mechanics

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(New page: <math>F=\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}</math> where <math>F</math> is the force on a particle on the surface of Mars, <math>{{m}_{1}}</math> is the mass of Mars, <math>{{m}_{2}...)
Current revision (16:16, 3 February 2011) (edit) (undo)
 
(One intermediate revision not shown.)
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<math>F=\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}</math>
+
The Law of gravitation applied to a particle on Mars gives,
 +
 
 +
<math>F=\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{\, 2}}}</math>
where
where
Line 17: Line 19:
is the acceleration of the particle on Mars,
is the acceleration of the particle on Mars,
 +
<math>a=\frac{G{{m}_{1}}}{{{d}^{\, 2}}}</math>
-
<math>a=\frac{G{{m}_{1}}}{{{d}^{2}}}</math>
+
The radius of Mars must be expressed in SI units.
 +
<math>d=3\textrm{.}4\times {{10}^{6}}\ \text{m}</math>
-
As
+
and as
<math>G=6\textrm{.}67\times {{10}^{-11}}\text{ k}{{\text{g}}^{\text{-1}}}{{\text{m}}^{\text{3}}}{{\text{s}}^{\text{-2}}}</math>
<math>G=6\textrm{.}67\times {{10}^{-11}}\text{ k}{{\text{g}}^{\text{-1}}}{{\text{m}}^{\text{3}}}{{\text{s}}^{\text{-2}}}</math>
we get
we get
- 
<math>\begin{align}
<math>\begin{align}
& a=\frac{6\textrm{.}67\times {{10}^{-11}}\text{ k}{{\text{g}}^{\text{-1}}}{{\text{m}}^{\text{3}}}{{\text{s}}^{\text{-2}}}\times \text{
& a=\frac{6\textrm{.}67\times {{10}^{-11}}\text{ k}{{\text{g}}^{\text{-1}}}{{\text{m}}^{\text{3}}}{{\text{s}}^{\text{-2}}}\times \text{
6}\textrm{.}\text{42}\times \text{1}{{0}^{\text{23}}}\text{kg}}{{{\left( \text{3}\textrm{.}\text{4}\times \text{1}{{0}^{\text{6}}}\text{m} \right)}^{2}}} \\
6}\textrm{.}\text{42}\times \text{1}{{0}^{\text{23}}}\text{kg}}{{{\left( \text{3}\textrm{.}\text{4}\times \text{1}{{0}^{\text{6}}}\text{m} \right)}^{2}}} \\
-
& =\frac{6\textrm{.}67\times \text{7}\textrm{.}\text{38}}{\text{1}\textrm{.}\text{7}{{\text{3}}^{2}}\times 10}\text{m}{{\text{s}}^{-2}}=1\textrm{.}64\text{m}{{\text{s}}^{-2}} \\
+
& =\frac{6\textrm{.}67\times 6\textrm{.}42}{{{3\textrm{.}4}^{2}}}\ \text{m}{{\text{s}}^{-2}}=3\textrm{.}7\ \text{m}{{\text{s}}^{-2}} \\
\end{align}</math>
\end{align}</math>

Current revision

The Law of gravitation applied to a particle on Mars gives,

F=d2Gm1m2

where F is the force on a particle on the surface of Mars, m1 is the mass of Mars, m2 is the mass of the particle and d is the radius of Mars.

As F=m2a where a is the acceleration of the particle on Mars,

a=d2Gm1

The radius of Mars must be expressed in SI units.

d=3.4106 m

and as G=6.671011 kg-1m3s-2 we get

a=3.4106m26.671011 kg-1m3s-2 6.421023kg=3.426.676.42 ms2=3.7 ms2