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The mass of the aspirin is $320\;{\rm mg}=3.2\times 10^{-4}\;{\rm
kg}$. The energy 'equivalent' is

\begin{displaymath}E=mc^2=(3.2\times 10^{-4}\;{\rm kg})(3\times 10^8\;{\rm
m/s})^2 = 2.88\times 10^{13}\;\rm J.\end{displaymath}

Now, the car goes 12.75 km for every liter of gas and each liter of gas provides $3.65\times 10^7$ joules of energy. Thus the distance traveled for a given amount of energy is

\begin{displaymath}\frac{\rm dist}{\rm energy} = \frac{12.75\;{\rm km}}{\rm L} \...
... L}{3.65\times 10^7\;{\rm J}} = 3.49\times
10^{-7}\;{\rm km/J}.\end{displaymath}

Thus the distance traveled when powered by an aspirin is

\begin{eqnarray*}
{\rm dist} &=& \frac{\rm dist}{\rm energy}\cdot {\rm energy}\\...
...7}\;{\rm km/J})(2.88\times 10^{13}\;\rm J)\\
&=&10^7\;{\rm km}!
\end{eqnarray*}

By comparison, the circumference of the earth is $4\times 10^4$ km, so that the aspirin would allow the car to go around the earth about 250 times before running out! Now that's some sweet gas mileage.



Daniel Cross 2006-11-15