Energy at your fingertips: $E = mc^2$

Posted by Diego Assencio on 2014.02.11 under Physics (Relativity)

The theory of relativity says that a body at rest with rest mass $m$ contains an amount of energy (called its "rest energy") given by: $$ E=mc^2 $$ where $c \approx 3 \times 10^8\textrm{m/s}$ is the speed of light. Assuming the tip of a human finger contains approximately $1\textrm{g}$ of mass, the energy content of a fingertip is then: $$ E \approx (10^{-3}\textrm{kg}) \times (3\times 10^8 \textrm{m/s})^2 = 9 \times 10^{13} \textrm{J} $$ This is a large amount of energy. If you were capable of converting mass into energy, would you be able to survive your entire life by merely converting your fingertip into energy? The answer is yes.

The U.S. Department of Agriculture and the U.S. Department of Health and Human Services recommends a daily consumption of approximately $2500 \textrm{kcal} \approx 10500\textrm{kJ}$ for adult males between $20$ and $50$ years of age (see the Dietary Guidelines for Americans, appendix 6). Younger or older males are recommended to consume less than that amount per day (on average). This means one can expect the energy consumption of a male's body over his entire life span (say 100 years just to be sure we are not underestimating things) to be around: $$ E_{\textrm{life}} = (365 \textrm{days/year}) \times (100 \textrm{years}) \times 10500\textrm{kJ/day} \approx 3.8 \times 10^{11} \textrm{J} $$ In other words, the energy content of a fingertip is about $E / E_{\textrm{life}} \approx 240$ times larger than the amount of energy consumed by a person during his/her entire lifetime!


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