food

food_energy.tex

@@ -69,13 +69,24 @@ In medicine, these slopes are related to ``Metabolic Equivalent of Task'' (METS)
 Imagine that after eating a $600~kcal$ bacon-maple long-john (donut), you decide to go for a hike to ``work off'' the Calories.  Winona State  is in a river valley bounded by $200m$ tall bluffs.  How high up the bluff would you have to hike to burn off the donut?  
 Useful information: human muscle is about $1/3$ efficient and on Earth's surface gravitational energy has a slope of about $10~\frac{Joules}{kg\cdot m}$.
 
-One way to approach this problem is by using Energy Bar Charts \cite{energy_bar_charts} to illustrate how the food energy can change form as it is absorbed and used.    
-Energy bar charts
+\begin{figure}[h]
+\centering
+\includegraphics[width=\columnwidth]{bar_chart.png}
+\caption{An Energy Bar Chart to illustrate the $1/3$ efficient student hiking up a bluff to burn off the morning's donut.  The initial state (left) is the hiker at the bottom of the hill, with donut in stomach.  The final state (right) is the hiker at the top of the bluff with $2/3$ of the energy removed to the atmosphere by sweat and exhalation of warm air. $1/3$ of the donut's energy is stored in elevation.  The system for this diagram includes the earth, the hiker, and the donut.  The system does not include the atmosphere around the hiker.  
+}
+\label{bar_chart}
+\end{figure}
+
+One way to approach this problem is by using Energy Bar Charts \cite{energy_bar_charts} to illustrate how the food energy  changes form as it is absorbed and used.  An approximation for this question is shown in figure \ref{bar_chart}.  In this story, the ``system'' is taken to be the earth, food, and hiker.  The hiker's body is assumed to be $1/3$ efficient, which means one of the Food Energy blocks of energy is transformed into gravitational energy (elevation) at the end of the hike.  The other $2$ blocks of energy are transformed into heat and are removed from the hiker's body via body heat, most likely by mechanisms of respiration and sweat evaporation. The purpose of a bar chart like this is to provide a pictoral and mathematical representation of the energy conservation equation given in \ref{eq:bar_chart}.         
+
 \bea
 \frac{1}{3}\cdot600kcal\cdot\frac{4200J}{1kcal} 
-	&=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height\\
+	&=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height \label{eq:bar_chart}\\
 height &\approx&  1000 m
 \eea
+This estimate is again surprising to students.  Five trips up the bluff to burn off $\$2$ of saturated fat, sugar, and flour!  A nice followup calculation is to imagine a car that can burn a $100kcal$ piece of toast -- from rest, what speed will the toast propel it to? If (again) the engine converts $1/3$ of the energy into motion (kinetic energy), a 1300kg Honda Civic will reach a speed of about $13\frac{m}{s}\approx33mph$!  
+
+The point of these energy conversion calculations is not to give students an eating disorder.  Rather, they are meant to illustrate how powerful and amazing the food we eat is.  A single slice of toast will bring a car up to the speed limit on a residential road!  Food and our bodies are amazing, and increases in food production have made our comforts, unimaginable 150 years ago, possible and taken for granted.  
 
 increase in yields since 1917 (graph)