Human power
What was your power, climbing stairs
How long did it take you?
Your powers
Tour de France racers
Floyd Landis placed 6th in 21 m 53 s
Average Speed: 32.3 mph (52.1 km/h)
Estimated Total Energy ("Work" that he did): 582 Kjoules
Cycling power.
Time = 21 min 53 sec/
Work = 582 Kjoules.
Power = Work / time
What was his average power in Watts?
Average athletes
More
typical figures for non-elite athletes: Vigorous, but sustained exercise is
output of ~ 100 W = 100 J/s for sustained periods.
Calories in food
1 calorie = energy needed to raise 1 gram of water by 1${}^o$C.
The accepted conversion factor: $$1 \text{ cal} = 4.187 \text{ Joules}.$$ [Google 1 calorie in Joules.]
This is *not* the same unit as what you find on food labels.
One "Calorie" on a food label is actually 1 kilocalorie
in terms of our thermal definition.
1 "Calorie" = 1 kcal = $10^3$ calories = 4187 J
Some dieticians try to point out the difference by writing food Calories with a capital "C". But it's better just to know this from context. Anytime you hear "food" you know that what they *really* mean is kilocalories.
Average athletes
Vigorous, but sustained exercise: ~ 100 W = 100 J/s. (This is over-and-above what your body needs even if you're resting).
Problem: How many food Calories do you need to consume to exercise for 1/2 hour??
- How many Joules of energy when you exert at 100 W for 1/2 hour?
100 J/s * 1800 s=180,000J
- How many Calories for that many Joules? Use 4187 J / 1 Cal.
180,000 J/4187 J/C=43 Cal
- It turns out that the human body is ~25% efficiency: you must eat 4 Calories
for every 1 Calorie you expend. So... how many Calories of food energy do you
need to eat to exercise for 1/2 hour?
43 Cal work * 4 Cal food / 1 Cal work=172 Cal
1/2 hr vigorous exercise requires ~ 700,000 J $\times$ 1 Cal/4200 J = 167
Cal $\approx$ 
1/2 hr 
=
Just sitting around...
Humans require about 12 Cal of food / lb / day. How many calories/day for a person weighing 150 lbs?
So, the number of Calories you use, just sitting around in one day....
 |
= | / per day |
Losing weight
How many Calories do we have to burn to lose 1 lb?
1 lb (~450 g) of butter has about the same number of Calories as 1 lb of body fat: 3200 Cal.
To lose 1 lb / week, you'd need to either
- reduce your Calorie intake by about
3200/7 ~ 450 Cal each day $\approx$
- Or you could exercise more: about how much *more* exercise would do it?