1. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Lecture Notes Human Body Bicycling and Calories

2. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Question How long do I have to ride my bicycle to burn off a doughnut? You often find numbers relating exercise and calorie consumption (in magazine articles, on the web...) For example, a 68 kg person cycling at 15 km/h for one hour burns approximately 400 Calories (approximately 1.5 - 2.0 donuts). Where do these numbers come from? Bicycling and Calories

3. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Big Ideas Food (like gasoline) is chemical energy that the body transforms into heat and mechanical energy. The mechanical work done on the bicycle is linked to the metabolic energy of the rider. Bicycling and Calories

4. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Energy in food is like other forms of energy - it can be transformed into mechanical energy. Like other real-life engines, our body cannot transfer 100% of the chemical energy in food into mechanical energy (motion). Bicycling and Calories Background

5. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia During sedentary periods, the body consumes 100 W to keep the internal organs functioning. The efficiency to convert chemical energy into mechanical energy is ~25% Note: these numbers vary somewhat with the person and the activity but can conveniently be used to get a good estimate. Bicycling and Calories Background

6. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Why does bicycling consume energy, even on a flat road and a day without wind? You have to overcome rolling friction and air drag (the relative air speed is 15 km/h) Bicycling and Calories Background

7. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia The road is level No wind (relative wind speed = 15 km/h) Mass: 68 kg person +10 kg bike = 78 kg Rubber on concrete: μ r = 0.02 Density of air ρ = 1.28 kg/m 3 Bicycling and Calories Assumptions:

8. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia F D = ¼ ρ A v 2 (The equation above follows from F D = ½ ρ C D A v 2 by using C D = 0.5, which is typical for everyday moving objects) Estimate the frontal area A of person & bike A = (1.5 m) · (0.6 m) = 0.9 m 2. v = 4.2 m/s, so the distance traveled each second is d = 4.2 m Bicycling and Calories Air drag

9. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia F D = ¼ ρ A v 2 F = ¼ (1.28 kg/m 3 )(0.9 m 2 )(4.2 m/s) 2 = 5.1 N W = F d = (5.1 N)(4.2 m) = 21 J in 1 second So, P air drag = 21 W Bicycling and Calories Air drag

10. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia F r = μ r m g F r = (0.02) (78kg) (9.8 m/s 2 ) = 15.3 N, W = (15.3 N)(4.2 m) = 64 J in 1 second P rolling friction = 64 W. Bicycling and Calories Rolling Friction

11. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia The total power= 21 W + 64 W = 85 W We need 85 W of mechanical power to maintain our speed. Bicycling and Calories Total Power

12. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Multiply the result by 4 and add 100 W to account for efficiency and the energy consumed by internal organs. P = (85 W x 4) + 100 W = 440 W = 440 J/s We know: 1 Cal = 1kcal = 4200 J (440 J/s)(3600 s/h)(1 Cal/4200 J) = 377 Cal Bicycling and Calories Metabolic Power

13. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia A chocolate glazed donut from Tim Horton's has 260 Calories and is 70 g. An old fashioned plain timbit is 16 g and has 70 Calories. You can replenish your energy by eating ~ 1.5 donuts or just over 5 timbits. Also, if you eat one donut it will take you (260 Cal)(1 h/377 Cal)(60 min/h) = 41 min of biking to burn it off. Bicycling and Calories Donuts

14. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Our result is close to the published value showing that the calorie consumption in bicycling is mainly due to overcoming air drag and rolling friction. Bicycling and Calories Interpretation

15. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia 1.Many web-based resources. See for example: www.dietandfitnesstoday.com or www.nutristrategy.com www.dietandfitnesstoday.comwww.nutristrategy.com 2.Knight, Jones, Field, "College Physics: a strategic approach", 1st edition, p. 339, Pearson Addison-Wesley (2007) 3.Tim Hortons. Nutritional Information (online). www.timhortons.com/ca/en/menu/menu_info.html [13 August 2009].www.timhortons.com/ca/en/menu/menu_info.html Bicycling and Calories Bibliography