Question

Suppose that a bicyclist is traveling at an energetic 20 mph on a flat road, and the combination of rolling resistance and air drag is 10 pounds. (48 pts, 8 pts each part) a. What is the rate at which the bicyclist is doing useful work at this speed, in watts and horsepower? b. Measurements indicate that this performance requires conversion of food energy at a rate of 8 kcal/min. What is the first-law efficiency of the cyclist as a machine in converting energy to work at 20 mph? Assume that in a sedentary state, the rate of energy consumed by the cyclist’s body is 1.5 kcal/min. c. What is the bicyclist’s “miles per gallon” equivalent if the energy in the extra food consumed to power the bicycle is equated to the energy in gasoline? d. If the needed energy is obtained from energy bars containing 200 Calories and costing $1.50 each, what is the bicyclist’s fuel cost in cents per mile? What is the fuel cost in cents per mile for a car that gets 20 mpg using $3 per gallon gasoline? e. What are the CO2 emissions per mile for the bicyclist and the car? Consider only what is being emitted as they proceed. Do not include lifecycle considerations, and for the bicyclist only include the CO2 associated with propulsion. For the bicyclist, assume the energy bar consists of carbohydrates with a simplified molecular formula of CH2O and an energy content of 4 kcal/g. For the car, assume the gasoline consists of entirely of iso-octane, C8H18, with a specific gravity of 0.7 and an energy content of 45 MJ/kg. f. Without doing a calculation, name at least three elements of a lifecycle CO2 analysis that would change the emissions per mile calculation above, and whether they would tend to increase or decrease the value for each of the transportation modes.

Answer 1

guven bycyclist travelling at an energetic
u = 20 mph = 8.9408 m/s
drag force, Fd = 10 lbs = 44.4822 N

a. rate at which useful work is being done = Fd*u
   P = 44.4822*8.9408 = 397.70645 W
   P = 0.533 HP

b. conversion rate of food energy, r = 8 kcal/min = 33472 J/min = 557.866 W = 0.74811 HP
   efficiency = (0.533)/(0.74811) = 0.7124

c. calorific value of gasoline = 30 kcal per gallon
   so, in 1 gallon gasoline, input energy = 30 kcal
   usable energy = 0.7124*30 = 21.372 kcal = 89420.448 J

   in time t
   power = P = 397.70645 W = 89420.448/t W
   t = 224.84032 s
   hence
   miles = s
   s = ut = 2010.25239 m = 1.24911 miles
   hence
   the cyclist has 1.24911 miles per gallon

d. 1 bar = 1.5 dollrs = 200 cal = 836800 J
   for 1 mile
   s = 1 mile = 1609.34 m
   ut = s
   t = s/u = 179.999 s

   energy required = 557.866*t J = 100415.6304 J
   hence
   bars required = 100415.6304/836800 = 66.94367 bars = 10041.55104 cents per mile