4) (34 points) Beyond the Textbook Problem (a) (7) The 1968 Summer Olympics were held in Mexico City in October and the 1964 Summer Olympics were held in Tokyo, Japan in October. Using the following city data from the internet, estimate 1) The air density (in kg/m') at the two locations and 2) The mass of oxygen in a single breath (V = 0.5 L) for each Olympics. Use 28.97 g/mol for the molar mass of air. Also note that oxygen comprises approximately 0.21 moles per 1 mole of air. (How many kg Or per kg air?) City Altitude Air Pressure Average Temperature Tokyo (1964 131 ft 101 kPa Olympics) Mexico City (1968 7382 ft 78 kPa 64OF Olympics) Pressure data from http://www.altitude.org/air_pressure.php (b) (10) Comment on the table of the winning times for men's' race events, and discuss possible effects of the air density. Your discussion should provide a possible explanation for both the better short-distance performance and the worse long-distance performance in Mexico City vs. Tokyo (2-5 sentences). Important consideration: for short-distance events, athletes rely mainly on stored muscle energy, with no need to supply new oxygen. Men's race times. Source: Wikipedia. WR = world record. (We couldn't assemble a complete set of women's times because women did not have Olympic long-distance races in 1964 or 1968.) Differences in Difference in Distance Run 1964 Winning 1968 Winning Winning Winning Times (m) Time (s) Time (5) Times (5) (9%) 100 10 9.95 (WR) -0.05 -0.5 200 20.3 19.83 (WR) -0.47 -2.3 400 45.1 43.86 (WR) -1.24 -2.7 5000 828.8 845.01 16.21 1.9 10,000 1704.4 1767.4 63 3.7 42,196 6.3 (marathon) 7931.2 8427 495.8(c) (7) The data at the end of the problem set shows position vs. time in a race for "the greatest sprinter of all time," Usain Bolt. You can see in the plot that almost all the acceleration occurs in the first 2 seconds of the race. Calculate the average rate of change of Usain Bolt's kinetic energy over just the first two seconds. of the race. You will need to look up his mass. (d) [10] Now you will perform a back-of-the-envelope calculation on the power requirements for a sprint, and then estimate how much inhaled air would be required to generate this power by reaction with fuel. Your calculation should show that this route of energy production is not realistic for sprinting. In fact, sprinters rely mainly on stored chemical energy that does not require additional oxygen (i.e. anaerobic routes). Sprinters don't need to breathe while sprinting! Specifically, let's assume that a sprinter can have approximately the same efficiency as a combustion engine. We will calculate the mass flowrate of fuel and air required to produce the rate of change of KE found in part (d). Assume 30% efficiency converting fuel chemical energy to kinetic energy Fuel chemical energy (heating value): 41 MJ/kg Oz: fuel mass ratio: 2.5 for complete conversion of fuel to H20 and CO2, releasing energy. Air composition as in part a. Don't forget to convert between masses and moles and between oxygen and air. Find the fuel and air mass flowrates required to produce Usain Bolt's rate of increase of KE. Use these findings and your results from a) to calculate whether it is reasonable for Usain Bolt to breathe in an adequate amount of On to produce the rate of change of kinetic energy found above.Source of plot: https://www.wired.com/2012/08/maximum-acceleration-in-the-100-m-dash/ 120 100 80 60 Position [m] 40 20 -20 -2 10 12 Time [s] Usain Bolt's position vs time in a 100-meter sprint