Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by Lance Armstrong (m = 75.0 kg) is 6.50 W per kilogram of his body mass. (a) How much work does he do during a 117-km race in which his average speed is 11.5 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule = 2.389 x 10-4 nutritional Calories.
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To find the work done by Lance Armstrong in a 117-km race with an average speed of 11.5 m/s, we can use the formula:
Work = Force x Distance
First, we need to calculate the force Lance Armstrong generates during the race. The average power per kilogram is given as 6.50 W/kg, so we can find the total power by multiplying the power per kilogram by his body mass:
Power = 6.50 W/kg * 75.0 kg = 487.5 W
Next, we can calculate force using the formula:
Force = Power / Velocity
Force = 487.5 W / 11.5 m/s = 42.39 N
Finally, we can calculate the work by multiplying the force by the distance:
Work = Force x Distance
Work = 42.39 N * 117,000 m = 4,964,430 J
To express the work done in nutritional Calories, we can use the conversion factor:
1 joule = 2.389 x 10^-4 nutritional Calories
So, to convert the work done in joules to nutritional Calories, we divide by the conversion factor:
Work in Calories = 4,964,430 J * (1 Cal / 2.389 x 10^-4 J) = 20,776,583 Calories
Therefore, Lance Armstrong would do approximately 20,776,583 nutritional Calories of work during the 117-km race at an average speed of 11.5 m/s.