Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by seven-time-winner 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 145-km race in which his average speed is 13.5 m/s?
Express answer in joules
(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 10-4 nutritional Calories.
Express answer in nurtitional calories.
Work= •m•t= P•m•s/v =6.5•75•145000/13.5=5.23•10⁶J =1.25 nutr.Cal.
Work=P •m•t= P•m•s/v =6.5•75•145000/13.5=5.23•10⁶J =1.25 nutr.Cal.
Work=P •m•t= P•m•s/v= =6.5•75•145000/13.5=5.23•10⁶J =
= 1.25•10³ nutr.Cal.
Now it's OK
To find the amount of work done by Lance Armstrong during the race, we need to calculate the total energy expended. The formula to calculate work is:
Work = Power × Time
Let's start by calculating the total time it takes for Lance Armstrong to complete the race. We can do this by dividing the total distance by the average speed:
Time = Distance / Speed
(a) Calculating the work done in joules:
Given:
Distance = 145 km
Speed = 13.5 m/s
First, we need to convert the distance from kilometers to meters:
Distance = 145 km × 1000 m/km = 145000 m
Now we can calculate the time:
Time = Distance / Speed = 145000 m / 13.5 m/s ≈ 10740 s
Next, we multiply the time by the power per kilogram of Lance Armstrong's body mass to find the work done:
Work = Power × Time = (6.50 W/kg) × (75.0 kg) × (10740 s) = 5527500 J
Therefore, Lance Armstrong does approximately 5,527,500 joules of work during the race.
(b) Converting the work from joules to nutritional Calories:
Given:
1 joule = 2.389 × 10^-4 nutritional Calories
To convert from joules to nutritional Calories, we can multiply the work done in joules by the conversion factor:
Work (in Calories) = (Work in joules) × (Conversion factor)
= 5527500 J × (2.389 × 10^-4 Cal/J)
≈ 1319.94 Cal
Therefore, Lance Armstrong does approximately 1319.94 nutritional Calories of work during the race.