Bicyclists in the Tour de France do enormous amounts of work during a race. For
ID: 1436521 • Letter: B
Question
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 116-km race in which his average speed is 12.1 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.
Explanation / Answer
Given,
m = 75 kg ; Pavg = 6.5 W / kg ;
Total power = Pt = 6.5 x 75 = 487.5 J/s
(a) d = 116 km = 116000 m ; v = 12.1 m/s
we know that, speed = distance/time
time = distance/speed = 116000/12.1 = 9586.78 s
We know from the defination of power,
Power = Energy / time
Energy = Power x time
energy = E = 487.5 J/s x 9586.78 = 4673555.25 J
Hence, He does, E = 4673555.25 = 4.67 x 106 J
(b)We know that,
1 J = 2.389 x 10-4 Cal
So, 4673555.25 J will be
E = 4673555.25 x 2.389 x 10-4 C = 1116.5 Joules
Hence, E = 1116.5 Joules.
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